{"version":"2026-05-13.path-family.v1","generatedAt":"2026-05-13T06:59:20.216Z","site":{"id":"theorempath","url":"https://theorempath.com","role":"canonical formal spine"},"publicContract":"Public graph snapshot with topic prerequisite edges plus the Path-family overlay. This does not expose retrieval chunks, user state, private ranking, or mastery models.","counts":{"theoremPathTopicNodes":641,"theoremPathPrerequisiteEdges":1975,"pathFamilySites":18,"globalConceptSeeds":20,"familyEdges":15},"theoremPath":{"nodes":[{"id":"theorempath:ablation-study-design","site":"theorempath","slug":"ablation-study-design","title":"Ablation Study Design","layer":"3","tier":2,"module":"methodology","url":"https://theorempath.com/topics/ablation-study-design","prerequisites":["hypothesis-testing-for-ml","benchmarking-methodology","experiment-tracking-and-tooling","reproducibility-and-experimental-rigor"],"leadsTo":["reproducibility-and-experimental-rigor"]},{"id":"theorempath:activation-checkpointing","site":"theorempath","slug":"activation-checkpointing","title":"Activation Checkpointing","layer":"3","tier":2,"module":"training-techniques","url":"https://theorempath.com/topics/activation-checkpointing","prerequisites":["feedforward-networks-and-backpropagation","mixed-precision-training"],"leadsTo":[]},{"id":"theorempath:activation-functions","site":"theorempath","slug":"activation-functions","title":"Activation Functions","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/activation-functions","prerequisites":["differentiation-in-rn","convex-optimization-basics"],"leadsTo":["batch-normalization","weight-initialization","feedforward-networks-and-backpropagation","kolmogorov-arnold-networks"]},{"id":"theorempath:active-slam-and-pomdps","site":"theorempath","slug":"active-slam-and-pomdps","title":"Active SLAM and POMDPs","layer":"4","tier":3,"module":"applied-math","url":"https://theorempath.com/topics/active-slam-and-pomdps","prerequisites":["graphslam-and-factor-graphs","markov-decision-processes","visual-semantic-slam"],"leadsTo":[]},{"id":"theorempath:actor-critic-methods","site":"theorempath","slug":"actor-critic-methods","title":"Actor-Critic Methods","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/actor-critic-methods","prerequisites":["policy-gradient-theorem","q-learning","reward-systems-and-reinforcement-learning-neuroscience","td-learning"],"leadsTo":["rlhf-and-alignment","dpo-vs-grpo-vs-rl-reasoning","ddpg","deep-rl-for-control","policy-optimization-ppo-trpo"]},{"id":"theorempath:adaboost","site":"theorempath","slug":"adaboost","title":"AdaBoost","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/adaboost","prerequisites":["decision-trees-and-ensembles"],"leadsTo":["gradient-boosting","regularization-theory"]},{"id":"theorempath:adam-optimizer","site":"theorempath","slug":"adam-optimizer","title":"Adam Optimizer","layer":"2","tier":1,"module":"training-techniques","url":"https://theorempath.com/topics/adam-optimizer","prerequisites":["gradient-descent-variants","stochastic-gradient-descent-convergence"],"leadsTo":["learning-rate-scheduling","optimizer-theory-sgd-adam-muon","mixed-precision-training","transformer-architecture","batch-size-and-learning-dynamics"]},{"id":"theorempath:adaptive-learning-is-not-iid","site":"theorempath","slug":"adaptive-learning-is-not-iid","title":"Adaptive Learning Is Not IID","layer":"3","tier":2,"module":"learning-theory","url":"https://theorempath.com/topics/adaptive-learning-is-not-iid","prerequisites":["random-variables","radon-nikodym-and-conditional-expectation","martingale-theory","concentration-inequalities"],"leadsTo":["online-learning-and-bandits","stochastic-approximation-theory","uniform-convergence"]},{"id":"theorempath:adaptive-rejection-sampling","site":"theorempath","slug":"adaptive-rejection-sampling","title":"Adaptive Rejection Sampling","layer":"2","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/adaptive-rejection-sampling","prerequisites":["rejection-sampling","griddy-gibbs","squeezed-rejection-sampling"],"leadsTo":[]},{"id":"theorempath:adjoint-sensitivity-method","site":"theorempath","slug":"adjoint-sensitivity-method","title":"Adjoint Sensitivity Method","layer":"3","tier":2,"module":"scientific-ml","url":"https://theorempath.com/topics/adjoint-sensitivity-method","prerequisites":["neural-odes","classical-odes","automatic-differentiation"],"leadsTo":["continuous-normalizing-flows","neural-sdes","physics-informed-neural-networks"]},{"id":"theorempath:adjusted-density-maximization","site":"theorempath","slug":"adjusted-density-maximization","title":"Adjusted Density Maximization","layer":"4","tier":3,"module":"methodology","url":"https://theorempath.com/topics/adjusted-density-maximization","prerequisites":["small-area-estimation","reml-and-variance-component-estimation","prasad-rao-mse-correction"],"leadsTo":["prasad-rao-mse-correction","empirical-bayes-vs-hierarchical-bayes"]},{"id":"theorempath:adversarial-machine-learning","site":"theorempath","slug":"adversarial-machine-learning","title":"Adversarial Machine Learning","layer":"4","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/adversarial-machine-learning","prerequisites":["feedforward-networks-and-backpropagation","minimax-saddle-points","minimax-theorem"],"leadsTo":["llm-application-security"]},{"id":"theorempath:agent-based-modeling-with-ml","site":"theorempath","slug":"agent-based-modeling-with-ml","title":"Agent-Based Modeling with ML","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/agent-based-modeling-with-ml","prerequisites":["multi-armed-bandits-theory","markov-games-and-self-play"],"leadsTo":["self-play-and-multi-agent-rl","mean-field-games"]},{"id":"theorempath:agent-protocols-mcp-a2a","site":"theorempath","slug":"agent-protocols-mcp-a2a","title":"Agent Protocols: MCP and A2A","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/agent-protocols-mcp-a2a","prerequisites":["agentic-rl-and-tool-use","tool-augmented-reasoning"],"leadsTo":["context-engineering","hallucination-theory"]},{"id":"theorempath:agentic-rl-and-tool-use","site":"theorempath","slug":"agentic-rl-and-tool-use","title":"Agentic RL and Tool Use","layer":"5","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/agentic-rl-and-tool-use","prerequisites":["markov-decision-processes","policy-gradient-theorem","offline-reinforcement-learning","video-world-models","world-models-and-planning"],"leadsTo":["post-training-overview","test-time-compute-and-search","agent-protocols-mcp-a2a","tool-augmented-reasoning"]},{"id":"theorempath:ai-labs-landscape","site":"theorempath","slug":"ai-labs-landscape","title":"AI Labs Landscape","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/ai-labs-landscape","prerequisites":["model-timeline","key-researchers-and-ideas"],"leadsTo":["key-researchers-and-ideas","ineffable-intelligence"]},{"id":"theorempath:aic-and-bic","site":"theorempath","slug":"aic-and-bic","title":"AIC and BIC","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/aic-and-bic","prerequisites":["maximum-likelihood-estimation","decision-trees-and-ensembles","gauss-markov-theorem","kolmogorov-complexity-and-mdl"],"leadsTo":["cross-validation-theory"]},{"id":"theorempath:alexnet-and-deep-learning-history","site":"theorempath","slug":"alexnet-and-deep-learning-history","title":"AlexNet and Deep Learning History","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/alexnet-and-deep-learning-history","prerequisites":["convolutional-neural-networks"],"leadsTo":[]},{"id":"theorempath:algorithmic-stability","site":"theorempath","slug":"algorithmic-stability","title":"Algorithmic Stability","layer":"3","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/algorithmic-stability","prerequisites":["empirical-risk-minimization","vc-dimension","concentration-inequalities","contraction-inequality","cross-validation-theory","kolmogorov-complexity-and-mdl","mcdiarmids-inequality","pac-bayes-bounds","rademacher-complexity","regularization-theory","sample-complexity-bounds","symmetrization-inequality"],"leadsTo":["implicit-bias-and-modern-generalization"]},{"id":"theorempath:alphaproof-and-ai-theorem-proving","site":"theorempath","slug":"alphaproof-and-ai-theorem-proving","title":"AlphaProof and AI-Assisted Theorem Proving","layer":"4","tier":1,"module":"formal-verification","url":"https://theorempath.com/topics/alphaproof-and-ai-theorem-proving","prerequisites":["theorem-proving-in-lean","ineffable-intelligence"],"leadsTo":["reasoning-data-curation"]},{"id":"theorempath:amd-competition-landscape","site":"theorempath","slug":"amd-competition-landscape","title":"AMD Competition Landscape","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/amd-competition-landscape","prerequisites":["gpu-compute-model"],"leadsTo":[]},{"id":"theorempath:analysis-of-variance","site":"theorempath","slug":"analysis-of-variance","title":"Analysis of Variance","layer":"1","tier":1,"module":"statistics","url":"https://theorempath.com/topics/analysis-of-variance","prerequisites":["central-limit-theorem","multivariate-normal-distribution","linear-regression","hypothesis-testing-for-ml","expectation-variance-covariance-moments"],"leadsTo":["linear-regression","hypothesis-testing-for-ml","variance-stabilizing-transformations","bootstrap-methods"]},{"id":"theorempath:anomaly-detection-gravitational-waves","site":"theorempath","slug":"anomaly-detection-gravitational-waves","title":"Anomaly Detection for Gravitational Waves","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/anomaly-detection-gravitational-waves","prerequisites":["convolutional-neural-networks","signal-detection-theory"],"leadsTo":["anomaly-detection","out-of-distribution-detection"]},{"id":"theorempath:anomaly-detection","site":"theorempath","slug":"anomaly-detection","title":"Anomaly Detection","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/anomaly-detection","prerequisites":["common-probability-distributions","anomaly-detection-gravitational-waves"],"leadsTo":[]},{"id":"theorempath:anthropic-bias-and-observation-selection","site":"theorempath","slug":"anthropic-bias-and-observation-selection","title":"Anthropic Bias and Observation Selection","layer":"3","tier":3,"module":"methodology","url":"https://theorempath.com/topics/anthropic-bias-and-observation-selection","prerequisites":["bayesian-estimation"],"leadsTo":["types-of-bias-in-statistics","statistical-paradoxes-collection"]},{"id":"theorempath:arrows-impossibility","site":"theorempath","slug":"arrows-impossibility","title":"Arrow's Impossibility Theorem","layer":"2","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/arrows-impossibility","prerequisites":["basic-logic-and-proof-techniques","sets-functions-and-relations"],"leadsTo":["mechanism-design","game-theory"]},{"id":"theorempath:ascent-algorithms","site":"theorempath","slug":"ascent-algorithms","title":"Ascent Algorithms and Hill Climbing","layer":"1","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/ascent-algorithms","prerequisites":["convex-optimization-basics"],"leadsTo":["tabu-search"]},{"id":"theorempath:asml-and-chip-manufacturing","site":"theorempath","slug":"asml-and-chip-manufacturing","title":"ASML and Chip Manufacturing","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/asml-and-chip-manufacturing","prerequisites":[],"leadsTo":["gpu-compute-model"]},{"id":"theorempath:asymptotic-statistics","site":"theorempath","slug":"asymptotic-statistics","title":"Asymptotic Statistics: M-Estimators, Delta Method, LAN","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/asymptotic-statistics","prerequisites":["central-limit-theorem","maximum-likelihood-estimation","modes-of-convergence-random-variables","cramer-rao-bound","cramer-wold-theorem","fisher-information"],"leadsTo":["bootstrap-methods","fisher-information","cramer-rao-bound","empirical-processes-and-chaining","double-debiased-machine-learning"]},{"id":"theorempath:attention-as-kernel-regression","site":"theorempath","slug":"attention-as-kernel-regression","title":"Attention as Kernel Regression","layer":"4","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/attention-as-kernel-regression","prerequisites":["attention-mechanism-theory","kernels-and-rkhs"],"leadsTo":[]},{"id":"theorempath:attention-for-protein-structure-alphafold","site":"theorempath","slug":"attention-for-protein-structure-alphafold","title":"Attention for Protein Structure: AlphaFold and Successors","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/attention-for-protein-structure-alphafold","prerequisites":["attention-mechanism-theory","transformer-architecture"],"leadsTo":["equivariant-deep-learning","self-supervised-vision"]},{"id":"theorempath:attention-is-all-you-need-paper","site":"theorempath","slug":"attention-is-all-you-need-paper","title":"Attention Is All You Need (Paper)","layer":"4","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/attention-is-all-you-need-paper","prerequisites":["transformer-architecture"],"leadsTo":["flash-attention","positional-encoding","kv-cache"]},{"id":"theorempath:attention-mechanism-theory","site":"theorempath","slug":"attention-mechanism-theory","title":"Attention Mechanism Theory","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/attention-mechanism-theory","prerequisites":["matrix-operations-and-properties","softmax-and-numerical-stability","gram-matrices-and-kernel-matrices","linear-layer-shapes-memory","word-embeddings"],"leadsTo":["kv-cache","positional-encoding","attention-as-kernel-regression","attention-for-protein-structure-alphafold","attention-sinks-and-retrieval-decay","attention-variants-and-efficiency","context-engineering","flash-attention","fox-forget-gate","gpt-series-evolution","induction-heads","mamba-and-state-space-models","mistral-models","sparse-attention-and-long-context","transformer-architecture"]},{"id":"theorempath:attention-mechanisms-history","site":"theorempath","slug":"attention-mechanisms-history","title":"Attention Mechanisms History","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/attention-mechanisms-history","prerequisites":["recurrent-neural-networks","byte-level-language-models"],"leadsTo":["transformer-architecture","positional-encoding"]},{"id":"theorempath:attention-sinks-and-retrieval-decay","site":"theorempath","slug":"attention-sinks-and-retrieval-decay","title":"Attention Sinks and Retrieval Decay","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/attention-sinks-and-retrieval-decay","prerequisites":["attention-mechanism-theory","fox-forget-gate"],"leadsTo":["context-engineering"]},{"id":"theorempath:attention-variants-and-efficiency","site":"theorempath","slug":"attention-variants-and-efficiency","title":"Attention Variants and Efficiency","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/attention-variants-and-efficiency","prerequisites":["attention-mechanism-theory","fast-fourier-transform"],"leadsTo":["kv-cache","efficient-transformers-survey","fox-forget-gate"]},{"id":"theorempath:auction-theory","site":"theorempath","slug":"auction-theory","title":"Auction Theory","layer":"3","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/auction-theory","prerequisites":["game-theory","nash-equilibrium","common-probability-distributions","stable-matching-and-deferred-acceptance"],"leadsTo":["mechanism-design","reinforcement-learning-for-auction-design"]},{"id":"theorempath:audio-language-models","site":"theorempath","slug":"audio-language-models","title":"Audio Language Models","layer":"5","tier":3,"module":"beyond-llms","url":"https://theorempath.com/topics/audio-language-models","prerequisites":["speech-and-audio-ml","transformer-architecture"],"leadsTo":["multimodal-rag"]},{"id":"theorempath:augmented-lagrangian-and-admm","site":"theorempath","slug":"augmented-lagrangian-and-admm","title":"Augmented Lagrangian and ADMM","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/augmented-lagrangian-and-admm","prerequisites":["convex-optimization-basics","convex-duality","nonlinear-gauss-seidel","projected-gradient-descent"],"leadsTo":["trust-region-methods","interior-point-methods"]},{"id":"theorempath:autoencoders-for-low-dimensional-dynamical-structures","site":"theorempath","slug":"autoencoders-for-low-dimensional-dynamical-structures","title":"Autoencoders for Low-Dimensional Dynamical Structures","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/autoencoders-for-low-dimensional-dynamical-structures","prerequisites":["autoencoders","principal-component-analysis"],"leadsTo":["variational-autoencoders","reservoir-computing-and-echo-state-networks"]},{"id":"theorempath:autoencoders-for-single-cell-rna-seq","site":"theorempath","slug":"autoencoders-for-single-cell-rna-seq","title":"Autoencoders for Single-Cell RNA-seq","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/autoencoders-for-single-cell-rna-seq","prerequisites":["variational-autoencoders","autoencoders"],"leadsTo":["dimensionality-reduction-theory","tsne-and-umap"]},{"id":"theorempath:autoencoders","site":"theorempath","slug":"autoencoders","title":"Autoencoders","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/autoencoders","prerequisites":["feedforward-networks-and-backpropagation","vectors-matrices-and-linear-maps","boltzmann-machines-and-hopfield-networks","dimensionality-reduction-theory","expectation-maximization-variants","tsne-and-umap"],"leadsTo":["variational-autoencoders","dimensionality-reduction-theory","autoencoders-for-low-dimensional-dynamical-structures","autoencoders-for-single-cell-rna-seq","jepa-and-joint-embedding","predictive-coding-and-autoencoders-in-the-brain","sparse-autoencoders","sparse-coding-and-efficient-coding"]},{"id":"theorempath:automatic-differentiation","site":"theorempath","slug":"automatic-differentiation","title":"Automatic Differentiation","layer":"1","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/automatic-differentiation","prerequisites":["the-jacobian-matrix","differentiation-in-rn","matrix-calculus","taylor-expansion","the-hessian-matrix","vector-calculus-chain-rule"],"leadsTo":["feedforward-networks-and-backpropagation","optimizer-theory-sgd-adam-muon","adjoint-sensitivity-method","implicit-differentiation","neural-odes","physics-informed-neural-networks","webgpu-for-ml"]},{"id":"theorempath:backward-sde-theory","site":"theorempath","slug":"backward-sde-theory","title":"Backward Stochastic Differential Equations","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/backward-sde-theory","prerequisites":["stochastic-differential-equations","ito-lemma","feynman-kac-formula","hamilton-jacobi-bellman-equation"],"leadsTo":["deep-bsde-method","hamilton-jacobi-bellman-equation","feynman-kac-formula"]},{"id":"theorempath:bagging","site":"theorempath","slug":"bagging","title":"Bagging","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/bagging","prerequisites":["bootstrap-methods","decision-trees-and-ensembles"],"leadsTo":["random-forests","gradient-boosting","ensemble-methods-theory"]},{"id":"theorempath:base-rate-fallacy","site":"theorempath","slug":"base-rate-fallacy","title":"Base Rate Fallacy","layer":"1","tier":2,"module":"methodology","url":"https://theorempath.com/topics/base-rate-fallacy","prerequisites":["common-probability-distributions","birthday-paradox","confusion-matrices-and-classification-metrics","monty-hall-problem","simpsons-paradox"],"leadsTo":["confusion-matrices-and-classification-metrics","simpsons-paradox","statistical-paradoxes-collection"]},{"id":"theorempath:basic-logic-and-proof-techniques","site":"theorempath","slug":"basic-logic-and-proof-techniques","title":"Basic Logic and Proof Techniques","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/basic-logic-and-proof-techniques","prerequisites":[],"leadsTo":["sets-functions-and-relations","counting-and-combinatorics","p-vs-np","sat-smt-and-automated-reasoning","arrows-impossibility","cap-theorem","category-theory","distributed-consensus","information-retrieval","model-theory-basics","proof-theory-and-cut-elimination","relational-algebra","type-theory","concentration-inequalities","hoeffdings-lemma","pac-learning-framework","uniform-convergence","vc-dimension"]},{"id":"theorempath:basu-theorem","site":"theorempath","slug":"basu-theorem","title":"Basu's Theorem","layer":"0B","tier":3,"module":"statistical-estimation","url":"https://theorempath.com/topics/basu-theorem","prerequisites":["sufficient-statistics-and-exponential-families"],"leadsTo":["fisher-information"]},{"id":"theorempath:batch-normalization","site":"theorempath","slug":"batch-normalization","title":"Batch Normalization","layer":"2","tier":1,"module":"training-techniques","url":"https://theorempath.com/topics/batch-normalization","prerequisites":["feedforward-networks-and-backpropagation","expectation-variance-covariance-moments","activation-functions","gradient-flow-and-vanishing-gradients","regularization-in-practice","skip-connections-and-resnets","weight-initialization","whitening-and-decorrelation"],"leadsTo":[]},{"id":"theorempath:batch-size-and-learning-dynamics","site":"theorempath","slug":"batch-size-and-learning-dynamics","title":"Batch Size and Learning Dynamics","layer":"2","tier":2,"module":"training-techniques","url":"https://theorempath.com/topics/batch-size-and-learning-dynamics","prerequisites":["stochastic-gradient-descent-convergence","adam-optimizer"],"leadsTo":["learning-rate-scheduling","distributed-training-theory"]},{"id":"theorempath:bayesian-estimation","site":"theorempath","slug":"bayesian-estimation","title":"Bayesian Estimation","layer":"0B","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/bayesian-estimation","prerequisites":["maximum-likelihood-estimation","common-probability-distributions","joint-marginal-conditional-distributions","shrinkage-estimation-james-stein"],"leadsTo":["gaussian-processes-for-ml","variational-autoencoders","anthropic-bias-and-observation-selection","bayesian-neural-networks","bayesian-state-estimation","causal-inference-pearl","decision-theory-foundations","detection-theory","empirical-bayes-vs-hierarchical-bayes","meta-analysis","no-u-turn-sampler-and-neals-funnel","pac-bayes-bounds","small-area-estimation","tabular-foundation-models-bayesian-inference","bayesian-linear-regression","conjugate-priors","maximum-a-posteriori-estimation"]},{"id":"theorempath:bayesian-linear-regression","site":"theorempath","slug":"bayesian-linear-regression","title":"Bayesian Linear Regression","layer":"2","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/bayesian-linear-regression","prerequisites":["linear-regression","ridge-regression","multivariate-normal-distribution","bayesian-estimation","conjugate-priors","maximum-a-posteriori-estimation","maximum-likelihood-estimation"],"leadsTo":["gaussian-processes-for-ml","gaussian-processes-regression","empirical-bayes-vs-hierarchical-bayes","kernel-trick"]},{"id":"theorempath:bayesian-neural-networks","site":"theorempath","slug":"bayesian-neural-networks","title":"Bayesian Neural Networks","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/bayesian-neural-networks","prerequisites":["bayesian-estimation","feedforward-networks-and-backpropagation","gaussian-processes-for-ml","no-u-turn-sampler-and-neals-funnel"],"leadsTo":[]},{"id":"theorempath:bayesian-optimization-for-hyperparameters","site":"theorempath","slug":"bayesian-optimization-for-hyperparameters","title":"Bayesian Optimization for Hyperparameters","layer":"3","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/bayesian-optimization-for-hyperparameters","prerequisites":["gaussian-processes-regression","gaussian-processes-for-ml"],"leadsTo":["multi-armed-bandits-theory","model-evaluation-best-practices"]},{"id":"theorempath:bayesian-state-estimation","site":"theorempath","slug":"bayesian-state-estimation","title":"Bayesian State Estimation","layer":"2","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/bayesian-state-estimation","prerequisites":["bayesian-estimation","common-probability-distributions","gaussian-processes-in-astronomy","kalman-filter","no-u-turn-sampler-and-neals-funnel"],"leadsTo":["markov-decision-processes"]},{"id":"theorempath:bellman-equations","site":"theorempath","slug":"bellman-equations","title":"Bellman Equations","layer":"2","tier":1,"module":"rl-theory","url":"https://theorempath.com/topics/bellman-equations","prerequisites":["markov-decision-processes","expectation-variance-covariance-moments"],"leadsTo":["value-iteration-and-policy-iteration","td-learning","q-learning","model-based-rl","reward-design"]},{"id":"theorempath:benchmarking-methodology","site":"theorempath","slug":"benchmarking-methodology","title":"Benchmarking Methodology","layer":"3","tier":3,"module":"methodology","url":"https://theorempath.com/topics/benchmarking-methodology","prerequisites":["evaluation-metrics-and-properties","reproducibility-and-experimental-rigor"],"leadsTo":["data-contamination-and-evaluation","ablation-study-design"]},{"id":"theorempath:benfords-law","site":"theorempath","slug":"benfords-law","title":"Benford's Law","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/benfords-law","prerequisites":["common-probability-distributions"],"leadsTo":["hypothesis-testing-for-ml","goodness-of-fit-tests"]},{"id":"theorempath:benign-overfitting","site":"theorempath","slug":"benign-overfitting","title":"Benign Overfitting","layer":"4","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/benign-overfitting","prerequisites":["implicit-bias-and-modern-generalization","random-matrix-theory-overview","double-descent","neural-network-optimization-landscape","neural-tangent-kernel","ridge-regression"],"leadsTo":["neural-tangent-kernel","double-descent"]},{"id":"theorempath:bennetts-inequality","site":"theorempath","slug":"bennetts-inequality","title":"Bennett's Inequality","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/bennetts-inequality","prerequisites":["concentration-inequalities","chernoff-bounds","moment-generating-functions","expectation-variance-covariance-moments"],"leadsTo":["bernstein-inequality","subexponential-random-variables","matrix-concentration"]},{"id":"theorempath:bernstein-inequality","site":"theorempath","slug":"bernstein-inequality","title":"Bernstein Inequality","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/bernstein-inequality","prerequisites":["concentration-inequalities","expectation-variance-covariance-moments","moment-generating-functions","bennetts-inequality","hoeffdings-lemma"],"leadsTo":["subexponential-random-variables","matrix-concentration","uniform-convergence"]},{"id":"theorempath:bert-and-pretrain-finetune-paradigm","site":"theorempath","slug":"bert-and-pretrain-finetune-paradigm","title":"BERT and the Pretrain-Finetune Paradigm","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/bert-and-pretrain-finetune-paradigm","prerequisites":["transformer-architecture","token-prediction-and-language-modeling","nlp-for-economic-text-analysis"],"leadsTo":["gpt-series-evolution","post-training-overview"]},{"id":"theorempath:beta-distribution","site":"theorempath","slug":"beta-distribution","title":"Beta Distribution","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/beta-distribution","prerequisites":["common-probability-distributions","distributions-atlas","gamma-distribution"],"leadsTo":["bayesian-estimation","order-statistics","chi-squared-distribution-and-tests"]},{"id":"theorempath:bias-complexity-tradeoff","site":"theorempath","slug":"bias-complexity-tradeoff","title":"Bias-Complexity Tradeoff","layer":"2","tier":2,"module":"learning-theory-core","url":"https://theorempath.com/topics/bias-complexity-tradeoff","prerequisites":["pac-learning-framework","empirical-risk-minimization","no-free-lunch-theorem"],"leadsTo":["vc-dimension","regularization-theory","bias-variance-tradeoff"]},{"id":"theorempath:bias-variance-tradeoff","site":"theorempath","slug":"bias-variance-tradeoff","title":"Bias-Variance Tradeoff","layer":"2","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/bias-variance-tradeoff","prerequisites":["expectation-variance-covariance-moments","empirical-risk-minimization","elastic-net","elements-of-statistical-learning-book","generalized-additive-models","knn","linear-regression","bias-complexity-tradeoff"],"leadsTo":["ridge-regression","double-descent","implicit-bias-and-modern-generalization","cross-validation-theory","decision-trees-and-ensembles","overfitting-and-underfitting","regularization-theory"]},{"id":"theorempath:birthday-paradox","site":"theorempath","slug":"birthday-paradox","title":"Birthday Paradox","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/birthday-paradox","prerequisites":["common-probability-distributions","monty-hall-problem"],"leadsTo":["monty-hall-problem","base-rate-fallacy"]},{"id":"theorempath:bits-nats-perplexity-bpb","site":"theorempath","slug":"bits-nats-perplexity-bpb","title":"Bits, Nats, Perplexity, and BPB","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/bits-nats-perplexity-bpb","prerequisites":["information-theory-foundations","kl-divergence"],"leadsTo":["perplexity-and-language-model-evaluation","calibration-and-uncertainty"]},{"id":"theorempath:bitter-lesson","site":"theorempath","slug":"bitter-lesson","title":"The Bitter Lesson","layer":"3","tier":1,"module":"methodology","url":"https://theorempath.com/topics/bitter-lesson","prerequisites":[],"leadsTo":["era-of-experience","exploration-vs-exploitation"]},{"id":"theorempath:boltzmann-machines-and-hopfield-networks","site":"theorempath","slug":"boltzmann-machines-and-hopfield-networks","title":"Boltzmann Machines and Hopfield Networks","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/boltzmann-machines-and-hopfield-networks","prerequisites":["common-probability-distributions"],"leadsTo":["autoencoders","diffusion-models"]},{"id":"theorempath:bootstrap-methods","site":"theorempath","slug":"bootstrap-methods","title":"Bootstrap Methods","layer":"2","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/bootstrap-methods","prerequisites":["common-probability-distributions","asymptotic-statistics","central-limit-theorem","cross-validation-theory","neyman-pearson-and-hypothesis-testing-theory","order-statistics","statistical-significance-and-multiple-comparisons"],"leadsTo":["hypothesis-testing-for-ml","bagging","random-forests"]},{"id":"theorempath:borel-cantelli-lemmas","site":"theorempath","slug":"borel-cantelli-lemmas","title":"Borel-Cantelli Lemmas","layer":"0B","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/borel-cantelli-lemmas","prerequisites":["measure-theoretic-probability","modes-of-convergence-random-variables"],"leadsTo":["law-of-large-numbers","stochastic-approximation-theory"]},{"id":"theorempath:bounded-rationality","site":"theorempath","slug":"bounded-rationality","title":"Bounded Rationality","layer":"2","tier":1,"module":"decision-theory","url":"https://theorempath.com/topics/bounded-rationality","prerequisites":["decision-theory-foundations","convex-optimization-basics","convex-tinkering","editorial-principles","leverage-points-systems"],"leadsTo":["game-theory","expected-utility"]},{"id":"theorempath:broadcast-joins-distributed-compute","site":"theorempath","slug":"broadcast-joins-distributed-compute","title":"Broadcast Joins in Distributed Compute","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/broadcast-joins-distributed-compute","prerequisites":[],"leadsTo":["distributed-training-theory","parallel-processing-fundamentals"]},{"id":"theorempath:burn-in-convergence-diagnostics","site":"theorempath","slug":"burn-in-convergence-diagnostics","title":"Burn-in and Convergence Diagnostics","layer":"2","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/burn-in-convergence-diagnostics","prerequisites":["metropolis-hastings","markov-chains-and-steady-state","coupling-arguments-and-mixing-time","gibbs-sampling","hamiltonian-monte-carlo","markov-chain-monte-carlo","mcmc-for-markov-random-fields","perfect-sampling","slice-sampling","variance-reduction-techniques"],"leadsTo":["gibbs-sampling","hamiltonian-monte-carlo","no-u-turn-sampler-and-neals-funnel"]},{"id":"theorempath:byte-level-language-models","site":"theorempath","slug":"byte-level-language-models","title":"Byte-Level Language Models","layer":"4","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/byte-level-language-models","prerequisites":["tokenization-and-information-theory","morphology-and-subword-modeling"],"leadsTo":["transformer-architecture","attention-mechanisms-history"]},{"id":"theorempath:calibration-and-uncertainty","site":"theorempath","slug":"calibration-and-uncertainty","title":"Calibration and Uncertainty Quantification","layer":"3","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/calibration-and-uncertainty","prerequisites":["logistic-regression","bits-nats-perplexity-bpb","decoding-strategies","goodness-of-fit-tests","roc-curve-and-auc","split-conformal-prediction"],"leadsTo":["red-teaming-and-adversarial-eval","out-of-distribution-detection"]},{"id":"theorempath:cantors-theorem-and-uncountability","site":"theorempath","slug":"cantors-theorem-and-uncountability","title":"Cantor's Theorem and Uncountability","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/cantors-theorem-and-uncountability","prerequisites":["zermelo-fraenkel-set-theory"],"leadsTo":["zermelo-fraenkel-set-theory","godels-incompleteness-theorems"]},{"id":"theorempath:cap-theorem","site":"theorempath","slug":"cap-theorem","title":"CAP Theorem","layer":"3","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/cap-theorem","prerequisites":["basic-logic-and-proof-techniques","distributed-consensus"],"leadsTo":[]},{"id":"theorempath:cardinality-and-countability","site":"theorempath","slug":"cardinality-and-countability","title":"Cardinality and Countability","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/cardinality-and-countability","prerequisites":["sets-functions-and-relations"],"leadsTo":["measure-theoretic-probability"]},{"id":"theorempath:catastrophic-forgetting","site":"theorempath","slug":"catastrophic-forgetting","title":"Catastrophic Forgetting","layer":"4","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/catastrophic-forgetting","prerequisites":["fine-tuning-and-adaptation"],"leadsTo":[]},{"id":"theorempath:category-theory","site":"theorempath","slug":"category-theory","title":"Category Theory","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/category-theory","prerequisites":["sets-functions-and-relations","basic-logic-and-proof-techniques"],"leadsTo":[]},{"id":"theorempath:causal-inference-basics","site":"theorempath","slug":"causal-inference-basics","title":"Causal Inference Basics","layer":"3","tier":3,"module":"methodology","url":"https://theorempath.com/topics/causal-inference-basics","prerequisites":["hypothesis-testing-for-ml","feature-importance-and-interpretability","survival-analysis"],"leadsTo":["causal-inference-pearl","causal-inference-for-policy-evaluation","simpsons-paradox","double-debiased-machine-learning","weighted-conformal-prediction"]},{"id":"theorempath:causal-inference-for-policy-evaluation","site":"theorempath","slug":"causal-inference-for-policy-evaluation","title":"Causal Inference for Policy Evaluation","layer":"4","tier":2,"module":"applied-ml","url":"https://theorempath.com/topics/causal-inference-for-policy-evaluation","prerequisites":["causal-inference-basics","causal-inference-pearl","hypothesis-testing-for-ml"],"leadsTo":["design-based-vs-model-based-inference","longitudinal-surveys-and-panel-data"]},{"id":"theorempath:causal-inference-pearl","site":"theorempath","slug":"causal-inference-pearl","title":"Causal Inference and the Ladder of Causation","layer":"3","tier":1,"module":"methodology","url":"https://theorempath.com/topics/causal-inference-pearl","prerequisites":["common-probability-distributions","bayesian-estimation","causal-inference-basics","double-debiased-machine-learning","editorial-principles"],"leadsTo":["decision-theory-foundations","causal-inference-for-policy-evaluation"]},{"id":"theorempath:central-limit-theorem","site":"theorempath","slug":"central-limit-theorem","title":"Central Limit Theorem","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/central-limit-theorem","prerequisites":["law-of-large-numbers","expectation-variance-covariance-moments","common-probability-distributions","characteristic-functions","modes-of-convergence-random-variables"],"leadsTo":["asymptotic-statistics","maximum-likelihood-estimation","bootstrap-methods","concentration-inequalities","cramer-wold-theorem","double-debiased-machine-learning","monte-carlo-methods","non-probability-sampling"]},{"id":"theorempath:chain-of-thought-and-reasoning","site":"theorempath","slug":"chain-of-thought-and-reasoning","title":"Chain-of-Thought and Reasoning","layer":"5","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/chain-of-thought-and-reasoning","prerequisites":["prompt-engineering-and-in-context-learning","transformer-architecture","decoding-strategies","scaling-laws"],"leadsTo":["dpo-vs-grpo-vs-rl-reasoning","scaling-laws","hallucination-theory","tool-augmented-reasoning"]},{"id":"theorempath:characteristic-functions","site":"theorempath","slug":"characteristic-functions","title":"Characteristic Functions","layer":"1","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/characteristic-functions","prerequisites":["measure-theoretic-probability","moment-generating-functions"],"leadsTo":["central-limit-theorem","kernels-and-rkhs","fat-tails","multivariate-normal-distribution"]},{"id":"theorempath:chernoff-bounds","site":"theorempath","slug":"chernoff-bounds","title":"Chernoff Bounds","layer":"1","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/chernoff-bounds","prerequisites":["concentration-inequalities","moment-generating-functions"],"leadsTo":["subgaussian-random-variables","subexponential-random-variables","bennetts-inequality","chi-squared-concentration","hoeffdings-lemma"]},{"id":"theorempath:chi-squared-concentration","site":"theorempath","slug":"chi-squared-concentration","title":"Chi-Squared Concentration","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/chi-squared-concentration","prerequisites":["concentration-inequalities","chernoff-bounds","common-probability-distributions","moment-generating-functions"],"leadsTo":["subexponential-random-variables","hanson-wright-inequality"]},{"id":"theorempath:chi-squared-distribution-and-tests","site":"theorempath","slug":"chi-squared-distribution-and-tests","title":"Chi-Squared Distribution and Tests","layer":"1","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/chi-squared-distribution-and-tests","prerequisites":["distributions-atlas","normal-distribution","gamma-distribution","hypothesis-testing-for-ml"],"leadsTo":["student-t-distribution-and-t-test","f-distribution-and-anova","goodness-of-fit-tests","likelihood-ratio-wald-score-tests"]},{"id":"theorempath:class-imbalance-and-resampling","site":"theorempath","slug":"class-imbalance-and-resampling","title":"Class Imbalance and Resampling","layer":"1","tier":2,"module":"methodology","url":"https://theorempath.com/topics/class-imbalance-and-resampling","prerequisites":["confusion-matrices-and-classification-metrics"],"leadsTo":["cross-validation-theory","hypothesis-testing-for-ml"]},{"id":"theorempath:classical-odes","site":"theorempath","slug":"classical-odes","title":"Classical ODEs: Existence, Stability, and Numerical Methods","layer":"1","tier":1,"module":"scientific-ml","url":"https://theorempath.com/topics/classical-odes","prerequisites":["continuity-in-rn","the-jacobian-matrix"],"leadsTo":["physics-informed-neural-networks","neural-odes","stochastic-calculus-for-ml","adjoint-sensitivity-method","nonlinear-dynamics-and-chaos-fundamentals"]},{"id":"theorempath:claude-model-family","site":"theorempath","slug":"claude-model-family","title":"Claude Model Family","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/claude-model-family","prerequisites":["transformer-architecture"],"leadsTo":["model-comparison-table"]},{"id":"theorempath:clip-and-openclip-in-practice","site":"theorempath","slug":"clip-and-openclip-in-practice","title":"CLIP, OpenCLIP, and SigLIP: Contrastive Language-Image Pretraining","layer":"4","tier":1,"module":"beyond-llms","url":"https://theorempath.com/topics/clip-and-openclip-in-practice","prerequisites":["contrastive-learning","vision-transformer-lineage","information-theory-foundations","florence-and-vision-foundation-models"],"leadsTo":["florence-and-vision-foundation-models","diffusion-models","multimodal-rag","self-supervised-vision"]},{"id":"theorempath:clustering-and-latent-variable-models-in-psychology","site":"theorempath","slug":"clustering-and-latent-variable-models-in-psychology","title":"Clustering and Latent Variable Models in Psychology","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/clustering-and-latent-variable-models-in-psychology","prerequisites":[],"leadsTo":[]},{"id":"theorempath:clustering-for-gene-expression","site":"theorempath","slug":"clustering-for-gene-expression","title":"Clustering for Gene Expression","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/clustering-for-gene-expression","prerequisites":["k-means-clustering","spectral-clustering"],"leadsTo":["tsne-and-umap","graph-neural-networks"]},{"id":"theorempath:cnns-for-medical-imaging","site":"theorempath","slug":"cnns-for-medical-imaging","title":"CNNs for Medical Imaging","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/cnns-for-medical-imaging","prerequisites":["convolutional-neural-networks","object-detection-and-segmentation"],"leadsTo":["vision-transformer-lineage","out-of-distribution-detection"]},{"id":"theorempath:cnns-for-signal-feature-extraction","site":"theorempath","slug":"cnns-for-signal-feature-extraction","title":"CNNs for Signal Feature Extraction","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/cnns-for-signal-feature-extraction","prerequisites":["convolutional-neural-networks","signals-and-systems-for-ml"],"leadsTo":["self-supervised-vision","speech-and-audio-ml"]},{"id":"theorempath:cohere-models","site":"theorempath","slug":"cohere-models","title":"Cohere Models","layer":"4","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/cohere-models","prerequisites":["transformer-architecture","tokenization-and-information-theory","information-retrieval"],"leadsTo":["llama-and-open-weight-models","mistral-models"]},{"id":"theorempath:common-inequalities","site":"theorempath","slug":"common-inequalities","title":"Common Inequalities","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/common-inequalities","prerequisites":["common-probability-distributions","kolmogorov-probability-axioms"],"leadsTo":["concentration-inequalities","convex-optimization-basics","empirical-risk-minimization","convex-tinkering"]},{"id":"theorempath:common-probability-distributions","site":"theorempath","slug":"common-probability-distributions","title":"Common Probability Distributions","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/common-probability-distributions","prerequisites":["sets-functions-and-relations","exponential-function-properties","integration-and-change-of-variables","measure-theoretic-probability","random-variables"],"leadsTo":["concentration-inequalities","common-inequalities","empirical-risk-minimization","anomaly-detection","auction-theory","base-rate-fallacy","bayesian-estimation","bayesian-state-estimation","benfords-law","birthday-paradox","boltzmann-machines-and-hopfield-networks","bootstrap-methods","causal-inference-pearl","central-limit-theorem","confusion-matrices-and-classification-metrics","copulas","data-preprocessing-and-feature-engineering","decision-theory-foundations","differential-privacy","dropout","expectation-variance-covariance-moments","expected-utility","extreme-value-theory","fat-tails","game-theory","goodness-of-fit-tests","hash-functions","importance-sampling","information-retrieval","joint-marginal-conditional-distributions","k-means-clustering","kalman-filter","kelly-criterion","kl-divergence","knn","law-of-large-numbers","markov-chains-and-steady-state","maximum-likelihood-estimation","method-of-moments","metropolis-hastings","moment-generating-functions","monty-hall-problem","multi-armed-bandits-theory","naive-bayes","neyman-pearson-and-hypothesis-testing-theory","no-regret-learning","nonresponse-and-missing-data","normalization-flows","number-theory-and-ml","order-statistics","prospect-theory","public-key-cryptography","roc-curve-and-auc","sample-size-determination","signal-detection-theory","skewness-kurtosis-and-higher-moments","survey-sampling-methods","synthetic-data-generation","token-prediction-and-language-modeling","tokenization-and-information-theory","total-variation-distance","triangular-distribution","wasserstein-distances","winsorization","chi-squared-concentration","conjugate-priors","kernel-trick","maximum-a-posteriori-estimation","multivariate-normal-distribution","sluds-inequality"]},{"id":"theorempath:commons-governance-ostrom","site":"theorempath","slug":"commons-governance-ostrom","title":"Commons Governance and Institutional Analysis","layer":"3","tier":2,"module":"methodology","url":"https://theorempath.com/topics/commons-governance-ostrom","prerequisites":["game-theory","editorial-principles"],"leadsTo":["mechanism-design"]},{"id":"theorempath:compactness-and-heine-borel","site":"theorempath","slug":"compactness-and-heine-borel","title":"Compactness and Heine-Borel","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/compactness-and-heine-borel","prerequisites":["metric-spaces-convergence-completeness"],"leadsTo":[]},{"id":"theorempath:complex-numbers-for-fourier","site":"theorempath","slug":"complex-numbers-for-fourier","title":"Complex Numbers for Fourier","layer":"0A","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/complex-numbers-for-fourier","prerequisites":["vectors-matrices-and-linear-maps"],"leadsTo":["fast-fourier-transform","fourier-neural-operator","spectral-theory-of-operators","wave-based-neural-networks"]},{"id":"theorempath:computer-architecture-for-ml","site":"theorempath","slug":"computer-architecture-for-ml","title":"Computer Architecture for ML","layer":"2","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/computer-architecture-for-ml","prerequisites":["floating-point-arithmetic"],"leadsTo":["flash-attention","webgpu-for-ml"]},{"id":"theorempath:concentration-inequalities","site":"theorempath","slug":"concentration-inequalities","title":"Concentration Inequalities","layer":"1","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/concentration-inequalities","prerequisites":["common-probability-distributions","expectation-variance-covariance-moments","central-limit-theorem","common-inequalities","law-of-large-numbers","martingale-theory","measure-theoretic-probability","moment-generating-functions","radon-nikodym-and-conditional-expectation","skewness-kurtosis-and-higher-moments","basic-logic-and-proof-techniques","sets-functions-and-relations"],"leadsTo":["subgaussian-random-variables","bernstein-inequality","subexponential-random-variables","mcdiarmids-inequality","adaptive-learning-is-not-iid","algorithmic-stability","chernoff-bounds","empirical-risk-minimization","epsilon-nets-and-covering-numbers","glivenko-cantelli-theorem","markov-decision-processes","matrix-concentration","minimax-lower-bounds","no-regret-learning","pac-learning-framework","rademacher-complexity","stochastic-gradient-descent-convergence","stochastic-processes-ml","symmetrization-inequality","vc-dimension","bennetts-inequality","chi-squared-concentration","hoeffdings-lemma","sluds-inequality"]},{"id":"theorempath:conditioning-and-condition-number","site":"theorempath","slug":"conditioning-and-condition-number","title":"Conditioning and Condition Number","layer":"1","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/conditioning-and-condition-number","prerequisites":["eigenvalues-and-eigenvectors","matrix-operations-and-properties","matrix-norms","numerical-stability","singular-value-decomposition","softmax-and-numerical-stability"],"leadsTo":[]},{"id":"theorempath:confusion-matrices-and-classification-metrics","site":"theorempath","slug":"confusion-matrices-and-classification-metrics","title":"Confusion Matrices and Classification Metrics","layer":"1","tier":1,"module":"methodology","url":"https://theorempath.com/topics/confusion-matrices-and-classification-metrics","prerequisites":["common-probability-distributions","multi-class-and-multi-label-classification","signal-detection-theory"],"leadsTo":["base-rate-fallacy","cross-validation-theory","class-imbalance-and-resampling","model-evaluation-best-practices","roc-curve-and-auc"]},{"id":"theorempath:confusion-matrix-deep-dive","site":"theorempath","slug":"confusion-matrix-deep-dive","title":"Confusion Matrix: MCC, Kappa, and Cost-Sensitive Evaluation","layer":"1","tier":1,"module":"methodology","url":"https://theorempath.com/topics/confusion-matrix-deep-dive","prerequisites":[],"leadsTo":["cross-validation-theory","hypothesis-testing-for-ml"]},{"id":"theorempath:conjugate-gradient-methods","site":"theorempath","slug":"conjugate-gradient-methods","title":"Conjugate Gradient Methods","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/conjugate-gradient-methods","prerequisites":["line-search-methods","matrix-operations-and-properties","matrix-norms","numerical-linear-algebra"],"leadsTo":["preconditioned-optimizers","second-order-optimization-methods","trust-region-methods"]},{"id":"theorempath:conjugate-priors","site":"theorempath","slug":"conjugate-priors","title":"Conjugate Priors","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/conjugate-priors","prerequisites":["bayesian-estimation","maximum-likelihood-estimation","sufficient-statistics-and-exponential-families","common-probability-distributions","multivariate-normal-distribution","maximum-a-posteriori-estimation"],"leadsTo":["bayesian-linear-regression","empirical-bayes-vs-hierarchical-bayes","em-algorithm","gaussian-processes-for-ml"]},{"id":"theorempath:constitutional-ai","site":"theorempath","slug":"constitutional-ai","title":"Constitutional AI","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/constitutional-ai","prerequisites":["rlhf-and-alignment","reinforcement-learning-from-human-feedback-deep-dive","reward-hacking"],"leadsTo":[]},{"id":"theorempath:context-engineering","site":"theorempath","slug":"context-engineering","title":"Context Engineering","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/context-engineering","prerequisites":["kv-cache","attention-mechanism-theory","agent-protocols-mcp-a2a","attention-sinks-and-retrieval-decay","inference-systems-overview","mamba-and-state-space-models","prompt-engineering-and-in-context-learning","semantic-search-and-embeddings","sparse-attention-and-long-context","speculative-decoding-and-quantization"],"leadsTo":["speculative-decoding-and-quantization","hallucination-theory","memory-systems-for-llms","multimodal-rag"]},{"id":"theorempath:continual-learning-and-forgetting","site":"theorempath","slug":"continual-learning-and-forgetting","title":"Continual Learning and Forgetting","layer":"3","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/continual-learning-and-forgetting","prerequisites":["optimizer-theory-sgd-adam-muon"],"leadsTo":[]},{"id":"theorempath:continuity-in-rn","site":"theorempath","slug":"continuity-in-rn","title":"Continuity in Rⁿ","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/continuity-in-rn","prerequisites":["metric-spaces-convergence-completeness"],"leadsTo":["convex-optimization-basics","taylor-expansion","classical-odes","differentiation-in-rn"]},{"id":"theorempath:continuous-normalizing-flows","site":"theorempath","slug":"continuous-normalizing-flows","title":"Continuous Normalizing Flows","layer":"3","tier":3,"module":"scientific-ml","url":"https://theorempath.com/topics/continuous-normalizing-flows","prerequisites":["neural-odes","normalization-flows","the-jacobian-matrix","adjoint-sensitivity-method"],"leadsTo":["diffusion-models","neural-sdes"]},{"id":"theorempath:continuous-thought-machines","site":"theorempath","slug":"continuous-thought-machines","title":"Continuous Thought Machines","layer":"5","tier":3,"module":"beyond-llms","url":"https://theorempath.com/topics/continuous-thought-machines","prerequisites":["neural-odes","equilibrium-and-implicit-models"],"leadsTo":["test-time-training","open-problems-in-ml-theory"]},{"id":"theorempath:contraction-inequality","site":"theorempath","slug":"contraction-inequality","title":"Contraction Inequality","layer":"3","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/contraction-inequality","prerequisites":["rademacher-complexity"],"leadsTo":["algorithmic-stability","epsilon-nets-and-covering-numbers"]},{"id":"theorempath:contrastive-learning","site":"theorempath","slug":"contrastive-learning","title":"Contrastive Learning","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/contrastive-learning","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["data-augmentation-theory","diffusion-models","clip-and-openclip-in-practice","representation-learning-in-cosmology"]},{"id":"theorempath:convex-duality","site":"theorempath","slug":"convex-duality","title":"Convex Duality","layer":"2","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/convex-duality","prerequisites":["convex-optimization-basics","inverse-and-implicit-function-theorem","subgradients-and-subdifferentials"],"leadsTo":["support-vector-machines","regularization-theory","kernels-and-rkhs","augmented-lagrangian-and-admm","information-geometry","minimax-saddle-points","minimax-theorem","mirror-descent-and-frank-wolfe","optimal-transport-and-earth-movers-distance","wasserstein-distances"]},{"id":"theorempath:convex-optimization-basics","site":"theorempath","slug":"convex-optimization-basics","title":"Convex Optimization Basics","layer":"1","tier":1,"module":"optimization-function-classes","url":"https://theorempath.com/topics/convex-optimization-basics","prerequisites":["differentiation-in-rn","matrix-operations-and-properties","common-inequalities","continuity-in-rn","dynamic-programming","graphslam-and-factor-graphs","inverse-and-implicit-function-theorem","positive-semidefinite-matrices","submodular-optimization","taylor-expansion","the-hessian-matrix"],"leadsTo":["regularization-theory","kernels-and-rkhs","activation-functions","ascent-algorithms","augmented-lagrangian-and-admm","bounded-rationality","convex-duality","coordinate-descent","em-algorithm","expected-utility","game-theory","gradient-descent-variants","interior-point-methods","k-means-clustering","lasso-regression","line-search-methods","logistic-regression","markov-decision-processes","minimax-saddle-points","mirror-descent-and-frank-wolfe","nash-equilibrium","newtons-method","online-convex-optimization","optimizer-theory-sgd-adam-muon","policy-gradient-theorem","preconditioned-optimizers","projected-gradient-descent","proximal-gradient-methods","ridge-regression","riemannian-optimization","scaling-laws","stability-and-optimization-dynamics","stochastic-approximation-theory","subgradients-and-subdifferentials","support-vector-machines","training-dynamics-and-loss-landscapes","kernel-trick","maximum-a-posteriori-estimation"]},{"id":"theorempath:convex-tinkering","site":"theorempath","slug":"convex-tinkering","title":"Convex Tinkering","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/convex-tinkering","prerequisites":["common-inequalities","editorial-principles","non-probability-sampling"],"leadsTo":["fat-tails","kelly-criterion","bounded-rationality"]},{"id":"theorempath:convolutional-neural-networks","site":"theorempath","slug":"convolutional-neural-networks","title":"Convolutional Neural Networks","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/convolutional-neural-networks","prerequisites":["feedforward-networks-and-backpropagation","vectors-matrices-and-linear-maps","fast-fourier-transform","signals-and-systems-for-ml","skip-connections-and-resnets","svm-for-rf-classification"],"leadsTo":["recurrent-neural-networks","transformer-architecture","alexnet-and-deep-learning-history","anomaly-detection-gravitational-waves","cnns-for-medical-imaging","cnns-for-signal-feature-extraction","equivariant-deep-learning","graph-neural-networks","object-detection-and-segmentation","spiking-neural-networks","vision-transformer-lineage"]},{"id":"theorempath:coordinate-descent","site":"theorempath","slug":"coordinate-descent","title":"Coordinate Descent","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/coordinate-descent","prerequisites":["convex-optimization-basics","mirror-descent-and-frank-wolfe","proximal-gradient-methods"],"leadsTo":["proximal-gradient-methods","stochastic-gradient-descent-convergence","nonlinear-gauss-seidel"]},{"id":"theorempath:copulas","site":"theorempath","slug":"copulas","title":"Copulas","layer":"3","tier":3,"module":"statistical-foundations","url":"https://theorempath.com/topics/copulas","prerequisites":["common-probability-distributions"],"leadsTo":[]},{"id":"theorempath:counting-and-combinatorics","site":"theorempath","slug":"counting-and-combinatorics","title":"Counting and Combinatorics","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/counting-and-combinatorics","prerequisites":["basic-logic-and-proof-techniques"],"leadsTo":["vc-dimension","pac-learning-framework"]},{"id":"theorempath:coupling-arguments-and-mixing-time","site":"theorempath","slug":"coupling-arguments-and-mixing-time","title":"Coupling Arguments and Mixing Time","layer":"3","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/coupling-arguments-and-mixing-time","prerequisites":["metropolis-hastings","martingale-theory","total-variation-distance"],"leadsTo":["burn-in-convergence-diagnostics"]},{"id":"theorempath:cramer-rao-bound","site":"theorempath","slug":"cramer-rao-bound","title":"Cramér-Rao Bound: Information Inequality, Achievability, and Sharper Variants","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/cramer-rao-bound","prerequisites":["fisher-information","maximum-likelihood-estimation","kl-divergence"],"leadsTo":["asymptotic-statistics","minimax-lower-bounds","shrinkage-estimation-james-stein"]},{"id":"theorempath:cramer-wold-theorem","site":"theorempath","slug":"cramer-wold-theorem","title":"Cramér-Wold Theorem","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/cramer-wold-theorem","prerequisites":["central-limit-theorem","measure-theoretic-probability"],"leadsTo":["asymptotic-statistics","high-dimensional-probability-book"]},{"id":"theorempath:cross-entropy-loss-deep-dive","site":"theorempath","slug":"cross-entropy-loss-deep-dive","title":"Cross-Entropy Loss: MLE, KL Divergence, and Classification","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/cross-entropy-loss-deep-dive","prerequisites":["information-theory-foundations","logistic-regression","log-probability-computation","multi-class-and-multi-label-classification"],"leadsTo":["multi-class-and-multi-label-classification","regularization-in-practice"]},{"id":"theorempath:cross-validation-theory","site":"theorempath","slug":"cross-validation-theory","title":"Cross-Validation Theory","layer":"2","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/cross-validation-theory","prerequisites":["empirical-risk-minimization","bias-variance-tradeoff","aic-and-bic","class-imbalance-and-resampling","confusion-matrices-and-classification-metrics","confusion-matrix-deep-dive","evaluation-metrics-and-properties","feature-importance-and-interpretability","gaussian-processes-regression","model-evaluation-best-practices","overfitting-and-underfitting","proper-scoring-rules","statistical-significance-and-multiple-comparisons","train-test-split-and-data-leakage","xgboost"],"leadsTo":["algorithmic-stability","bootstrap-methods","double-debiased-machine-learning","split-conformal-prediction"]},{"id":"theorempath:cubist-and-model-trees","site":"theorempath","slug":"cubist-and-model-trees","title":"Cubist and Model Trees","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/cubist-and-model-trees","prerequisites":["decision-trees-and-ensembles","linear-regression"],"leadsTo":["gradient-boosting","generalized-additive-models"]},{"id":"theorempath:cuda-programming-fundamentals","site":"theorempath","slug":"cuda-programming-fundamentals","title":"CUDA Programming Fundamentals","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/cuda-programming-fundamentals","prerequisites":["gpu-compute-model"],"leadsTo":["nvidia-gpu-architectures","fused-kernels","flash-attention"]},{"id":"theorempath:curriculum-learning","site":"theorempath","slug":"curriculum-learning","title":"Curriculum Learning","layer":"2","tier":3,"module":"training-techniques","url":"https://theorempath.com/topics/curriculum-learning","prerequisites":["synthetic-data-distillation"],"leadsTo":[]},{"id":"theorempath:cv-for-intelligence-imagery","site":"theorempath","slug":"cv-for-intelligence-imagery","title":"Computer Vision for Intelligence Imagery","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/cv-for-intelligence-imagery","prerequisites":["hough-transform-and-circle-detection"],"leadsTo":[]},{"id":"theorempath:dask-parallel-python","site":"theorempath","slug":"dask-parallel-python","title":"Dask Parallel Python","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/dask-parallel-python","prerequisites":[],"leadsTo":["parallel-processing-fundamentals","distributed-training-theory"]},{"id":"theorempath:data-augmentation-theory","site":"theorempath","slug":"data-augmentation-theory","title":"Data Augmentation Theory","layer":"2","tier":2,"module":"training-techniques","url":"https://theorempath.com/topics/data-augmentation-theory","prerequisites":["contrastive-learning","regularization-in-practice","self-supervised-vision","synthetic-data-generation"],"leadsTo":[]},{"id":"theorempath:data-contamination-and-evaluation","site":"theorempath","slug":"data-contamination-and-evaluation","title":"Data Contamination and Evaluation","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/data-contamination-and-evaluation","prerequisites":["hypothesis-testing-for-ml","benchmarking-methodology","model-collapse-and-data-quality","synthetic-data-generation"],"leadsTo":["hallucination-theory","scaling-laws"]},{"id":"theorempath:data-preprocessing-and-feature-engineering","site":"theorempath","slug":"data-preprocessing-and-feature-engineering","title":"Data Preprocessing and Feature Engineering","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/data-preprocessing-and-feature-engineering","prerequisites":["common-probability-distributions","linear-regression"],"leadsTo":["linear-regression","logistic-regression"]},{"id":"theorempath:ddpg","site":"theorempath","slug":"ddpg","title":"DDPG: Deep Deterministic Policy Gradient","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/ddpg","prerequisites":["policy-gradient-theorem","q-learning","actor-critic-methods"],"leadsTo":["td3","policy-optimization-ppo-trpo"]},{"id":"theorempath:de-moivre-laplace-theorem","site":"theorempath","slug":"de-moivre-laplace-theorem","title":"De Moivre-Laplace Theorem","layer":"1","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/de-moivre-laplace-theorem","prerequisites":["common-probability-distributions","central-limit-theorem","moment-generating-functions"],"leadsTo":["central-limit-theorem","poisson-limit-theorem","characteristic-functions"]},{"id":"theorempath:decision-theory-foundations","site":"theorempath","slug":"decision-theory-foundations","title":"Decision Theory Foundations","layer":"2","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/decision-theory-foundations","prerequisites":["common-probability-distributions","bayesian-estimation","causal-inference-pearl"],"leadsTo":["expected-utility","game-theory","bounded-rationality","leverage-points-systems"]},{"id":"theorempath:decision-trees-and-ensembles","site":"theorempath","slug":"decision-trees-and-ensembles","title":"Decision Trees and Ensembles","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/decision-trees-and-ensembles","prerequisites":["empirical-risk-minimization","bias-variance-tradeoff","knn"],"leadsTo":["feedforward-networks-and-backpropagation","aic-and-bic","adaboost","bagging","cubist-and-model-trees","feature-importance-and-interpretability","gradient-boosting","random-forests"]},{"id":"theorempath:decoding-strategies","site":"theorempath","slug":"decoding-strategies","title":"Decoding Strategies","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/decoding-strategies","prerequisites":["softmax-and-numerical-stability"],"leadsTo":["chain-of-thought-and-reasoning","calibration-and-uncertainty"]},{"id":"theorempath:deep-generative-models-for-cosmic-structures","site":"theorempath","slug":"deep-generative-models-for-cosmic-structures","title":"Deep Generative Models for Cosmic Structures","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/deep-generative-models-for-cosmic-structures","prerequisites":["generative-adversarial-networks","normalization-flows"],"leadsTo":["diffusion-models","score-matching"]},{"id":"theorempath:deep-generative-models-for-molecules","site":"theorempath","slug":"deep-generative-models-for-molecules","title":"Deep Generative Models for Molecules","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/deep-generative-models-for-molecules","prerequisites":["variational-autoencoders","diffusion-models"],"leadsTo":["score-matching"]},{"id":"theorempath:deep-learning-goodfellow-book","site":"theorempath","slug":"deep-learning-goodfellow-book","title":"Deep Learning (Goodfellow, Bengio, Courville)","layer":"0B","tier":1,"module":"foundations","url":"https://theorempath.com/topics/deep-learning-goodfellow-book","prerequisites":[],"leadsTo":["feedforward-networks-and-backpropagation","transformer-architecture"]},{"id":"theorempath:deep-learning-time-series","site":"theorempath","slug":"deep-learning-time-series","title":"Deep Learning for Time Series","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/deep-learning-time-series","prerequisites":["time-series-foundations","state-space-models","recurrent-neural-networks","transformer-architecture"],"leadsTo":["time-series-forecasting-basics","mamba-and-state-space-models"]},{"id":"theorempath:deep-rl-for-control","site":"theorempath","slug":"deep-rl-for-control","title":"Deep RL for Control","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/deep-rl-for-control","prerequisites":["actor-critic-methods","policy-gradient-theorem"],"leadsTo":["model-based-rl","reinforcement-learning-environments-and-benchmarks"]},{"id":"theorempath:deeponet","site":"theorempath","slug":"deeponet","title":"DeepONet","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/deeponet","prerequisites":["spectral-theory-of-operators","navier-stokes-for-ml","fourier-neural-operator"],"leadsTo":["fourier-neural-operator","physics-informed-neural-networks","navier-stokes-for-ml"]},{"id":"theorempath:deepseek-models","site":"theorempath","slug":"deepseek-models","title":"DeepSeek Models","layer":"5","tier":1,"module":"model-timeline","url":"https://theorempath.com/topics/deepseek-models","prerequisites":["transformer-architecture","mixture-of-experts"],"leadsTo":["model-comparison-table"]},{"id":"theorempath:delta-method","site":"theorempath","slug":"delta-method","title":"Delta Method","layer":"1","tier":1,"module":"statistics","url":"https://theorempath.com/topics/delta-method","prerequisites":["central-limit-theorem","modes-of-convergence-random-variables","expectation-variance-covariance-moments","asymptotic-statistics"],"leadsTo":["variance-stabilizing-transformations","maximum-likelihood-estimation","method-of-moments","bootstrap-methods"]},{"id":"theorempath:design-based-vs-model-based-inference","site":"theorempath","slug":"design-based-vs-model-based-inference","title":"Design-Based vs. Model-Based Inference","layer":"2","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/design-based-vs-model-based-inference","prerequisites":["survey-sampling-methods","causal-inference-for-policy-evaluation","official-statistics-and-national-surveys"],"leadsTo":["small-area-estimation","nonresponse-and-missing-data","greg-estimator"]},{"id":"theorempath:detection-theory","site":"theorempath","slug":"detection-theory","title":"Detection Theory","layer":"2","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/detection-theory","prerequisites":["hypothesis-testing-for-ml","bayesian-estimation"],"leadsTo":[]},{"id":"theorempath:differential-privacy","site":"theorempath","slug":"differential-privacy","title":"Differential Privacy","layer":"3","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/differential-privacy","prerequisites":["common-probability-distributions","federated-learning"],"leadsTo":["federated-learning","hypothesis-testing-for-ml","number-theory-and-ml"]},{"id":"theorempath:differentiation-in-rn","site":"theorempath","slug":"differentiation-in-rn","title":"Differentiation in Rⁿ","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/differentiation-in-rn","prerequisites":["sets-functions-and-relations","vectors-matrices-and-linear-maps","continuity-in-rn"],"leadsTo":["the-jacobian-matrix","vector-calculus-chain-rule","taylor-expansion","the-hessian-matrix","automatic-differentiation","activation-functions","convex-optimization-basics","feedforward-networks-and-backpropagation","gradient-descent-variants","line-search-methods","maximum-likelihood-estimation"]},{"id":"theorempath:diffusion-models","site":"theorempath","slug":"diffusion-models","title":"Diffusion Models","layer":"4","tier":1,"module":"beyond-llms","url":"https://theorempath.com/topics/diffusion-models","prerequisites":["variational-autoencoders","score-matching","boltzmann-machines-and-hopfield-networks","clip-and-openclip-in-practice","continuous-normalizing-flows","contrastive-learning","deep-generative-models-for-cosmic-structures","energy-based-models","expectation-maximization-variants","fokker-planck-equation","ito-lemma","langevin-dynamics","neural-sdes","normalization-flows","pde-fundamentals-for-ml","probability-flow-ode","stochastic-calculus-for-ml","time-reversal-of-sdes","vision-transformer-lineage"],"leadsTo":["flow-matching","score-matching","video-world-models","gaussian-splatting","deep-generative-models-for-molecules"]},{"id":"theorempath:dimensionality-reduction-theory","site":"theorempath","slug":"dimensionality-reduction-theory","title":"Dimensionality Reduction Theory","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/dimensionality-reduction-theory","prerequisites":["principal-component-analysis","eigenvalues-and-eigenvectors","measure-concentration-and-geometric-fa"],"leadsTo":["kernels-and-rkhs","autoencoders"]},{"id":"theorempath:discrete-continuous-distribution-pairs","site":"theorempath","slug":"discrete-continuous-distribution-pairs","title":"Discrete and Continuous Distribution Pairs","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/discrete-continuous-distribution-pairs","prerequisites":["common-probability-distributions","random-variables"],"leadsTo":["central-limit-theorem","law-of-large-numbers","method-of-moments"]},{"id":"theorempath:distance-metrics-compared","site":"theorempath","slug":"distance-metrics-compared","title":"Distance Metrics Compared","layer":"1","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/distance-metrics-compared","prerequisites":["metric-spaces-convergence-completeness","non-euclidean-and-hyperbolic-geometry"],"leadsTo":["wasserstein-distances","kl-divergence","gram-matrices-and-kernel-matrices","non-euclidean-and-hyperbolic-geometry","fuzzy-matching-and-record-linkage"]},{"id":"theorempath:distributed-consensus","site":"theorempath","slug":"distributed-consensus","title":"Distributed Consensus","layer":"3","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/distributed-consensus","prerequisites":["basic-logic-and-proof-techniques","kafka-streaming-platform"],"leadsTo":["cap-theorem"]},{"id":"theorempath:distributed-training-theory","site":"theorempath","slug":"distributed-training-theory","title":"Distributed Training Theory","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/distributed-training-theory","prerequisites":["optimizer-theory-sgd-adam-muon","parallel-processing-fundamentals","batch-size-and-learning-dynamics","broadcast-joins-distributed-compute","dask-parallel-python","federated-learning","kafka-streaming-platform","ray-distributed-python","running-ml-workloads-on-gpus","tokenization-and-information-theory"],"leadsTo":["mixed-precision-training","scaling-laws","federated-learning"]},{"id":"theorempath:distributional-semantics","site":"theorempath","slug":"distributional-semantics","title":"Distributional Semantics","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/distributional-semantics","prerequisites":["singular-value-decomposition","maximum-likelihood-estimation","nlp-for-economic-text-analysis","syntax-and-parsing"],"leadsTo":["word-embeddings","transformer-architecture"]},{"id":"theorempath:distributions-atlas","site":"theorempath","slug":"distributions-atlas","title":"Distributions Atlas","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/distributions-atlas","prerequisites":["common-probability-distributions","random-variables","moment-generating-functions"],"leadsTo":["normal-distribution","exponential-distribution","gamma-distribution","beta-distribution","poisson-distribution","chi-squared-distribution-and-tests","student-t-distribution-and-t-test","f-distribution-and-anova","bayesian-estimation"]},{"id":"theorempath:divergence-curl-and-line-integrals","site":"theorempath","slug":"divergence-curl-and-line-integrals","title":"Divergence, Curl, and Line Integrals","layer":"0A","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/divergence-curl-and-line-integrals","prerequisites":["the-jacobian-matrix","vector-calculus-chain-rule"],"leadsTo":["pde-fundamentals-for-ml","fokker-planck-equation","physics-informed-neural-networks","navier-stokes-for-ml"]},{"id":"theorempath:docker-and-containers-for-ml","site":"theorempath","slug":"docker-and-containers-for-ml","title":"Docker and Containers for ML","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/docker-and-containers-for-ml","prerequisites":[],"leadsTo":["gpu-compute-model","inference-systems-overview"]},{"id":"theorempath:document-intelligence","site":"theorempath","slug":"document-intelligence","title":"Document Intelligence","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/document-intelligence","prerequisites":["multimodal-rag"],"leadsTo":["donut-and-ocr-free-document-understanding","paddleocr-and-practical-ocr","table-extraction-and-structure-recognition"]},{"id":"theorempath:donut-and-ocr-free-document-understanding","site":"theorempath","slug":"donut-and-ocr-free-document-understanding","title":"Donut and OCR-Free Document Understanding","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/donut-and-ocr-free-document-understanding","prerequisites":["transformer-architecture","document-intelligence","paddleocr-and-practical-ocr"],"leadsTo":[]},{"id":"theorempath:double-debiased-machine-learning","site":"theorempath","slug":"double-debiased-machine-learning","title":"Double/Debiased Machine Learning","layer":"3","tier":1,"module":"causal-semiparametric","url":"https://theorempath.com/topics/double-debiased-machine-learning","prerequisites":["asymptotic-statistics","maximum-likelihood-estimation","cross-validation-theory","causal-inference-basics","central-limit-theorem","weighted-conformal-prediction"],"leadsTo":["weighted-conformal-prediction","causal-inference-pearl","non-probability-sampling"]},{"id":"theorempath:double-descent","site":"theorempath","slug":"double-descent","title":"Double Descent","layer":"4","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/double-descent","prerequisites":["implicit-bias-and-modern-generalization","random-matrix-theory-overview","bias-variance-tradeoff","grokking","lazy-vs-feature-learning","neural-tangent-kernel","ridge-regression"],"leadsTo":["benign-overfitting"]},{"id":"theorempath:dpo-vs-grpo-vs-rl-reasoning","site":"theorempath","slug":"dpo-vs-grpo-vs-rl-reasoning","title":"DPO vs GRPO vs RL for Reasoning","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/dpo-vs-grpo-vs-rl-reasoning","prerequisites":["rlhf-and-alignment","policy-gradient-theorem","actor-critic-methods","chain-of-thought-and-reasoning","policy-optimization-ppo-trpo","post-training-overview","reasoning-data-curation","reinforcement-learning-from-human-feedback-deep-dive","reward-models-and-verifiers"],"leadsTo":["reward-models-and-verifiers","post-training-overview"]},{"id":"theorempath:dropout","site":"theorempath","slug":"dropout","title":"Dropout","layer":"2","tier":1,"module":"training-techniques","url":"https://theorempath.com/topics/dropout","prerequisites":["feedforward-networks-and-backpropagation","common-probability-distributions"],"leadsTo":[]},{"id":"theorempath:dynamic-programming","site":"theorempath","slug":"dynamic-programming","title":"Dynamic Programming","layer":"0A","tier":1,"module":"algorithms-foundations","url":"https://theorempath.com/topics/dynamic-programming","prerequisites":["sets-functions-and-relations","graph-algorithms-essentials","greedy-algorithms"],"leadsTo":["greedy-algorithms","convex-optimization-basics","knapsack-problem"]},{"id":"theorempath:e-values-and-anytime-valid-inference","site":"theorempath","slug":"e-values-and-anytime-valid-inference","title":"E-Values and Anytime-Valid Inference","layer":"3","tier":1,"module":"sequential-inference","url":"https://theorempath.com/topics/e-values-and-anytime-valid-inference","prerequisites":["measure-theoretic-probability","martingale-theory","hypothesis-testing-for-ml","neyman-pearson-and-hypothesis-testing-theory","maximum-likelihood-estimation","tabular-foundation-models-bayesian-inference","weighted-conformal-prediction"],"leadsTo":["split-conformal-prediction","weighted-conformal-prediction"]},{"id":"theorempath:edge-and-on-device-ml","site":"theorempath","slug":"edge-and-on-device-ml","title":"Edge and On-Device ML","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/edge-and-on-device-ml","prerequisites":["speculative-decoding-and-quantization"],"leadsTo":["inference-systems-overview"]},{"id":"theorempath:efficient-transformers-survey","site":"theorempath","slug":"efficient-transformers-survey","title":"Efficient Transformers Survey","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/efficient-transformers-survey","prerequisites":["attention-variants-and-efficiency"],"leadsTo":["mamba-and-state-space-models","kv-cache"]},{"id":"theorempath:eigenvalues-and-eigenvectors","site":"theorempath","slug":"eigenvalues-and-eigenvectors","title":"Eigenvalues and Eigenvectors","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/eigenvalues-and-eigenvectors","prerequisites":["matrix-operations-and-properties","inner-product-spaces-and-orthogonality","linear-independence","matrix-norms","vectors-matrices-and-linear-maps"],"leadsTo":["singular-value-decomposition","principal-component-analysis","conditioning-and-condition-number","dimensionality-reduction-theory","gram-matrices-and-kernel-matrices","graph-neural-networks","kalman-filter","markov-chains-and-steady-state","nmf-nonnegative-matrix-factorization","nonlinear-dynamics-and-chaos-fundamentals","numerical-linear-algebra","open-problems-in-matrix-computation","pagerank-algorithm","pde-fundamentals-for-ml","positive-semidefinite-matrices","quantization-theory","recommender-systems","riemannian-optimization","spectral-clustering","spectral-theory-of-operators","tensors-and-tensor-operations","the-hessian-matrix","weight-initialization","whitening-and-decorrelation"]},{"id":"theorempath:elastic-net","site":"theorempath","slug":"elastic-net","title":"Elastic Net","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/elastic-net","prerequisites":["ridge-regression","lasso-regression"],"leadsTo":["bias-variance-tradeoff","regularization-theory"]},{"id":"theorempath:elements-of-statistical-learning-book","site":"theorempath","slug":"elements-of-statistical-learning-book","title":"The Elements of Statistical Learning (Hastie, Tibshirani, Friedman)","layer":"0B","tier":1,"module":"foundations","url":"https://theorempath.com/topics/elements-of-statistical-learning-book","prerequisites":[],"leadsTo":["linear-regression","ridge-regression","gradient-boosting","bias-variance-tradeoff"]},{"id":"theorempath:em-algorithm","site":"theorempath","slug":"em-algorithm","title":"The EM Algorithm","layer":"2","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/em-algorithm","prerequisites":["maximum-likelihood-estimation","convex-optimization-basics","sufficient-statistics-and-exponential-families","conjugate-priors"],"leadsTo":["expectation-maximization-variants","gaussian-mixture-models-and-em"]},{"id":"theorempath:empirical-bayes-vs-hierarchical-bayes","site":"theorempath","slug":"empirical-bayes-vs-hierarchical-bayes","title":"Empirical Bayes vs Hierarchical Bayes","layer":"2","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/empirical-bayes-vs-hierarchical-bayes","prerequisites":["bayesian-estimation","shrinkage-estimation-james-stein","adjusted-density-maximization","bayesian-linear-regression","conjugate-priors"],"leadsTo":["small-area-estimation","reml-and-variance-component-estimation","prasad-rao-mse-correction"]},{"id":"theorempath:empirical-processes-and-chaining","site":"theorempath","slug":"empirical-processes-and-chaining","title":"Empirical Processes and Chaining","layer":"3","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/empirical-processes-and-chaining","prerequisites":["rademacher-complexity","epsilon-nets-and-covering-numbers","asymptotic-statistics","glivenko-cantelli-theorem","measure-concentration-and-geometric-fa","stochastic-processes-ml"],"leadsTo":["minimax-lower-bounds","matrix-concentration"]},{"id":"theorempath:empirical-risk-minimization","site":"theorempath","slug":"empirical-risk-minimization","title":"Empirical Risk Minimization","layer":"2","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/empirical-risk-minimization","prerequisites":["concentration-inequalities","common-probability-distributions","common-inequalities","high-dimensional-probability-book","law-of-large-numbers","loss-functions-catalog","maximum-likelihood-estimation","robust-statistics-and-m-estimators","sequences-and-series-of-functions","understanding-machine-learning-book"],"leadsTo":["uniform-convergence","vc-dimension","rademacher-complexity","algorithmic-stability","bias-variance-tradeoff","cross-validation-theory","decision-trees-and-ensembles","hallucination-theory","hypothesis-classes-and-function-spaces","overfitting-and-underfitting","realizability-assumption","bias-complexity-tradeoff","no-free-lunch-theorem"]},{"id":"theorempath:energy-based-models","site":"theorempath","slug":"energy-based-models","title":"Energy-Based Models","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/energy-based-models","prerequisites":["maximum-likelihood-estimation","feedforward-networks-and-backpropagation","neural-sdes","normalization-flows","score-matching"],"leadsTo":["diffusion-models","score-matching","variational-autoencoders"]},{"id":"theorempath:energy-efficiency-and-green-ai","site":"theorempath","slug":"energy-efficiency-and-green-ai","title":"Energy Efficiency and Green AI","layer":"5","tier":3,"module":"methodology","url":"https://theorempath.com/topics/energy-efficiency-and-green-ai","prerequisites":[],"leadsTo":[]},{"id":"theorempath:ensemble-methods-theory","site":"theorempath","slug":"ensemble-methods-theory","title":"Ensemble Methods Theory","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/ensemble-methods-theory","prerequisites":["bagging","gradient-boosting"],"leadsTo":["decision-trees-and-ensembles","cross-validation-theory"]},{"id":"theorempath:epsilon-nets-and-covering-numbers","site":"theorempath","slug":"epsilon-nets-and-covering-numbers","title":"Epsilon-Nets and Covering Numbers","layer":"3","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/epsilon-nets-and-covering-numbers","prerequisites":["subgaussian-random-variables","concentration-inequalities","contraction-inequality","subexponential-random-variables","symmetrization-inequality"],"leadsTo":["rademacher-complexity","vc-dimension","empirical-processes-and-chaining","measure-concentration-and-geometric-fa","random-matrix-theory-overview"]},{"id":"theorempath:equilibrium-and-implicit-models","site":"theorempath","slug":"equilibrium-and-implicit-models","title":"Equilibrium and Implicit-Layer Models","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/equilibrium-and-implicit-models","prerequisites":["skip-connections-and-resnets","implicit-differentiation"],"leadsTo":["neural-odes","second-order-optimization-methods","continuous-thought-machines"]},{"id":"theorempath:equivariant-deep-learning","site":"theorempath","slug":"equivariant-deep-learning","title":"Equivariant Deep Learning","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/equivariant-deep-learning","prerequisites":["convolutional-neural-networks","graph-neural-networks","attention-for-protein-structure-alphafold"],"leadsTo":["riemannian-optimization","representation-learning-theory","graph-neural-networks-for-molecules"]},{"id":"theorempath:era-of-experience","site":"theorempath","slug":"era-of-experience","title":"The Era of Experience","layer":"4","tier":1,"module":"methodology","url":"https://theorempath.com/topics/era-of-experience","prerequisites":["bitter-lesson","markov-decision-processes"],"leadsTo":["world-models-and-planning"]},{"id":"theorempath:ethics-and-fairness-in-ml","site":"theorempath","slug":"ethics-and-fairness-in-ml","title":"Ethics and Fairness in ML","layer":"3","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/ethics-and-fairness-in-ml","prerequisites":[],"leadsTo":[]},{"id":"theorempath:evaluation-metrics-and-properties","site":"theorempath","slug":"evaluation-metrics-and-properties","title":"Evaluation Metrics and Properties","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/evaluation-metrics-and-properties","prerequisites":[],"leadsTo":["benchmarking-methodology","cross-validation-theory","hypothesis-testing-for-ml","proper-scoring-rules"]},{"id":"theorempath:expectation-maximization-variants","site":"theorempath","slug":"expectation-maximization-variants","title":"EM Algorithm Variants","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/expectation-maximization-variants","prerequisites":["em-algorithm"],"leadsTo":["diffusion-models","autoencoders"]},{"id":"theorempath:expectation-variance-covariance-moments","site":"theorempath","slug":"expectation-variance-covariance-moments","title":"Expectation, Variance, Covariance, and Moments","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/expectation-variance-covariance-moments","prerequisites":["random-variables","common-probability-distributions","joint-marginal-conditional-distributions","triangular-distribution"],"leadsTo":["joint-marginal-conditional-distributions","moment-generating-functions","concentration-inequalities","batch-normalization","bellman-equations","bernstein-inequality","bias-variance-tradeoff","central-limit-theorem","fat-tails","law-of-large-numbers","monte-carlo-methods","non-probability-sampling","prasad-rao-mse-correction","reml-and-variance-component-estimation","score-matching","skewness-kurtosis-and-higher-moments","state-space-models","stochastic-processes-ml","survey-sampling-methods","time-series-foundations","bennetts-inequality","hoeffdings-lemma","loss-functions","multivariate-normal-distribution"]},{"id":"theorempath:expected-utility","site":"theorempath","slug":"expected-utility","title":"Expected Utility Theory","layer":"2","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/expected-utility","prerequisites":["common-probability-distributions","convex-optimization-basics","bounded-rationality","decision-theory-foundations"],"leadsTo":["kelly-criterion","game-theory","prospect-theory"]},{"id":"theorempath:experiment-tracking-and-tooling","site":"theorempath","slug":"experiment-tracking-and-tooling","title":"Experiment Tracking and Tooling","layer":"2","tier":3,"module":"methodology","url":"https://theorempath.com/topics/experiment-tracking-and-tooling","prerequisites":["reproducibility-and-experimental-rigor","hardware-for-ml-practitioners","ml-project-lifecycle","weights-and-biases-experiment-tracking"],"leadsTo":["ablation-study-design"]},{"id":"theorempath:exploration-vs-exploitation","site":"theorempath","slug":"exploration-vs-exploitation","title":"Exploration vs Exploitation","layer":"2","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/exploration-vs-exploitation","prerequisites":["multi-armed-bandits-theory","markov-decision-processes","bitter-lesson","reinforcement-learning-for-drug-discovery"],"leadsTo":["q-learning","policy-gradient-theorem","td-learning"]},{"id":"theorempath:exploratory-data-analysis","site":"theorempath","slug":"exploratory-data-analysis","title":"Exploratory Data Analysis","layer":"1","tier":2,"module":"methodology","url":"https://theorempath.com/topics/exploratory-data-analysis","prerequisites":["ml-project-lifecycle","pandas-and-numpy-fundamentals","train-test-split-and-data-leakage"],"leadsTo":["train-test-split-and-data-leakage","feature-importance-and-interpretability"]},{"id":"theorempath:exponential-distribution","site":"theorempath","slug":"exponential-distribution","title":"Exponential Distribution","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/exponential-distribution","prerequisites":["common-probability-distributions","distributions-atlas","exponential-function-properties"],"leadsTo":["gamma-distribution","poisson-distribution","chi-squared-distribution-and-tests","survival-analysis","maximum-likelihood-estimation"]},{"id":"theorempath:exponential-function-properties","site":"theorempath","slug":"exponential-function-properties","title":"Exponential Function Properties","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/exponential-function-properties","prerequisites":[],"leadsTo":["moment-generating-functions","common-probability-distributions","maximum-likelihood-estimation","fast-fourier-transform"]},{"id":"theorempath:extreme-value-theory","site":"theorempath","slug":"extreme-value-theory","title":"Extreme Value Theory","layer":"3","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/extreme-value-theory","prerequisites":["common-probability-distributions","order-statistics","fat-tails"],"leadsTo":[]},{"id":"theorempath:f-distribution-and-anova","site":"theorempath","slug":"f-distribution-and-anova","title":"F-Distribution and ANOVA","layer":"1","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/f-distribution-and-anova","prerequisites":["distributions-atlas","chi-squared-distribution-and-tests","hypothesis-testing-for-ml","student-t-distribution-and-t-test"],"leadsTo":["linear-regression","permutation-tests","likelihood-ratio-wald-score-tests"]},{"id":"theorempath:fanos-inequality","site":"theorempath","slug":"fanos-inequality","title":"Fano Inequality","layer":"3","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/fanos-inequality","prerequisites":["minimax-lower-bounds","information-theory-foundations"],"leadsTo":[]},{"id":"theorempath:fast-fourier-transform","site":"theorempath","slug":"fast-fourier-transform","title":"Fast Fourier Transform","layer":"1","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/fast-fourier-transform","prerequisites":["exponential-function-properties","complex-numbers-for-fourier"],"leadsTo":["attention-variants-and-efficiency","convolutional-neural-networks","fourier-neural-operator","pde-fundamentals-for-ml"]},{"id":"theorempath:fat-tails","site":"theorempath","slug":"fat-tails","title":"Fat Tails and Heavy-Tailed Distributions","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/fat-tails","prerequisites":["common-probability-distributions","expectation-variance-covariance-moments","law-of-large-numbers","characteristic-functions","convex-tinkering","editorial-principles","kelly-criterion"],"leadsTo":["extreme-value-theory","subexponential-random-variables"]},{"id":"theorempath:feature-importance-and-interpretability","site":"theorempath","slug":"feature-importance-and-interpretability","title":"Feature Importance and Interpretability","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/feature-importance-and-interpretability","prerequisites":["decision-trees-and-ensembles","linear-regression","exploratory-data-analysis","mechanistic-interpretability","sparse-autoencoders"],"leadsTo":["causal-inference-basics","mechanistic-interpretability","cross-validation-theory"]},{"id":"theorempath:federated-learning","site":"theorempath","slug":"federated-learning","title":"Federated Learning","layer":"3","tier":2,"module":"methodology","url":"https://theorempath.com/topics/federated-learning","prerequisites":["optimizer-theory-sgd-adam-muon"],"leadsTo":["differential-privacy","distributed-training-theory"]},{"id":"theorempath:feedforward-networks-and-backpropagation","site":"theorempath","slug":"feedforward-networks-and-backpropagation","title":"Feedforward Networks and Backpropagation","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/feedforward-networks-and-backpropagation","prerequisites":["differentiation-in-rn","matrix-calculus","activation-functions","automatic-differentiation","decision-trees-and-ensembles","deep-learning-goodfellow-book","gradient-boosting","mars-multivariate-adaptive-regression-splines","perceptron","tensors-and-tensor-operations","vector-calculus-chain-rule"],"leadsTo":["convolutional-neural-networks","recurrent-neural-networks","batch-normalization","activation-checkpointing","adversarial-machine-learning","autoencoders","bayesian-neural-networks","contrastive-learning","dropout","energy-based-models","fine-tuning-and-adaptation","generative-adversarial-networks","gradient-flow-and-vanishing-gradients","hebbian-learning","iterative-magnitude-pruning-and-lottery-ticket-hypothesis","knowledge-distillation","kolmogorov-arnold-networks","linear-layer-shapes-memory","meta-learning","mixture-density-networks","model-compression-and-pruning","neural-architecture-search","occupancy-networks-and-neural-fields","optimal-brain-surgery-and-pruning-theory","physics-informed-neural-networks","quantization-theory","skip-connections-and-resnets","spiking-neural-networks","token-prediction-and-language-modeling","transfer-learning","transformer-architecture","universal-approximation-theorem","weight-initialization"]},{"id":"theorempath:feynman-kac-formula","site":"theorempath","slug":"feynman-kac-formula","title":"Feynman–Kac Formula","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/feynman-kac-formula","prerequisites":["stochastic-differential-equations","ito-lemma"],"leadsTo":["deep-bsde-method","backward-sde-theory","fokker-planck-equation","hamilton-jacobi-bellman-equation"]},{"id":"theorempath:fine-tuning-and-adaptation","site":"theorempath","slug":"fine-tuning-and-adaptation","title":"Fine-Tuning and Adaptation","layer":"3","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/fine-tuning-and-adaptation","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["rlhf-and-alignment","catastrophic-forgetting","llama-and-open-weight-models"]},{"id":"theorempath:fisher-information","site":"theorempath","slug":"fisher-information","title":"Fisher Information: Curvature, KL Geometry, and the Natural Gradient","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/fisher-information","prerequisites":["maximum-likelihood-estimation","kl-divergence","basu-theorem","positive-semidefinite-matrices","sufficient-statistics-and-exponential-families"],"leadsTo":["cramer-rao-bound","asymptotic-statistics","hypothesis-testing-for-ml","minimax-lower-bounds","information-geometry","preconditioned-optimizers","score-matching"]},{"id":"theorempath:flash-attention","site":"theorempath","slug":"flash-attention","title":"Flash Attention","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/flash-attention","prerequisites":["attention-mechanism-theory","softmax-and-numerical-stability","attention-is-all-you-need-paper","computer-architecture-for-ml","cuda-programming-fundamentals","gpu-compute-model","nvidia-gpu-architectures"],"leadsTo":["fused-kernels"]},{"id":"theorempath:floating-point-arithmetic","site":"theorempath","slug":"floating-point-arithmetic","title":"Floating-Point Arithmetic","layer":"0A","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/floating-point-arithmetic","prerequisites":[],"leadsTo":["whitening-and-decorrelation","computer-architecture-for-ml","mixed-precision-training","numerical-stability"]},{"id":"theorempath:florence-and-vision-foundation-models","site":"theorempath","slug":"florence-and-vision-foundation-models","title":"Florence and Vision Foundation Models","layer":"5","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/florence-and-vision-foundation-models","prerequisites":["vision-transformer-lineage","self-supervised-vision"],"leadsTo":["clip-and-openclip-in-practice"]},{"id":"theorempath:flow-matching","site":"theorempath","slug":"flow-matching","title":"Flow Matching","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/flow-matching","prerequisites":["diffusion-models","ito-lemma","pde-fundamentals-for-ml"],"leadsTo":[]},{"id":"theorempath:fokker-planck-equation","site":"theorempath","slug":"fokker-planck-equation","title":"Fokker–Planck Equation","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/fokker-planck-equation","prerequisites":["stochastic-differential-equations","pde-fundamentals-for-ml","divergence-curl-and-line-integrals","feynman-kac-formula"],"leadsTo":["langevin-dynamics","diffusion-models","score-matching","probability-flow-ode","sgd-as-sde","time-reversal-of-sdes"]},{"id":"theorempath:foundational-dependencies","site":"theorempath","slug":"foundational-dependencies","title":"Foundational Dependencies","layer":"0A","tier":3,"module":"foundations","url":"https://theorempath.com/topics/foundational-dependencies","prerequisites":["zermelo-fraenkel-set-theory","peano-axioms"],"leadsTo":[]},{"id":"theorempath:fourier-neural-operator","site":"theorempath","slug":"fourier-neural-operator","title":"Fourier Neural Operator","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/fourier-neural-operator","prerequisites":["fast-fourier-transform","navier-stokes-for-ml","spectral-theory-of-operators","complex-numbers-for-fourier"],"leadsTo":["deeponet","navier-stokes-for-ml","physics-informed-neural-networks","spectral-theory-of-operators","pde-fundamentals-for-ml"]},{"id":"theorempath:fox-forget-gate","site":"theorempath","slug":"fox-forget-gate","title":"Forgetting Transformer (FoX)","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/fox-forget-gate","prerequisites":["attention-mechanism-theory","recurrent-neural-networks","transformer-architecture","attention-variants-and-efficiency","sparse-attention-and-long-context"],"leadsTo":["attention-sinks-and-retrieval-decay","residual-stream-and-transformer-internals"]},{"id":"theorempath:functional-analysis-core","site":"theorempath","slug":"functional-analysis-core","title":"Functional Analysis Core","layer":"0B","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/functional-analysis-core","prerequisites":["metric-spaces-convergence-completeness","inner-product-spaces-and-orthogonality","measure-theoretic-probability"],"leadsTo":["kernels-and-rkhs","spectral-theory-of-operators","pde-fundamentals-for-ml"]},{"id":"theorempath:fused-kernels","site":"theorempath","slug":"fused-kernels","title":"Fused Kernels","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/fused-kernels","prerequisites":["gpu-compute-model","cuda-programming-fundamentals","flash-attention","nvidia-gpu-architectures","webgpu-for-ml"],"leadsTo":["megakernels"]},{"id":"theorempath:game-theory","site":"theorempath","slug":"game-theory","title":"Game Theory Foundations","layer":"2","tier":1,"module":"decision-theory","url":"https://theorempath.com/topics/game-theory","prerequisites":["common-probability-distributions","convex-optimization-basics","arrows-impossibility","bounded-rationality","decision-theory-foundations","expected-utility"],"leadsTo":["nash-equilibrium","mechanism-design","minimax-theorem","auction-theory","commons-governance-ostrom","stable-matching-and-deferred-acceptance"]},{"id":"theorempath:gamma-distribution","site":"theorempath","slug":"gamma-distribution","title":"Gamma Distribution","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/gamma-distribution","prerequisites":["common-probability-distributions","distributions-atlas","exponential-distribution","exponential-function-properties"],"leadsTo":["chi-squared-distribution-and-tests","beta-distribution","bayesian-estimation","poisson-distribution"]},{"id":"theorempath:gauss-markov-theorem","site":"theorempath","slug":"gauss-markov-theorem","title":"Gauss-Markov Theorem","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/gauss-markov-theorem","prerequisites":["linear-regression","multivariate-normal-distribution"],"leadsTo":["aic-and-bic","ridge-regression"]},{"id":"theorempath:gaussian-mixture-models-and-em","site":"theorempath","slug":"gaussian-mixture-models-and-em","title":"Gaussian Mixture Models and EM","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/gaussian-mixture-models-and-em","prerequisites":["k-means-clustering","em-algorithm","maximum-likelihood-estimation"],"leadsTo":["variational-autoencoders","mixture-density-networks"]},{"id":"theorempath:gaussian-processes-for-ml","site":"theorempath","slug":"gaussian-processes-for-ml","title":"Gaussian Processes for Machine Learning","layer":"4","tier":3,"module":"modern-generalization","url":"https://theorempath.com/topics/gaussian-processes-for-ml","prerequisites":["kernels-and-rkhs","joint-marginal-conditional-distributions","ridge-regression","gram-matrices-and-kernel-matrices","bayesian-estimation","bayesian-linear-regression","conjugate-priors","kernel-trick","multivariate-normal-distribution","time-series-forecasting-basics"],"leadsTo":["bayesian-optimization-for-hyperparameters","neural-tangent-kernel","bayesian-neural-networks","gaussian-processes-in-astronomy","kernel-methods-for-molecules","gaussian-processes-regression"]},{"id":"theorempath:gaussian-processes-in-astronomy","site":"theorempath","slug":"gaussian-processes-in-astronomy","title":"Gaussian Processes in Astronomy","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/gaussian-processes-in-astronomy","prerequisites":["gaussian-processes-for-ml","gaussian-processes-regression"],"leadsTo":["bayesian-state-estimation","time-series-forecasting-basics"]},{"id":"theorempath:gaussian-processes-regression","site":"theorempath","slug":"gaussian-processes-regression","title":"Gaussian Process Regression","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/gaussian-processes-regression","prerequisites":["kernels-and-rkhs","joint-marginal-conditional-distributions","ridge-regression","gram-matrices-and-kernel-matrices","gaussian-processes-for-ml","bayesian-linear-regression","kernel-methods-for-molecules","kernel-trick"],"leadsTo":["neural-tangent-kernel","cross-validation-theory","bayesian-optimization-for-hyperparameters","gaussian-processes-in-astronomy"]},{"id":"theorempath:gaussian-splatting","site":"theorempath","slug":"gaussian-splatting","title":"3D Gaussian Splatting","layer":"4","tier":3,"module":"beyond-llms","url":"https://theorempath.com/topics/gaussian-splatting","prerequisites":["occupancy-networks-and-neural-fields","positive-semidefinite-matrices","diffusion-models","webgpu-for-ml"],"leadsTo":["webgpu-for-ml","graphslam-and-factor-graphs"]},{"id":"theorempath:gemini-and-google-models","site":"theorempath","slug":"gemini-and-google-models","title":"Gemini and Google Models","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/gemini-and-google-models","prerequisites":["transformer-architecture"],"leadsTo":["model-comparison-table","llama-and-open-weight-models","sparse-attention-and-long-context"]},{"id":"theorempath:generalized-additive-models","site":"theorempath","slug":"generalized-additive-models","title":"Generalized Additive Models","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/generalized-additive-models","prerequisites":["linear-regression","mars-multivariate-adaptive-regression-splines"],"leadsTo":["mars-multivariate-adaptive-regression-splines","bias-variance-tradeoff"]},{"id":"theorempath:generative-adversarial-networks","site":"theorempath","slug":"generative-adversarial-networks","title":"Generative Adversarial Networks","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/generative-adversarial-networks","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["deep-generative-models-for-cosmic-structures"]},{"id":"theorempath:gibbs-sampling","site":"theorempath","slug":"gibbs-sampling","title":"Gibbs Sampling","layer":"2","tier":1,"module":"sampling-mcmc","url":"https://theorempath.com/topics/gibbs-sampling","prerequisites":["metropolis-hastings","markov-chain-monte-carlo"],"leadsTo":["burn-in-convergence-diagnostics","hamiltonian-monte-carlo","no-u-turn-sampler-and-neals-funnel","griddy-gibbs","mcmc-for-markov-random-fields","perfect-sampling"]},{"id":"theorempath:git-and-gitlab-for-ml-research","site":"theorempath","slug":"git-and-gitlab-for-ml-research","title":"Git and GitLab for ML Research","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/git-and-gitlab-for-ml-research","prerequisites":[],"leadsTo":["reproducibility-and-experimental-rigor"]},{"id":"theorempath:glivenko-cantelli-theorem","site":"theorempath","slug":"glivenko-cantelli-theorem","title":"Glivenko-Cantelli Theorem","layer":"2","tier":2,"module":"learning-theory-core","url":"https://theorempath.com/topics/glivenko-cantelli-theorem","prerequisites":["concentration-inequalities","uniform-convergence","vc-dimension","pac-learning-framework"],"leadsTo":["empirical-processes-and-chaining","rademacher-complexity"]},{"id":"theorempath:goodness-of-fit-tests","site":"theorempath","slug":"goodness-of-fit-tests","title":"Goodness-of-Fit Tests","layer":"1","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/goodness-of-fit-tests","prerequisites":["common-probability-distributions","benfords-law","hypothesis-testing-for-ml"],"leadsTo":["neyman-pearson-and-hypothesis-testing-theory","calibration-and-uncertainty"]},{"id":"theorempath:gpt-series-evolution","site":"theorempath","slug":"gpt-series-evolution","title":"GPT Series Evolution","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/gpt-series-evolution","prerequisites":["transformer-architecture","attention-mechanism-theory","scaling-laws","bert-and-pretrain-finetune-paradigm","tokenization-and-information-theory","post-training-overview","prompt-engineering-and-in-context-learning","rlhf-and-alignment"],"leadsTo":["llama-and-open-weight-models","post-training-overview"]},{"id":"theorempath:gpu-compute-model","site":"theorempath","slug":"gpu-compute-model","title":"GPU Compute Model","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/gpu-compute-model","prerequisites":["asml-and-chip-manufacturing","docker-and-containers-for-ml","kubernetes-for-ml-workloads","modal-serverless-gpu-platform"],"leadsTo":["flash-attention","fused-kernels","amd-competition-landscape","cuda-programming-fundamentals","megakernels","nvidia-gpu-architectures","running-ml-workloads-on-gpus"]},{"id":"theorempath:gradient-boosting","site":"theorempath","slug":"gradient-boosting","title":"Gradient Boosting","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/gradient-boosting","prerequisites":["decision-trees-and-ensembles","gradient-descent-variants","adaboost","cubist-and-model-trees","elements-of-statistical-learning-book"],"leadsTo":["regularization-theory","feedforward-networks-and-backpropagation","ensemble-methods-theory","xgboost"]},{"id":"theorempath:gradient-descent-variants","site":"theorempath","slug":"gradient-descent-variants","title":"Gradient Descent Variants","layer":"1","tier":1,"module":"optimization-function-classes","url":"https://theorempath.com/topics/gradient-descent-variants","prerequisites":["convex-optimization-basics","differentiation-in-rn"],"leadsTo":["learning-rate-scheduling","optimizer-theory-sgd-adam-muon","adam-optimizer","gradient-boosting","implicit-bias-and-modern-generalization","physics-informed-neural-networks","stochastic-gradient-descent-convergence"]},{"id":"theorempath:gradient-flow-and-vanishing-gradients","site":"theorempath","slug":"gradient-flow-and-vanishing-gradients","title":"Gradient Flow and Vanishing Gradients","layer":"2","tier":1,"module":"optimization-function-classes","url":"https://theorempath.com/topics/gradient-flow-and-vanishing-gradients","prerequisites":["feedforward-networks-and-backpropagation","the-jacobian-matrix"],"leadsTo":["batch-normalization","residual-stream-and-transformer-internals","neural-odes"]},{"id":"theorempath:gram-matrices-and-kernel-matrices","site":"theorempath","slug":"gram-matrices-and-kernel-matrices","title":"Gram Matrices and Kernel Matrices","layer":"1","tier":1,"module":"foundations","url":"https://theorempath.com/topics/gram-matrices-and-kernel-matrices","prerequisites":["inner-product-spaces-and-orthogonality","eigenvalues-and-eigenvectors","distance-metrics-compared","matrix-multiplication-algorithms","kernel-trick"],"leadsTo":["kernels-and-rkhs","principal-component-analysis","attention-mechanism-theory","gaussian-processes-for-ml","gaussian-processes-regression"]},{"id":"theorempath:graph-algorithms-essentials","site":"theorempath","slug":"graph-algorithms-essentials","title":"Graph Algorithms Essentials","layer":"0A","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/graph-algorithms-essentials","prerequisites":["sets-functions-and-relations"],"leadsTo":["dynamic-programming","pagerank-algorithm"]},{"id":"theorempath:graph-neural-networks-for-molecules","site":"theorempath","slug":"graph-neural-networks-for-molecules","title":"Graph Neural Networks for Molecules","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/graph-neural-networks-for-molecules","prerequisites":["graph-neural-networks","equivariant-deep-learning"],"leadsTo":["equivariant-deep-learning"]},{"id":"theorempath:graph-neural-networks","site":"theorempath","slug":"graph-neural-networks","title":"Graph Neural Networks","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/graph-neural-networks","prerequisites":["convolutional-neural-networks","eigenvalues-and-eigenvectors","clustering-for-gene-expression","pagerank-algorithm"],"leadsTo":["equivariant-deep-learning","graph-neural-networks-for-molecules"]},{"id":"theorempath:graphslam-and-factor-graphs","site":"theorempath","slug":"graphslam-and-factor-graphs","title":"GraphSLAM and Factor Graphs","layer":"3","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/graphslam-and-factor-graphs","prerequisites":[],"leadsTo":["particle-filters","convex-optimization-basics","active-slam-and-pomdps","visual-semantic-slam"]},{"id":"theorempath:greedy-algorithms","site":"theorempath","slug":"greedy-algorithms","title":"Greedy Algorithms","layer":"0A","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/greedy-algorithms","prerequisites":[],"leadsTo":["dynamic-programming","knapsack-problem","submodular-optimization","tabu-search"]},{"id":"theorempath:greg-estimator","site":"theorempath","slug":"greg-estimator","title":"GREG Estimator","layer":"3","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/greg-estimator","prerequisites":["linear-regression","survey-sampling-methods","design-based-vs-model-based-inference"],"leadsTo":["survey-weight-calibration-and-raking","small-area-estimation","official-statistics-and-national-surveys"]},{"id":"theorempath:griddy-gibbs","site":"theorempath","slug":"griddy-gibbs","title":"Griddy Gibbs Sampling","layer":"2","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/griddy-gibbs","prerequisites":["gibbs-sampling"],"leadsTo":["adaptive-rejection-sampling","hamiltonian-monte-carlo"]},{"id":"theorempath:grokking","site":"theorempath","slug":"grokking","title":"Grokking","layer":"4","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/grokking","prerequisites":["regularization-theory","stochastic-gradient-descent-convergence","implicit-bias-and-modern-generalization","history-of-ai"],"leadsTo":["double-descent","mechanistic-interpretability","open-problems-in-ml-theory"]},{"id":"theorempath:hadoop-and-distributed-storage","site":"theorempath","slug":"hadoop-and-distributed-storage","title":"Hadoop and Distributed Storage","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/hadoop-and-distributed-storage","prerequisites":[],"leadsTo":[]},{"id":"theorempath:hallucination-theory","site":"theorempath","slug":"hallucination-theory","title":"Hallucination Theory","layer":"4","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/hallucination-theory","prerequisites":["empirical-risk-minimization","transformer-architecture","reinforcement-learning-from-human-feedback-deep-dive","agent-protocols-mcp-a2a","chain-of-thought-and-reasoning","context-engineering","data-contamination-and-evaluation","multimodal-rag","out-of-distribution-detection","prompt-engineering-and-in-context-learning","rlhf-and-alignment"],"leadsTo":["rlhf-and-alignment","mechanistic-interpretability","reward-hacking"]},{"id":"theorempath:hamilton-jacobi-bellman-equation","site":"theorempath","slug":"hamilton-jacobi-bellman-equation","title":"Hamilton–Jacobi–Bellman Equation","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/hamilton-jacobi-bellman-equation","prerequisites":["stochastic-differential-equations","feynman-kac-formula"],"leadsTo":["deep-bsde-method","backward-sde-theory","feynman-kac-formula"]},{"id":"theorempath:hamiltonian-monte-carlo","site":"theorempath","slug":"hamiltonian-monte-carlo","title":"Hamiltonian Monte Carlo","layer":"3","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/hamiltonian-monte-carlo","prerequisites":["metropolis-hastings","markov-chain-monte-carlo","gibbs-sampling","griddy-gibbs","variance-reduction-techniques"],"leadsTo":["burn-in-convergence-diagnostics","no-u-turn-sampler-and-neals-funnel","langevin-dynamics"]},{"id":"theorempath:hanson-wright-inequality","site":"theorempath","slug":"hanson-wright-inequality","title":"Hanson-Wright Inequality","layer":"3","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/hanson-wright-inequality","prerequisites":["subgaussian-random-variables","matrix-concentration","chi-squared-concentration"],"leadsTo":["random-matrix-theory-overview","kernels-and-rkhs"]},{"id":"theorempath:hardware-for-ml-practitioners","site":"theorempath","slug":"hardware-for-ml-practitioners","title":"Hardware for ML Practitioners","layer":"1","tier":2,"module":"methodology","url":"https://theorempath.com/topics/hardware-for-ml-practitioners","prerequisites":[],"leadsTo":["ml-project-lifecycle","experiment-tracking-and-tooling"]},{"id":"theorempath:hash-functions","site":"theorempath","slug":"hash-functions","title":"Cryptographic Hash Functions","layer":"2","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/hash-functions","prerequisites":["common-probability-distributions","sets-functions-and-relations"],"leadsTo":["public-key-cryptography"]},{"id":"theorempath:hebbian-learning","site":"theorempath","slug":"hebbian-learning","title":"Hebbian Learning","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/hebbian-learning","prerequisites":["perceptron","feedforward-networks-and-backpropagation","predictive-coding-and-autoencoders-in-the-brain","spiking-neural-networks"],"leadsTo":["spiking-neural-networks","predictive-coding-and-autoencoders-in-the-brain"]},{"id":"theorempath:high-dimensional-covariance-estimation","site":"theorempath","slug":"high-dimensional-covariance-estimation","title":"High-Dimensional Covariance Estimation","layer":"3","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/high-dimensional-covariance-estimation","prerequisites":["matrix-concentration","lasso-regression"],"leadsTo":["principal-component-analysis"]},{"id":"theorempath:high-dimensional-probability-book","site":"theorempath","slug":"high-dimensional-probability-book","title":"High-Dimensional Probability (Vershynin)","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/high-dimensional-probability-book","prerequisites":["cramer-wold-theorem"],"leadsTo":["empirical-risk-minimization"]},{"id":"theorempath:history-of-ai","site":"theorempath","slug":"history-of-ai","title":"History of Artificial Intelligence","layer":"5","tier":2,"module":"ai-history","url":"https://theorempath.com/topics/history-of-ai","prerequisites":[],"leadsTo":["model-timeline","scaling-laws","world-models-and-planning","jepa-and-joint-embedding","grokking"]},{"id":"theorempath:hoeffdings-lemma","site":"theorempath","slug":"hoeffdings-lemma","title":"Hoeffding's Lemma","layer":"1","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/hoeffdings-lemma","prerequisites":["concentration-inequalities","moment-generating-functions","chernoff-bounds","expectation-variance-covariance-moments","basic-logic-and-proof-techniques","sets-functions-and-relations"],"leadsTo":["subgaussian-random-variables","bernstein-inequality","mcdiarmids-inequality"]},{"id":"theorempath:hyperbolic-embeddings-for-graphs","site":"theorempath","slug":"hyperbolic-embeddings-for-graphs","title":"Hyperbolic Embeddings for Graphs","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/hyperbolic-embeddings-for-graphs","prerequisites":["non-euclidean-and-hyperbolic-geometry","metric-spaces-convergence-completeness"],"leadsTo":["riemannian-optimization","representation-learning-theory"]},{"id":"theorempath:hypergeometric-distribution","site":"theorempath","slug":"hypergeometric-distribution","title":"Hypergeometric Distribution","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/hypergeometric-distribution","prerequisites":["common-probability-distributions","distributions-atlas"],"leadsTo":["chi-squared-distribution-and-tests"]},{"id":"theorempath:hypothesis-classes-and-function-spaces","site":"theorempath","slug":"hypothesis-classes-and-function-spaces","title":"Hypothesis Classes and Function Spaces","layer":"2","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/hypothesis-classes-and-function-spaces","prerequisites":["empirical-risk-minimization"],"leadsTo":["vc-dimension","rademacher-complexity","pac-learning-framework","realizability-assumption","loss-functions"]},{"id":"theorempath:hypothesis-testing-for-ml","site":"theorempath","slug":"hypothesis-testing-for-ml","title":"Hypothesis Testing for ML","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/hypothesis-testing-for-ml","prerequisites":["benfords-law","confusion-matrix-deep-dive","differential-privacy","evaluation-metrics-and-properties","fisher-information","maximum-likelihood-estimation","method-of-moments","neyman-pearson-and-hypothesis-testing-theory","reproducibility-and-experimental-rigor","robust-statistics-and-m-estimators","sufficient-statistics-and-exponential-families","survival-analysis"],"leadsTo":["statistical-significance-and-multiple-comparisons","goodness-of-fit-tests","ablation-study-design","causal-inference-basics","causal-inference-for-policy-evaluation","data-contamination-and-evaluation","detection-theory","e-values-and-anytime-valid-inference","meta-analysis","p-hacking-and-multiple-testing","sample-size-determination","signal-detection-theory","split-conformal-prediction"]},{"id":"theorempath:implicit-bias-and-modern-generalization","site":"theorempath","slug":"implicit-bias-and-modern-generalization","title":"Implicit Bias and Modern Generalization","layer":"4","tier":1,"module":"modern-generalization","url":"https://theorempath.com/topics/implicit-bias-and-modern-generalization","prerequisites":["gradient-descent-variants","linear-regression","vc-dimension","rademacher-complexity","algorithmic-stability","bias-variance-tradeoff","information-bottleneck","kernels-and-rkhs","neural-network-optimization-landscape","pac-bayes-bounds","random-matrix-theory-overview","sgd-as-sde","stability-and-optimization-dynamics","training-dynamics-and-loss-landscapes"],"leadsTo":["double-descent","benign-overfitting","neural-tangent-kernel","grokking","open-problems-in-ml-theory"]},{"id":"theorempath:implicit-differentiation","site":"theorempath","slug":"implicit-differentiation","title":"Implicit Differentiation","layer":"2","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/implicit-differentiation","prerequisites":["the-jacobian-matrix","automatic-differentiation"],"leadsTo":["equilibrium-and-implicit-models"]},{"id":"theorempath:importance-sampling","site":"theorempath","slug":"importance-sampling","title":"Importance Sampling","layer":"2","tier":1,"module":"sampling-mcmc","url":"https://theorempath.com/topics/importance-sampling","prerequisites":["common-probability-distributions","monte-carlo-methods","number-theory-and-ml","radon-nikodym-and-conditional-expectation","rejection-sampling","squeezed-rejection-sampling"],"leadsTo":["variance-reduction-techniques","rao-blackwellization","particle-filters","weighted-conformal-prediction"]},{"id":"theorempath:induction-heads","site":"theorempath","slug":"induction-heads","title":"Induction Heads","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/induction-heads","prerequisites":["attention-mechanism-theory","transformer-architecture","mechanistic-interpretability","residual-stream-and-transformer-internals","sparse-autoencoders"],"leadsTo":["mechanistic-interpretability","residual-stream-and-transformer-internals"]},{"id":"theorempath:ineffable-intelligence","site":"theorempath","slug":"ineffable-intelligence","title":"Ineffable Intelligence","layer":"4","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/ineffable-intelligence","prerequisites":["reinforcement-learning-from-human-feedback-deep-dive","ai-labs-landscape"],"leadsTo":["alphaproof-and-ai-theorem-proving","scaling-laws"]},{"id":"theorempath:inference-systems-overview","site":"theorempath","slug":"inference-systems-overview","title":"Inference Systems Overview","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/inference-systems-overview","prerequisites":["kv-cache","speculative-decoding-and-quantization","docker-and-containers-for-ml","edge-and-on-device-ml","kubernetes-for-ml-workloads","megakernels","model-compression-and-pruning"],"leadsTo":["scaling-laws","context-engineering"]},{"id":"theorempath:inference-time-scaling-laws","site":"theorempath","slug":"inference-time-scaling-laws","title":"Inference-Time Scaling Laws","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/inference-time-scaling-laws","prerequisites":["scaling-laws","test-time-compute-and-search"],"leadsTo":[]},{"id":"theorempath:information-bottleneck","site":"theorempath","slug":"information-bottleneck","title":"Information Bottleneck","layer":"3","tier":3,"module":"modern-generalization","url":"https://theorempath.com/topics/information-bottleneck","prerequisites":["information-theory-foundations"],"leadsTo":["implicit-bias-and-modern-generalization"]},{"id":"theorempath:information-geometry","site":"theorempath","slug":"information-geometry","title":"Information Geometry","layer":"3","tier":3,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/information-geometry","prerequisites":["fisher-information","convex-duality","non-euclidean-and-hyperbolic-geometry","whitening-and-decorrelation"],"leadsTo":["optimizer-theory-sgd-adam-muon","mean-field-theory"]},{"id":"theorempath:information-retrieval","site":"theorempath","slug":"information-retrieval","title":"Information Retrieval Foundations","layer":"2","tier":1,"module":"algorithms-foundations","url":"https://theorempath.com/topics/information-retrieval","prerequisites":["common-probability-distributions","basic-logic-and-proof-techniques","fuzzy-matching-and-record-linkage"],"leadsTo":["word-embeddings","cohere-models","semantic-search-and-embeddings"]},{"id":"theorempath:information-theory-foundations","site":"theorempath","slug":"information-theory-foundations","title":"Information Theory Foundations","layer":"0B","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/information-theory-foundations","prerequisites":[],"leadsTo":["variational-autoencoders","fanos-inequality","maximum-likelihood-estimation","bits-nats-perplexity-bpb","clip-and-openclip-in-practice","cross-entropy-loss-deep-dive","information-bottleneck","kelly-criterion","kl-divergence","perplexity-and-language-model-evaluation","representation-learning-theory","token-prediction-and-language-modeling","tokenization-and-information-theory"]},{"id":"theorempath:inner-product-spaces-and-orthogonality","site":"theorempath","slug":"inner-product-spaces-and-orthogonality","title":"Inner Product Spaces and Orthogonality","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/inner-product-spaces-and-orthogonality","prerequisites":["vectors-matrices-and-linear-maps"],"leadsTo":["eigenvalues-and-eigenvectors","functional-analysis-core","gram-matrices-and-kernel-matrices","random-matrix-theory-overview","semantic-search-and-embeddings"]},{"id":"theorempath:integration-and-change-of-variables","site":"theorempath","slug":"integration-and-change-of-variables","title":"Integration and Change of Variables","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/integration-and-change-of-variables","prerequisites":[],"leadsTo":["common-probability-distributions","measure-theoretic-probability"]},{"id":"theorempath:interior-point-methods","site":"theorempath","slug":"interior-point-methods","title":"Interior Point Methods","layer":"3","tier":3,"module":"numerical-optimization","url":"https://theorempath.com/topics/interior-point-methods","prerequisites":["convex-optimization-basics","newtons-method","augmented-lagrangian-and-admm","trust-region-methods"],"leadsTo":[]},{"id":"theorempath:inverse-and-implicit-function-theorem","site":"theorempath","slug":"inverse-and-implicit-function-theorem","title":"Inverse and Implicit Function Theorem","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/inverse-and-implicit-function-theorem","prerequisites":["the-jacobian-matrix"],"leadsTo":["convex-optimization-basics","convex-duality"]},{"id":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","site":"theorempath","slug":"iterative-magnitude-pruning-and-lottery-ticket-hypothesis","title":"Iterative Magnitude Pruning and the Lottery Ticket Hypothesis","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/iterative-magnitude-pruning-and-lottery-ticket-hypothesis","prerequisites":["model-compression-and-pruning","feedforward-networks-and-backpropagation"],"leadsTo":["optimal-brain-surgery-and-pruning-theory","quantization-theory","knowledge-distillation"]},{"id":"theorempath:ito-lemma","site":"theorempath","slug":"ito-lemma","title":"Ito's Lemma","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/ito-lemma","prerequisites":["stochastic-calculus-for-ml"],"leadsTo":["diffusion-models","flow-matching","backward-sde-theory","feynman-kac-formula","stochastic-differential-equations"]},{"id":"theorempath:jepa-and-joint-embedding","site":"theorempath","slug":"jepa-and-joint-embedding","title":"JEPA and Joint Embedding","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/jepa-and-joint-embedding","prerequisites":["autoencoders","variational-autoencoders","history-of-ai","self-supervised-vision","vision-transformer-lineage","world-models-and-planning"],"leadsTo":["world-models-and-planning","vision-transformer-lineage"]},{"id":"theorempath:joint-marginal-conditional-distributions","site":"theorempath","slug":"joint-marginal-conditional-distributions","title":"Joint, Marginal, and Conditional Distributions","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/joint-marginal-conditional-distributions","prerequisites":["random-variables","common-probability-distributions","kolmogorov-probability-axioms"],"leadsTo":["expectation-variance-covariance-moments","bayesian-estimation","gaussian-processes-for-ml","gaussian-processes-regression","multivariate-normal-distribution"]},{"id":"theorempath:k-means-clustering","site":"theorempath","slug":"k-means-clustering","title":"K-Means Clustering","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/k-means-clustering","prerequisites":["common-probability-distributions","convex-optimization-basics","nmf-nonnegative-matrix-factorization","self-organizing-maps","tsne-and-umap"],"leadsTo":["gaussian-mixture-models-and-em","clustering-for-gene-expression","spectral-clustering"]},{"id":"theorempath:kafka-streaming-platform","site":"theorempath","slug":"kafka-streaming-platform","title":"Kafka Streaming Platform","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/kafka-streaming-platform","prerequisites":[],"leadsTo":["distributed-consensus","distributed-training-theory"]},{"id":"theorempath:kalman-filter","site":"theorempath","slug":"kalman-filter","title":"Kalman Filter","layer":"2","tier":1,"module":"applied-math","url":"https://theorempath.com/topics/kalman-filter","prerequisites":["common-probability-distributions","eigenvalues-and-eigenvectors"],"leadsTo":["particle-filters","bayesian-state-estimation","state-space-models"]},{"id":"theorempath:kelly-criterion","site":"theorempath","slug":"kelly-criterion","title":"Kelly Criterion","layer":"2","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/kelly-criterion","prerequisites":["common-probability-distributions","information-theory-foundations","convex-tinkering","expected-utility"],"leadsTo":["fat-tails"]},{"id":"theorempath:kernel-methods-for-molecules","site":"theorempath","slug":"kernel-methods-for-molecules","title":"Kernel Methods for Molecules","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/kernel-methods-for-molecules","prerequisites":["kernels-and-rkhs","gaussian-processes-for-ml"],"leadsTo":["gaussian-processes-regression"]},{"id":"theorempath:kernel-trick","site":"theorempath","slug":"kernel-trick","title":"The Kernel Trick","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/kernel-trick","prerequisites":["support-vector-machines","ridge-regression","bayesian-linear-regression","convex-optimization-basics","common-probability-distributions"],"leadsTo":["kernels-and-rkhs","gaussian-processes-for-ml","gaussian-processes-regression","gram-matrices-and-kernel-matrices"]},{"id":"theorempath:kernel-two-sample-tests","site":"theorempath","slug":"kernel-two-sample-tests","title":"Kernel Two-Sample Tests","layer":"3","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/kernel-two-sample-tests","prerequisites":["kernels-and-rkhs"],"leadsTo":[]},{"id":"theorempath:kernels-and-rkhs","site":"theorempath","slug":"kernels-and-rkhs","title":"Kernels and Reproducing Kernel Hilbert Spaces","layer":"3","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/kernels-and-rkhs","prerequisites":["convex-optimization-basics","rademacher-complexity","characteristic-functions","convex-duality","dimensionality-reduction-theory","functional-analysis-core","gram-matrices-and-kernel-matrices","hanson-wright-inequality","regularization-theory","ridge-regression","spectral-clustering","support-vector-machines","svm-for-rf-classification","kernel-trick"],"leadsTo":["implicit-bias-and-modern-generalization","attention-as-kernel-regression","gaussian-processes-for-ml","gaussian-processes-regression","kernel-methods-for-molecules","kernel-two-sample-tests","neural-tangent-kernel"]},{"id":"theorempath:kl-divergence","site":"theorempath","slug":"kl-divergence","title":"KL Divergence","layer":"1","tier":1,"module":"foundations","url":"https://theorempath.com/topics/kl-divergence","prerequisites":["common-probability-distributions","information-theory-foundations","distance-metrics-compared","total-variation-distance"],"leadsTo":["variational-autoencoders","information-theory-foundations","bits-nats-perplexity-bpb","cramer-rao-bound","fisher-information","maximum-likelihood-estimation","minimax-lower-bounds","predictive-coding-and-autoencoders-in-the-brain"]},{"id":"theorempath:knapsack-problem","site":"theorempath","slug":"knapsack-problem","title":"Knapsack Problem","layer":"0A","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/knapsack-problem","prerequisites":["dynamic-programming","greedy-algorithms"],"leadsTo":[]},{"id":"theorempath:knn","site":"theorempath","slug":"knn","title":"K-Nearest Neighbors","layer":"1","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/knn","prerequisites":["common-probability-distributions","order-statistics"],"leadsTo":["bias-variance-tradeoff","decision-trees-and-ensembles","semantic-search-and-embeddings"]},{"id":"theorempath:knowledge-distillation","site":"theorempath","slug":"knowledge-distillation","title":"Knowledge Distillation","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/knowledge-distillation","prerequisites":["feedforward-networks-and-backpropagation","iterative-magnitude-pruning-and-lottery-ticket-hypothesis"],"leadsTo":["synthetic-data-distillation"]},{"id":"theorempath:kolmogorov-arnold-networks","site":"theorempath","slug":"kolmogorov-arnold-networks","title":"Kolmogorov-Arnold Networks (KANs)","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/kolmogorov-arnold-networks","prerequisites":["universal-approximation-theorem","feedforward-networks-and-backpropagation","activation-functions"],"leadsTo":["physics-informed-neural-networks","mechanistic-interpretability"]},{"id":"theorempath:kolmogorov-complexity-and-mdl","site":"theorempath","slug":"kolmogorov-complexity-and-mdl","title":"Kolmogorov Complexity and MDL","layer":"2","tier":2,"module":"learning-theory-core","url":"https://theorempath.com/topics/kolmogorov-complexity-and-mdl","prerequisites":["p-vs-np"],"leadsTo":["aic-and-bic","algorithmic-stability"]},{"id":"theorempath:kolmogorov-probability-axioms","site":"theorempath","slug":"kolmogorov-probability-axioms","title":"Kolmogorov Probability Axioms","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/kolmogorov-probability-axioms","prerequisites":["sets-functions-and-relations"],"leadsTo":["measure-theoretic-probability","joint-marginal-conditional-distributions","common-inequalities","random-variables","time-series-foundations"]},{"id":"theorempath:kubernetes-for-ml-workloads","site":"theorempath","slug":"kubernetes-for-ml-workloads","title":"Kubernetes for ML Workloads","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/kubernetes-for-ml-workloads","prerequisites":[],"leadsTo":["inference-systems-overview","gpu-compute-model"]},{"id":"theorempath:kv-cache-optimization","site":"theorempath","slug":"kv-cache-optimization","title":"KV Cache Optimization","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/kv-cache-optimization","prerequisites":["kv-cache"],"leadsTo":["prefix-caching"]},{"id":"theorempath:kv-cache","site":"theorempath","slug":"kv-cache","title":"KV Cache","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/kv-cache","prerequisites":["attention-mechanism-theory","attention-is-all-you-need-paper","attention-variants-and-efficiency","efficient-transformers-survey","linear-layer-shapes-memory"],"leadsTo":["context-engineering","inference-systems-overview","kv-cache-optimization","memory-systems-for-llms","prefix-caching","speculative-decoding-and-quantization"]},{"id":"theorempath:label-smoothing-and-regularization","site":"theorempath","slug":"label-smoothing-and-regularization","title":"Label Smoothing and Regularization","layer":"2","tier":2,"module":"training-techniques","url":"https://theorempath.com/topics/label-smoothing-and-regularization","prerequisites":["logistic-regression"],"leadsTo":[]},{"id":"theorempath:langevin-dynamics","site":"theorempath","slug":"langevin-dynamics","title":"Langevin Dynamics","layer":"3","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/langevin-dynamics","prerequisites":["stochastic-differential-equations","fokker-planck-equation","hamiltonian-monte-carlo","score-matching","sgd-as-sde","stochastic-calculus-for-ml","stochastic-processes-ml"],"leadsTo":["score-matching","diffusion-models","sgd-as-sde"]},{"id":"theorempath:lasso-regression","site":"theorempath","slug":"lasso-regression","title":"Lasso Regression","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/lasso-regression","prerequisites":["linear-regression","convex-optimization-basics","ridge-regression","subgradients-and-subdifferentials","maximum-a-posteriori-estimation"],"leadsTo":["elastic-net","sparse-recovery-and-compressed-sensing","high-dimensional-covariance-estimation","sparse-autoencoders","sparse-coding-and-efficient-coding","symbolic-regression-and-equation-discovery"]},{"id":"theorempath:latent-reasoning","site":"theorempath","slug":"latent-reasoning","title":"Latent Reasoning","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/latent-reasoning","prerequisites":["test-time-compute-and-search","memory-systems-for-llms","multi-token-prediction"],"leadsTo":["multi-token-prediction","memory-systems-for-llms"]},{"id":"theorempath:law-of-large-numbers","site":"theorempath","slug":"law-of-large-numbers","title":"Law of Large Numbers","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/law-of-large-numbers","prerequisites":["random-variables","expectation-variance-covariance-moments","common-probability-distributions","borel-cantelli-lemmas","modes-of-convergence-random-variables"],"leadsTo":["central-limit-theorem","empirical-risk-minimization","concentration-inequalities","fat-tails","monte-carlo-methods","non-probability-sampling","number-theory-and-ml"]},{"id":"theorempath:lazy-vs-feature-learning","site":"theorempath","slug":"lazy-vs-feature-learning","title":"Lazy vs Feature Learning","layer":"4","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/lazy-vs-feature-learning","prerequisites":["neural-tangent-kernel","mean-field-theory"],"leadsTo":["double-descent","implicit-bias-and-modern-generalization","scaling-laws"]},{"id":"theorempath:learning-rate-scheduling","site":"theorempath","slug":"learning-rate-scheduling","title":"Learning Rate Scheduling","layer":"2","tier":1,"module":"training-techniques","url":"https://theorempath.com/topics/learning-rate-scheduling","prerequisites":["stochastic-gradient-descent-convergence","adam-optimizer","batch-size-and-learning-dynamics","gradient-descent-variants"],"leadsTo":["mixed-precision-training"]},{"id":"theorempath:leverage-points-systems","site":"theorempath","slug":"leverage-points-systems","title":"Leverage Points in Complex Systems","layer":"3","tier":2,"module":"methodology","url":"https://theorempath.com/topics/leverage-points-systems","prerequisites":["decision-theory-foundations"],"leadsTo":["bounded-rationality"]},{"id":"theorempath:likelihood-ratio-wald-score-tests","site":"theorempath","slug":"likelihood-ratio-wald-score-tests","title":"Likelihood-Ratio, Wald, and Score Tests","layer":"2","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/likelihood-ratio-wald-score-tests","prerequisites":["maximum-likelihood-estimation","fisher-information","neyman-pearson-and-hypothesis-testing-theory","asymptotic-statistics","chi-squared-distribution-and-tests"],"leadsTo":["hypothesis-testing-for-ml","e-values-and-anytime-valid-inference","permutation-tests"]},{"id":"theorempath:line-search-methods","site":"theorempath","slug":"line-search-methods","title":"Line Search Methods","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/line-search-methods","prerequisites":["convex-optimization-basics","differentiation-in-rn","newtons-method"],"leadsTo":["conjugate-gradient-methods","quasi-newton-methods","trust-region-methods"]},{"id":"theorempath:linear-independence","site":"theorempath","slug":"linear-independence","title":"Linear Independence","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/linear-independence","prerequisites":["vectors-matrices-and-linear-maps"],"leadsTo":["eigenvalues-and-eigenvectors","singular-value-decomposition","matrix-operations-and-properties"]},{"id":"theorempath:linear-layer-shapes-memory","site":"theorempath","slug":"linear-layer-shapes-memory","title":"Linear Layer: Shapes, Bias, and Memory","layer":"2","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/linear-layer-shapes-memory","prerequisites":["matrix-operations-and-properties","matrix-calculus","feedforward-networks-and-backpropagation"],"leadsTo":["attention-mechanism-theory","transformer-architecture","kv-cache"]},{"id":"theorempath:linear-regression","site":"theorempath","slug":"linear-regression","title":"Linear Regression","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/linear-regression","prerequisites":["matrix-operations-and-properties","maximum-likelihood-estimation","elements-of-statistical-learning-book","naive-bayes"],"leadsTo":["ridge-regression","logistic-regression","bias-variance-tradeoff","cubist-and-model-trees","data-preprocessing-and-feature-engineering","feature-importance-and-interpretability","gauss-markov-theorem","generalized-additive-models","greg-estimator","implicit-bias-and-modern-generalization","lasso-regression","longitudinal-surveys-and-panel-data","mars-multivariate-adaptive-regression-splines","reml-and-variance-component-estimation","small-area-estimation","time-series-forecasting-basics","bayesian-linear-regression"]},{"id":"theorempath:llama-and-open-weight-models","site":"theorempath","slug":"llama-and-open-weight-models","title":"LLaMA and Open Weight Models","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/llama-and-open-weight-models","prerequisites":["transformer-architecture","token-prediction-and-language-modeling","scaling-laws","mixture-of-experts","post-training-overview","tokenization-and-information-theory","fine-tuning-and-adaptation","cohere-models","gemini-and-google-models","gpt-series-evolution"],"leadsTo":["post-training-overview","mixture-of-experts"]},{"id":"theorempath:llm-application-security","site":"theorempath","slug":"llm-application-security","title":"LLM Application Security","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/llm-application-security","prerequisites":["adversarial-machine-learning","rlhf-and-alignment"],"leadsTo":[]},{"id":"theorempath:lln-failures-heavy-tails","site":"theorempath","slug":"lln-failures-heavy-tails","title":"LLN and CLT Failures Under Heavy Tails","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/lln-failures-heavy-tails","prerequisites":["law-of-large-numbers","central-limit-theorem","characteristic-functions","fat-tails","common-probability-distributions","modes-of-convergence-random-variables"],"leadsTo":["fat-tails","extreme-value-theory","subexponential-random-variables"]},{"id":"theorempath:log-probability-computation","site":"theorempath","slug":"log-probability-computation","title":"Log-Probability Computation","layer":"1","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/log-probability-computation","prerequisites":["softmax-and-numerical-stability"],"leadsTo":["cross-entropy-loss-deep-dive","perplexity-and-language-model-evaluation"]},{"id":"theorempath:logistic-regression","site":"theorempath","slug":"logistic-regression","title":"Logistic Regression","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/logistic-regression","prerequisites":["maximum-likelihood-estimation","convex-optimization-basics","data-preprocessing-and-feature-engineering","linear-regression","naive-bayes"],"leadsTo":["support-vector-machines","calibration-and-uncertainty","cross-entropy-loss-deep-dive","label-smoothing-and-regularization","loss-functions-catalog","multi-class-and-multi-label-classification","word-embeddings"]},{"id":"theorempath:lognormal-distribution","site":"theorempath","slug":"lognormal-distribution","title":"Lognormal Distribution","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/lognormal-distribution","prerequisites":["common-probability-distributions","normal-distribution","central-limit-theorem","distributions-atlas"],"leadsTo":["pareto-distribution","weibull-distribution","fat-tails"]},{"id":"theorempath:logsplines","site":"theorempath","slug":"logsplines","title":"Logspline Density Estimation","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/logsplines","prerequisites":["maximum-likelihood-estimation"],"leadsTo":[]},{"id":"theorempath:longitudinal-surveys-and-panel-data","site":"theorempath","slug":"longitudinal-surveys-and-panel-data","title":"Longitudinal Surveys and Panel Data","layer":"3","tier":3,"module":"statistical-foundations","url":"https://theorempath.com/topics/longitudinal-surveys-and-panel-data","prerequisites":["linear-regression","causal-inference-for-policy-evaluation","nonresponse-and-missing-data","small-area-estimation"],"leadsTo":["small-area-estimation","nonresponse-and-missing-data"]},{"id":"theorempath:loss-functions-catalog","site":"theorempath","slug":"loss-functions-catalog","title":"Loss Functions Catalog","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/loss-functions-catalog","prerequisites":["logistic-regression"],"leadsTo":["empirical-risk-minimization","no-free-lunch-theorem"]},{"id":"theorempath:loss-functions","site":"theorempath","slug":"loss-functions","title":"Loss Functions","layer":"1","tier":2,"module":"learning-theory-core","url":"https://theorempath.com/topics/loss-functions","prerequisites":["random-variables","expectation-variance-covariance-moments","hypothesis-classes-and-function-spaces"],"leadsTo":["empirical-risk-minimization","pac-learning-framework","support-vector-machines","linear-regression"]},{"id":"theorempath:lyapunov-based-machine-learning-for-chaos","site":"theorempath","slug":"lyapunov-based-machine-learning-for-chaos","title":"Lyapunov-Based Machine Learning for Chaos","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/lyapunov-based-machine-learning-for-chaos","prerequisites":["nonlinear-dynamics-and-chaos-fundamentals","physics-informed-neural-networks"],"leadsTo":["reservoir-computing-and-echo-state-networks","neural-odes"]},{"id":"theorempath:macroeconomic-time-series-forecasting","site":"theorempath","slug":"macroeconomic-time-series-forecasting","title":"Macroeconomic Time-Series Forecasting","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/macroeconomic-time-series-forecasting","prerequisites":["time-series-forecasting-basics"],"leadsTo":["recurrent-neural-networks","transformer-architecture"]},{"id":"theorempath:mamba-and-state-space-models","site":"theorempath","slug":"mamba-and-state-space-models","title":"Mamba and State-Space Models","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/mamba-and-state-space-models","prerequisites":["recurrent-neural-networks","attention-mechanism-theory","deep-learning-time-series","efficient-transformers-survey","mixture-of-experts","reservoir-computing-and-echo-state-networks","state-space-models"],"leadsTo":["mixture-of-experts","context-engineering"]},{"id":"theorempath:markov-chain-monte-carlo","site":"theorempath","slug":"markov-chain-monte-carlo","title":"Markov Chain Monte Carlo","layer":"2","tier":1,"module":"sampling-mcmc","url":"https://theorempath.com/topics/markov-chain-monte-carlo","prerequisites":["markov-chains-and-steady-state","monte-carlo-methods","stochastic-processes-ml"],"leadsTo":["metropolis-hastings","gibbs-sampling","hamiltonian-monte-carlo","burn-in-convergence-diagnostics"]},{"id":"theorempath:markov-chains-and-steady-state","site":"theorempath","slug":"markov-chains-and-steady-state","title":"Markov Chains and Steady State","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/markov-chains-and-steady-state","prerequisites":["common-probability-distributions","eigenvalues-and-eigenvectors","pagerank-algorithm"],"leadsTo":["metropolis-hastings","markov-decision-processes","pagerank-algorithm","burn-in-convergence-diagnostics","markov-chain-monte-carlo","state-space-models"]},{"id":"theorempath:markov-decision-processes","site":"theorempath","slug":"markov-decision-processes","title":"Markov Decision Processes","layer":"2","tier":1,"module":"rl-theory","url":"https://theorempath.com/topics/markov-decision-processes","prerequisites":["convex-optimization-basics","concentration-inequalities","bayesian-state-estimation","markov-chains-and-steady-state","multi-armed-bandits-theory","online-learning-and-bandits"],"leadsTo":["policy-gradient-theorem","dynamic-programming","active-slam-and-pomdps","agentic-rl-and-tool-use","bellman-equations","era-of-experience","exploration-vs-exploitation","markov-games-and-self-play","mean-field-games","model-based-rl","multi-agent-collaboration","options-and-temporal-abstraction","policy-representations","reinforcement-learning-environments-and-benchmarks","reinforcement-learning-for-drug-discovery","reinforcement-learning-for-synthesis-planning","reward-design","reward-systems-and-reinforcement-learning-neuroscience","rlhf-and-alignment","robust-adversarial-policies","self-play-and-multi-agent-rl","td-learning","value-iteration-and-policy-iteration","world-models-and-planning"]},{"id":"theorempath:markov-games-and-self-play","site":"theorempath","slug":"markov-games-and-self-play","title":"Markov Games and Self-Play","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/markov-games-and-self-play","prerequisites":["markov-decision-processes","reinforcement-learning-for-auction-design"],"leadsTo":["agent-based-modeling-with-ml"]},{"id":"theorempath:mars-multivariate-adaptive-regression-splines","site":"theorempath","slug":"mars-multivariate-adaptive-regression-splines","title":"MARS (Multivariate Adaptive Regression Splines)","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/mars-multivariate-adaptive-regression-splines","prerequisites":["linear-regression"],"leadsTo":["generalized-additive-models","feedforward-networks-and-backpropagation"]},{"id":"theorempath:martingale-theory","site":"theorempath","slug":"martingale-theory","title":"Martingale Theory","layer":"0B","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/martingale-theory","prerequisites":["measure-theoretic-probability"],"leadsTo":["mcdiarmids-inequality","concentration-inequalities","stochastic-approximation-theory","adaptive-learning-is-not-iid","brownian-motion","coupling-arguments-and-mixing-time","e-values-and-anytime-valid-inference","stochastic-calculus-for-ml"]},{"id":"theorempath:matrix-calculus","site":"theorempath","slug":"matrix-calculus","title":"Matrix Calculus","layer":"1","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/matrix-calculus","prerequisites":["the-jacobian-matrix","the-hessian-matrix"],"leadsTo":["feedforward-networks-and-backpropagation","automatic-differentiation","linear-layer-shapes-memory","quantization-theory"]},{"id":"theorempath:matrix-concentration","site":"theorempath","slug":"matrix-concentration","title":"Matrix Concentration","layer":"3","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/matrix-concentration","prerequisites":["subgaussian-random-variables","subexponential-random-variables","concentration-inequalities","bernstein-inequality","empirical-processes-and-chaining","measure-concentration-and-geometric-fa","bennetts-inequality"],"leadsTo":["random-matrix-theory-overview","hanson-wright-inequality","high-dimensional-covariance-estimation"]},{"id":"theorempath:matrix-multiplication-algorithms","site":"theorempath","slug":"matrix-multiplication-algorithms","title":"Matrix Multiplication Algorithms","layer":"1","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/matrix-multiplication-algorithms","prerequisites":["vectors-matrices-and-linear-maps"],"leadsTo":["open-problems-in-matrix-computation","gram-matrices-and-kernel-matrices"]},{"id":"theorempath:matrix-norms","site":"theorempath","slug":"matrix-norms","title":"Matrix Norms","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/matrix-norms","prerequisites":["vectors-matrices-and-linear-maps"],"leadsTo":["eigenvalues-and-eigenvectors","singular-value-decomposition","conditioning-and-condition-number","numerical-stability","conjugate-gradient-methods"]},{"id":"theorempath:matrix-operations-and-properties","site":"theorempath","slug":"matrix-operations-and-properties","title":"Matrix Operations and Properties","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/matrix-operations-and-properties","prerequisites":["sets-functions-and-relations","linear-independence"],"leadsTo":["eigenvalues-and-eigenvectors","singular-value-decomposition","attention-mechanism-theory","conditioning-and-condition-number","conjugate-gradient-methods","convex-optimization-basics","linear-layer-shapes-memory","linear-regression","numerical-linear-algebra","numerical-stability","quantization-theory","the-hessian-matrix"]},{"id":"theorempath:maximum-a-posteriori-estimation","site":"theorempath","slug":"maximum-a-posteriori-estimation","title":"Maximum A Posteriori (MAP) Estimation","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/maximum-a-posteriori-estimation","prerequisites":["maximum-likelihood-estimation","bayesian-estimation","common-probability-distributions","convex-optimization-basics"],"leadsTo":["bayesian-linear-regression","conjugate-priors","ridge-regression","lasso-regression","logistic-regression","regularization-theory"]},{"id":"theorempath:maximum-likelihood-estimation","site":"theorempath","slug":"maximum-likelihood-estimation","title":"Maximum Likelihood Estimation: Theory, Information Identity, and Asymptotic Efficiency","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/maximum-likelihood-estimation","prerequisites":["common-probability-distributions","differentiation-in-rn","central-limit-theorem","kl-divergence","exponential-function-properties","information-theory-foundations","method-of-moments","radon-nikodym-and-conditional-expectation"],"leadsTo":["asymptotic-statistics","hypothesis-testing-for-ml","em-algorithm","empirical-risk-minimization","cramer-rao-bound","fisher-information","aic-and-bic","bayesian-estimation","distributional-semantics","double-debiased-machine-learning","e-values-and-anytime-valid-inference","energy-based-models","gaussian-mixture-models-and-em","linear-regression","logistic-regression","logsplines","minimax-lower-bounds","neyman-pearson-and-hypothesis-testing-theory","reml-and-variance-component-estimation","robust-statistics-and-m-estimators","shrinkage-estimation-james-stein","steins-paradox","sufficient-statistics-and-exponential-families","survival-analysis","variational-autoencoders","word-embeddings","bayesian-linear-regression","conjugate-priors","maximum-a-posteriori-estimation"]},{"id":"theorempath:mcdiarmids-inequality","site":"theorempath","slug":"mcdiarmids-inequality","title":"McDiarmid's Inequality","layer":"3","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/mcdiarmids-inequality","prerequisites":["concentration-inequalities","subgaussian-random-variables","martingale-theory","hoeffdings-lemma"],"leadsTo":["algorithmic-stability","rademacher-complexity"]},{"id":"theorempath:mcmc-for-markov-random-fields","site":"theorempath","slug":"mcmc-for-markov-random-fields","title":"MCMC for Markov Random Fields","layer":"3","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/mcmc-for-markov-random-fields","prerequisites":["gibbs-sampling","perfect-sampling"],"leadsTo":["perfect-sampling","burn-in-convergence-diagnostics"]},{"id":"theorempath:mean-field-games","site":"theorempath","slug":"mean-field-games","title":"Mean-Field Games","layer":"4","tier":3,"module":"rl-theory","url":"https://theorempath.com/topics/mean-field-games","prerequisites":["markov-decision-processes","mean-field-theory","agent-based-modeling-with-ml"],"leadsTo":[]},{"id":"theorempath:mean-field-theory","site":"theorempath","slug":"mean-field-theory","title":"Mean Field Theory","layer":"4","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/mean-field-theory","prerequisites":["neural-tangent-kernel","information-geometry"],"leadsTo":["lazy-vs-feature-learning","mean-field-games"]},{"id":"theorempath:measure-concentration-and-geometric-fa","site":"theorempath","slug":"measure-concentration-and-geometric-fa","title":"Measure Concentration and Geometric Functional Analysis","layer":"3","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/measure-concentration-and-geometric-fa","prerequisites":["subgaussian-random-variables","epsilon-nets-and-covering-numbers"],"leadsTo":["matrix-concentration","empirical-processes-and-chaining","dimensionality-reduction-theory"]},{"id":"theorempath:measure-theoretic-probability","site":"theorempath","slug":"measure-theoretic-probability","title":"Measure-Theoretic Probability","layer":"0B","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/measure-theoretic-probability","prerequisites":["cardinality-and-countability","integration-and-change-of-variables","kolmogorov-probability-axioms","random-variables","sets-functions-and-relations","zermelo-fraenkel-set-theory"],"leadsTo":["concentration-inequalities","common-probability-distributions","borel-cantelli-lemmas","brownian-motion","characteristic-functions","cramer-wold-theorem","e-values-and-anytime-valid-inference","functional-analysis-core","martingale-theory","modes-of-convergence-random-variables","pde-fundamentals-for-ml","radon-nikodym-and-conditional-expectation","random-matrix-theory-overview","stochastic-calculus-for-ml","stochastic-processes-ml","total-variation-distance","wasserstein-distances"]},{"id":"theorempath:mechanism-design","site":"theorempath","slug":"mechanism-design","title":"Mechanism Design","layer":"3","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/mechanism-design","prerequisites":["game-theory","nash-equilibrium","arrows-impossibility","auction-theory","commons-governance-ostrom","stable-matching-and-deferred-acceptance"],"leadsTo":["reinforcement-learning-for-auction-design"]},{"id":"theorempath:mechanistic-interpretability","site":"theorempath","slug":"mechanistic-interpretability","title":"Mechanistic Interpretability: Features, Circuits, and Causal Faithfulness","layer":"4","tier":1,"module":"ai-safety","url":"https://theorempath.com/topics/mechanistic-interpretability","prerequisites":["transformer-architecture","principal-component-analysis","kolmogorov-arnold-networks","residual-stream-and-transformer-internals","rlhf-and-alignment"],"leadsTo":["sparse-autoencoders","induction-heads","residual-stream-and-transformer-internals","feature-importance-and-interpretability","rlhf-and-alignment","truth-directions-and-linear-probes"]},{"id":"theorempath:megakernels","site":"theorempath","slug":"megakernels","title":"Megakernels","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/megakernels","prerequisites":["fused-kernels","gpu-compute-model"],"leadsTo":["inference-systems-overview","speculative-decoding-and-quantization"]},{"id":"theorempath:memory-systems-for-llms","site":"theorempath","slug":"memory-systems-for-llms","title":"Memory Systems for LLMs","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/memory-systems-for-llms","prerequisites":["context-engineering","kv-cache"],"leadsTo":["latent-reasoning","context-engineering"]},{"id":"theorempath:meta-analysis","site":"theorempath","slug":"meta-analysis","title":"Meta-Analysis","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/meta-analysis","prerequisites":["hypothesis-testing-for-ml","bayesian-estimation","reml-and-variance-component-estimation"],"leadsTo":["reproducibility-and-experimental-rigor","p-hacking-and-multiple-testing"]},{"id":"theorempath:meta-learning","site":"theorempath","slug":"meta-learning","title":"Meta-Learning","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/meta-learning","prerequisites":["feedforward-networks-and-backpropagation","test-time-training"],"leadsTo":[]},{"id":"theorempath:method-of-moments","site":"theorempath","slug":"method-of-moments","title":"Method of Moments","layer":"0B","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/method-of-moments","prerequisites":["common-probability-distributions"],"leadsTo":["maximum-likelihood-estimation","hypothesis-testing-for-ml"]},{"id":"theorempath:metric-spaces-convergence-completeness","site":"theorempath","slug":"metric-spaces-convergence-completeness","title":"Metric Spaces, Convergence, and Completeness","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/metric-spaces-convergence-completeness","prerequisites":["sets-functions-and-relations"],"leadsTo":["compactness-and-heine-borel","continuity-in-rn","distance-metrics-compared","functional-analysis-core","hyperbolic-embeddings-for-graphs","modes-of-convergence-random-variables","non-euclidean-and-hyperbolic-geometry","sequences-and-series-of-functions"]},{"id":"theorempath:metropolis-hastings","site":"theorempath","slug":"metropolis-hastings","title":"Metropolis-Hastings Algorithm","layer":"2","tier":1,"module":"sampling-mcmc","url":"https://theorempath.com/topics/metropolis-hastings","prerequisites":["common-probability-distributions","markov-chain-monte-carlo","markov-chains-and-steady-state","monte-carlo-methods"],"leadsTo":["gibbs-sampling","burn-in-convergence-diagnostics","hamiltonian-monte-carlo","coupling-arguments-and-mixing-time","particle-filters","perfect-sampling","reversible-jump-mcmc","slice-sampling"]},{"id":"theorempath:minimax-lower-bounds","site":"theorempath","slug":"minimax-lower-bounds","title":"Minimax Lower Bounds: Le Cam, Fano, Assouad, and the Reduction to Testing","layer":"3","tier":1,"module":"statistical-foundations","url":"https://theorempath.com/topics/minimax-lower-bounds","prerequisites":["concentration-inequalities","maximum-likelihood-estimation","kl-divergence","cramer-rao-bound","fisher-information","empirical-processes-and-chaining"],"leadsTo":["fanos-inequality","shrinkage-estimation-james-stein","rademacher-complexity","robust-adversarial-policies"]},{"id":"theorempath:minimax-saddle-points","site":"theorempath","slug":"minimax-saddle-points","title":"Minimax and Saddle Points","layer":"2","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/minimax-saddle-points","prerequisites":["convex-optimization-basics","convex-duality"],"leadsTo":["adversarial-machine-learning","robust-statistics-and-m-estimators"]},{"id":"theorempath:minimax-theorem","site":"theorempath","slug":"minimax-theorem","title":"Von Neumann Minimax Theorem","layer":"2","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/minimax-theorem","prerequisites":["game-theory","convex-duality","nash-equilibrium"],"leadsTo":["adversarial-machine-learning"]},{"id":"theorempath:mirror-descent-and-frank-wolfe","site":"theorempath","slug":"mirror-descent-and-frank-wolfe","title":"Mirror Descent and Frank-Wolfe","layer":"3","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/mirror-descent-and-frank-wolfe","prerequisites":["convex-optimization-basics","convex-duality","online-convex-optimization","projected-gradient-descent"],"leadsTo":["projected-gradient-descent","coordinate-descent"]},{"id":"theorempath:mistral-models","site":"theorempath","slug":"mistral-models","title":"Mistral Models","layer":"4","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/mistral-models","prerequisites":["transformer-architecture","mixture-of-experts","attention-mechanism-theory","tokenization-and-information-theory","cohere-models"],"leadsTo":["model-comparison-table","mixture-of-experts"]},{"id":"theorempath:mixed-precision-training","site":"theorempath","slug":"mixed-precision-training","title":"Mixed Precision Training","layer":"3","tier":2,"module":"training-techniques","url":"https://theorempath.com/topics/mixed-precision-training","prerequisites":["floating-point-arithmetic","adam-optimizer","distributed-training-theory","learning-rate-scheduling","running-ml-workloads-on-gpus","webgpu-for-ml"],"leadsTo":["activation-checkpointing"]},{"id":"theorempath:mixture-density-networks","site":"theorempath","slug":"mixture-density-networks","title":"Mixture Density Networks","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/mixture-density-networks","prerequisites":["gaussian-mixture-models-and-em","feedforward-networks-and-backpropagation"],"leadsTo":[]},{"id":"theorempath:mixture-of-experts","site":"theorempath","slug":"mixture-of-experts","title":"Mixture of Experts","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/mixture-of-experts","prerequisites":["transformer-architecture","model-compression-and-pruning","speculative-decoding-and-quantization"],"leadsTo":["speculative-decoding-and-quantization","mamba-and-state-space-models","deepseek-models","llama-and-open-weight-models","mistral-models"]},{"id":"theorempath:ml-for-intelligence-predictive-analytics","site":"theorempath","slug":"ml-for-intelligence-predictive-analytics","title":"ML for Intelligence Predictive Analytics","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/ml-for-intelligence-predictive-analytics","prerequisites":[],"leadsTo":[]},{"id":"theorempath:ml-for-personalized-psychiatric-diagnostics","site":"theorempath","slug":"ml-for-personalized-psychiatric-diagnostics","title":"ML for Personalized Psychiatric Diagnostics","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/ml-for-personalized-psychiatric-diagnostics","prerequisites":[],"leadsTo":[]},{"id":"theorempath:ml-project-lifecycle","site":"theorempath","slug":"ml-project-lifecycle","title":"ML Project Lifecycle","layer":"1","tier":2,"module":"methodology","url":"https://theorempath.com/topics/ml-project-lifecycle","prerequisites":["hardware-for-ml-practitioners"],"leadsTo":["train-test-split-and-data-leakage","exploratory-data-analysis","experiment-tracking-and-tooling"]},{"id":"theorempath:modal-serverless-gpu-platform","site":"theorempath","slug":"modal-serverless-gpu-platform","title":"Modal: Serverless GPU Platform","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/modal-serverless-gpu-platform","prerequisites":[],"leadsTo":["gpu-compute-model"]},{"id":"theorempath:model-based-rl","site":"theorempath","slug":"model-based-rl","title":"Model-Based Reinforcement Learning","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/model-based-rl","prerequisites":["bellman-equations","markov-decision-processes","deep-rl-for-control","reward-systems-and-reinforcement-learning-neuroscience"],"leadsTo":["world-models-and-planning"]},{"id":"theorempath:model-collapse-and-data-quality","site":"theorempath","slug":"model-collapse-and-data-quality","title":"Model Collapse and Data Quality","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/model-collapse-and-data-quality","prerequisites":["synthetic-data-generation"],"leadsTo":["data-contamination-and-evaluation"]},{"id":"theorempath:model-comparison-table","site":"theorempath","slug":"model-comparison-table","title":"Model Comparison Table","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/model-comparison-table","prerequisites":["transformer-architecture","claude-model-family","deepseek-models","gemini-and-google-models","mistral-models","qwen-and-chinese-models"],"leadsTo":[]},{"id":"theorempath:model-compression-and-pruning","site":"theorempath","slug":"model-compression-and-pruning","title":"Model Compression and Pruning","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/model-compression-and-pruning","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["inference-systems-overview","mixture-of-experts","iterative-magnitude-pruning-and-lottery-ticket-hypothesis"]},{"id":"theorempath:model-evaluation-best-practices","site":"theorempath","slug":"model-evaluation-best-practices","title":"Model Evaluation Best Practices","layer":"1","tier":1,"module":"methodology","url":"https://theorempath.com/topics/model-evaluation-best-practices","prerequisites":["confusion-matrices-and-classification-metrics","bayesian-optimization-for-hyperparameters"],"leadsTo":["cross-validation-theory","hypothesis-testing-for-ml"]},{"id":"theorempath:model-merging-and-weight-averaging","site":"theorempath","slug":"model-merging-and-weight-averaging","title":"Model Merging and Weight Averaging","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/model-merging-and-weight-averaging","prerequisites":["transformer-architecture"],"leadsTo":[]},{"id":"theorempath:model-theory-basics","site":"theorempath","slug":"model-theory-basics","title":"Model Theory Basics","layer":"2","tier":3,"module":"foundations","url":"https://theorempath.com/topics/model-theory-basics","prerequisites":["basic-logic-and-proof-techniques"],"leadsTo":[]},{"id":"theorempath:model-timeline","site":"theorempath","slug":"model-timeline","title":"Model Timeline","layer":"5","tier":2,"module":"model-timeline","url":"https://theorempath.com/topics/model-timeline","prerequisites":["history-of-ai","key-researchers-and-ideas"],"leadsTo":["ai-labs-landscape"]},{"id":"theorempath:modes-of-convergence-random-variables","site":"theorempath","slug":"modes-of-convergence-random-variables","title":"Modes of Convergence of Random Variables","layer":"0B","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/modes-of-convergence-random-variables","prerequisites":["measure-theoretic-probability","metric-spaces-convergence-completeness"],"leadsTo":["law-of-large-numbers","central-limit-theorem","borel-cantelli-lemmas","asymptotic-statistics"]},{"id":"theorempath:moment-generating-functions","site":"theorempath","slug":"moment-generating-functions","title":"Moment Generating Functions","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/moment-generating-functions","prerequisites":["expectation-variance-covariance-moments","common-probability-distributions","exponential-function-properties"],"leadsTo":["chernoff-bounds","concentration-inequalities","common-probability-distributions","bernstein-inequality","characteristic-functions","bennetts-inequality","chi-squared-concentration","hoeffdings-lemma","multivariate-normal-distribution"]},{"id":"theorempath:monte-carlo-methods","site":"theorempath","slug":"monte-carlo-methods","title":"Monte Carlo Methods","layer":"2","tier":1,"module":"sampling-mcmc","url":"https://theorempath.com/topics/monte-carlo-methods","prerequisites":["expectation-variance-covariance-moments","law-of-large-numbers","central-limit-theorem"],"leadsTo":["importance-sampling","rejection-sampling","markov-chain-monte-carlo","metropolis-hastings"]},{"id":"theorempath:monty-hall-problem","site":"theorempath","slug":"monty-hall-problem","title":"Monty Hall Problem","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/monty-hall-problem","prerequisites":["common-probability-distributions"],"leadsTo":["base-rate-fallacy","birthday-paradox"]},{"id":"theorempath:multi-agent-collaboration","site":"theorempath","slug":"multi-agent-collaboration","title":"Multi-Agent Collaboration","layer":"4","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/multi-agent-collaboration","prerequisites":["markov-decision-processes","policy-gradient-theorem"],"leadsTo":[]},{"id":"theorempath:multi-armed-bandits-theory","site":"theorempath","slug":"multi-armed-bandits-theory","title":"Multi-Armed Bandits Theory","layer":"2","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/multi-armed-bandits-theory","prerequisites":["common-probability-distributions","bayesian-optimization-for-hyperparameters","no-regret-learning","online-convex-optimization"],"leadsTo":["markov-decision-processes","policy-gradient-theorem","agent-based-modeling-with-ml","exploration-vs-exploitation"]},{"id":"theorempath:multi-class-and-multi-label-classification","site":"theorempath","slug":"multi-class-and-multi-label-classification","title":"Multi-Class and Multi-Label Classification","layer":"1","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/multi-class-and-multi-label-classification","prerequisites":["logistic-regression"],"leadsTo":["cross-entropy-loss-deep-dive","confusion-matrices-and-classification-metrics"]},{"id":"theorempath:multi-token-prediction","site":"theorempath","slug":"multi-token-prediction","title":"Multi-Token Prediction","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/multi-token-prediction","prerequisites":["transformer-architecture"],"leadsTo":["latent-reasoning","speculative-decoding-and-quantization"]},{"id":"theorempath:multimodal-rag","site":"theorempath","slug":"multimodal-rag","title":"Multimodal RAG","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/multimodal-rag","prerequisites":["context-engineering","audio-language-models","clip-and-openclip-in-practice","semantic-search-and-embeddings"],"leadsTo":["hallucination-theory","inference-systems-overview","document-intelligence"]},{"id":"theorempath:multivariate-distributions-atlas","site":"theorempath","slug":"multivariate-distributions-atlas","title":"Multivariate Distributions Atlas","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/multivariate-distributions-atlas","prerequisites":["multivariate-normal-distribution","common-probability-distributions","expectation-variance-covariance-moments"],"leadsTo":["copulas","scale-location-shape-parameters","moment-generating-functions"]},{"id":"theorempath:multivariate-normal-distribution","site":"theorempath","slug":"multivariate-normal-distribution","title":"The Multivariate Normal Distribution","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/multivariate-normal-distribution","prerequisites":["common-probability-distributions","joint-marginal-conditional-distributions","expectation-variance-covariance-moments","positive-semidefinite-matrices","the-jacobian-matrix","moment-generating-functions","characteristic-functions"],"leadsTo":["bayesian-linear-regression","conjugate-priors","gaussian-processes-for-ml","gauss-markov-theorem"]},{"id":"theorempath:naive-bayes","site":"theorempath","slug":"naive-bayes","title":"Naive Bayes","layer":"1","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/naive-bayes","prerequisites":["common-probability-distributions"],"leadsTo":["logistic-regression","linear-regression"]},{"id":"theorempath:nash-equilibrium","site":"theorempath","slug":"nash-equilibrium","title":"Nash Equilibrium","layer":"2","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/nash-equilibrium","prerequisites":["game-theory","convex-optimization-basics","no-regret-learning"],"leadsTo":["mechanism-design","minimax-theorem","auction-theory"]},{"id":"theorempath:natural-language-processing-foundations","site":"theorempath","slug":"natural-language-processing-foundations","title":"Natural Language Processing Foundations","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/natural-language-processing-foundations","prerequisites":["word-embeddings"],"leadsTo":["morphology-and-subword-modeling","nlp-for-economic-text-analysis","syntax-and-parsing"]},{"id":"theorempath:neural-architecture-search","site":"theorempath","slug":"neural-architecture-search","title":"Neural Architecture Search","layer":"4","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/neural-architecture-search","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":[]},{"id":"theorempath:neural-network-optimization-landscape","site":"theorempath","slug":"neural-network-optimization-landscape","title":"Neural Network Optimization Landscape","layer":"4","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/neural-network-optimization-landscape","prerequisites":["training-dynamics-and-loss-landscapes","the-hessian-matrix"],"leadsTo":["implicit-bias-and-modern-generalization","benign-overfitting"]},{"id":"theorempath:neural-odes","site":"theorempath","slug":"neural-odes","title":"Neural ODEs and Continuous-Depth Networks","layer":"4","tier":3,"module":"scientific-ml","url":"https://theorempath.com/topics/neural-odes","prerequisites":["classical-odes","skip-connections-and-resnets","gradient-flow-and-vanishing-gradients","automatic-differentiation","equilibrium-and-implicit-models","lyapunov-based-machine-learning-for-chaos","nonlinear-dynamics-and-chaos-fundamentals","pde-fundamentals-for-ml"],"leadsTo":["adjoint-sensitivity-method","neural-sdes","continuous-normalizing-flows","physics-informed-neural-networks","continuous-thought-machines"]},{"id":"theorempath:neural-sdes","site":"theorempath","slug":"neural-sdes","title":"Neural SDEs and the Diffusion Bridge","layer":"4","tier":3,"module":"scientific-ml","url":"https://theorempath.com/topics/neural-sdes","prerequisites":["neural-odes","stochastic-calculus-for-ml","adjoint-sensitivity-method","continuous-normalizing-flows","stochastic-differential-equations"],"leadsTo":["diffusion-models","energy-based-models"]},{"id":"theorempath:neural-tangent-kernel","site":"theorempath","slug":"neural-tangent-kernel","title":"Neural Tangent Kernel: Lazy Training, Kernel Equivalence, μP, and the Limits of Width","layer":"4","tier":1,"module":"modern-generalization","url":"https://theorempath.com/topics/neural-tangent-kernel","prerequisites":["kernels-and-rkhs","ridge-regression","implicit-bias-and-modern-generalization","gaussian-processes-for-ml","gaussian-processes-regression","stochastic-processes-ml"],"leadsTo":["double-descent","benign-overfitting","implicit-bias-and-modern-generalization","lazy-vs-feature-learning","mean-field-theory"]},{"id":"theorempath:newtons-method","site":"theorempath","slug":"newtons-method","title":"Newton's Method","layer":"1","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/newtons-method","prerequisites":["convex-optimization-basics","taylor-expansion","the-hessian-matrix"],"leadsTo":["quasi-newton-methods","line-search-methods","interior-point-methods","nonlinear-gauss-seidel","secant-method","second-order-optimization-methods","trust-region-methods"]},{"id":"theorempath:neyman-pearson-and-hypothesis-testing-theory","site":"theorempath","slug":"neyman-pearson-and-hypothesis-testing-theory","title":"Neyman-Pearson and Hypothesis Testing Theory","layer":"2","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/neyman-pearson-and-hypothesis-testing-theory","prerequisites":["common-probability-distributions","maximum-likelihood-estimation"],"leadsTo":["hypothesis-testing-for-ml","bootstrap-methods","e-values-and-anytime-valid-inference"]},{"id":"theorempath:nlp-for-economic-text-analysis","site":"theorempath","slug":"nlp-for-economic-text-analysis","title":"NLP for Economic Text Analysis","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/nlp-for-economic-text-analysis","prerequisites":["natural-language-processing-foundations","word-embeddings"],"leadsTo":["bert-and-pretrain-finetune-paradigm","distributional-semantics"]},{"id":"theorempath:nlp-for-intelligence-osint","site":"theorempath","slug":"nlp-for-intelligence-osint","title":"NLP for Open-Source Intelligence (OSINT)","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/nlp-for-intelligence-osint","prerequisites":[],"leadsTo":[]},{"id":"theorempath:nlp-for-psychology-text-data","site":"theorempath","slug":"nlp-for-psychology-text-data","title":"NLP for Psychology Text Data","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/nlp-for-psychology-text-data","prerequisites":[],"leadsTo":[]},{"id":"theorempath:nmf-nonnegative-matrix-factorization","site":"theorempath","slug":"nmf-nonnegative-matrix-factorization","title":"NMF (Nonnegative Matrix Factorization)","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/nmf-nonnegative-matrix-factorization","prerequisites":["eigenvalues-and-eigenvectors"],"leadsTo":["principal-component-analysis","k-means-clustering"]},{"id":"theorempath:no-free-lunch-theorem","site":"theorempath","slug":"no-free-lunch-theorem","title":"No-Free-Lunch Theorem","layer":"2","tier":2,"module":"learning-theory-core","url":"https://theorempath.com/topics/no-free-lunch-theorem","prerequisites":["pac-learning-framework","empirical-risk-minimization","loss-functions-catalog"],"leadsTo":["vc-dimension","bias-complexity-tradeoff"]},{"id":"theorempath:no-regret-learning","site":"theorempath","slug":"no-regret-learning","title":"No-Regret Learning","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/no-regret-learning","prerequisites":["common-probability-distributions","concentration-inequalities"],"leadsTo":["online-convex-optimization","multi-armed-bandits-theory","nash-equilibrium","self-play-and-multi-agent-rl","online-learning-and-bandits"]},{"id":"theorempath:no-u-turn-sampler-and-neals-funnel","site":"theorempath","slug":"no-u-turn-sampler-and-neals-funnel","title":"No-U-Turn Sampler and Neal's Funnel","layer":"3","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/no-u-turn-sampler-and-neals-funnel","prerequisites":["hamiltonian-monte-carlo","bayesian-estimation","burn-in-convergence-diagnostics","gibbs-sampling"],"leadsTo":["bayesian-neural-networks","bayesian-state-estimation"]},{"id":"theorempath:non-euclidean-and-hyperbolic-geometry","site":"theorempath","slug":"non-euclidean-and-hyperbolic-geometry","title":"Non-Euclidean and Hyperbolic Geometry","layer":"1","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/non-euclidean-and-hyperbolic-geometry","prerequisites":["metric-spaces-convergence-completeness","vectors-matrices-and-linear-maps"],"leadsTo":["riemannian-optimization","hyperbolic-embeddings-for-graphs","information-geometry","distance-metrics-compared"]},{"id":"theorempath:non-probability-sampling","site":"theorempath","slug":"non-probability-sampling","title":"Non-Probability Sampling","layer":"2","tier":1,"module":"applied-statistics","url":"https://theorempath.com/topics/non-probability-sampling","prerequisites":["expectation-variance-covariance-moments","law-of-large-numbers","central-limit-theorem","double-debiased-machine-learning"],"leadsTo":["double-debiased-machine-learning","weighted-conformal-prediction","convex-tinkering"]},{"id":"theorempath:nonlinear-dynamics-and-chaos-fundamentals","site":"theorempath","slug":"nonlinear-dynamics-and-chaos-fundamentals","title":"Nonlinear Dynamics and Chaos Fundamentals","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/nonlinear-dynamics-and-chaos-fundamentals","prerequisites":["classical-odes","eigenvalues-and-eigenvectors"],"leadsTo":["lyapunov-based-machine-learning-for-chaos","reservoir-computing-and-echo-state-networks","neural-odes"]},{"id":"theorempath:nonlinear-gauss-seidel","site":"theorempath","slug":"nonlinear-gauss-seidel","title":"Nonlinear Gauss-Seidel","layer":"3","tier":3,"module":"numerical-optimization","url":"https://theorempath.com/topics/nonlinear-gauss-seidel","prerequisites":["coordinate-descent","newtons-method"],"leadsTo":["augmented-lagrangian-and-admm","convex-optimization-basics"]},{"id":"theorempath:nonresponse-and-missing-data","site":"theorempath","slug":"nonresponse-and-missing-data","title":"Nonresponse and Missing Data","layer":"2","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/nonresponse-and-missing-data","prerequisites":["common-probability-distributions","design-based-vs-model-based-inference","fuzzy-matching-and-record-linkage","official-statistics-and-national-surveys","survey-sampling-methods","types-of-bias-in-statistics"],"leadsTo":["survey-sampling-methods","longitudinal-surveys-and-panel-data","imputation-in-official-statistics"]},{"id":"theorempath:normal-distribution","site":"theorempath","slug":"normal-distribution","title":"Normal Distribution","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/normal-distribution","prerequisites":["common-probability-distributions","distributions-atlas","exponential-function-properties","moment-generating-functions","integration-and-change-of-variables"],"leadsTo":["chi-squared-distribution-and-tests","student-t-distribution-and-t-test","central-limit-theorem","maximum-likelihood-estimation","linear-regression"]},{"id":"theorempath:normalization-flows","site":"theorempath","slug":"normalization-flows","title":"Normalizing Flows","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/normalization-flows","prerequisites":["common-probability-distributions","the-jacobian-matrix","variational-autoencoders"],"leadsTo":["diffusion-models","energy-based-models","continuous-normalizing-flows","deep-generative-models-for-cosmic-structures"]},{"id":"theorempath:number-theory-and-ml","site":"theorempath","slug":"number-theory-and-ml","title":"Number Theory and Machine Learning","layer":"4","tier":3,"module":"applied-math","url":"https://theorempath.com/topics/number-theory-and-ml","prerequisites":["common-probability-distributions","law-of-large-numbers","differential-privacy","peano-axioms"],"leadsTo":["differential-privacy","transformer-architecture","importance-sampling"]},{"id":"theorempath:numerical-linear-algebra","site":"theorempath","slug":"numerical-linear-algebra","title":"Numerical Linear Algebra","layer":"1","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/numerical-linear-algebra","prerequisites":["eigenvalues-and-eigenvectors","matrix-operations-and-properties"],"leadsTo":["conjugate-gradient-methods"]},{"id":"theorempath:numerical-stability","site":"theorempath","slug":"numerical-stability","title":"Numerical Stability and Conditioning","layer":"1","tier":1,"module":"foundations","url":"https://theorempath.com/topics/numerical-stability","prerequisites":["floating-point-arithmetic","matrix-operations-and-properties","matrix-norms"],"leadsTo":["conditioning-and-condition-number"]},{"id":"theorempath:nvidia-gpu-architectures","site":"theorempath","slug":"nvidia-gpu-architectures","title":"NVIDIA GPU Architectures","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/nvidia-gpu-architectures","prerequisites":["gpu-compute-model","cuda-programming-fundamentals","parallel-processing-fundamentals","running-ml-workloads-on-gpus"],"leadsTo":["flash-attention","fused-kernels"]},{"id":"theorempath:object-detection-and-segmentation","site":"theorempath","slug":"object-detection-and-segmentation","title":"Object Detection and Segmentation","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/object-detection-and-segmentation","prerequisites":["convolutional-neural-networks","hough-transform-and-circle-detection"],"leadsTo":["cnns-for-medical-imaging"]},{"id":"theorempath:occupancy-networks-and-neural-fields","site":"theorempath","slug":"occupancy-networks-and-neural-fields","title":"Occupancy Networks and Neural Fields","layer":"4","tier":3,"module":"beyond-llms","url":"https://theorempath.com/topics/occupancy-networks-and-neural-fields","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["gaussian-splatting"]},{"id":"theorempath:official-statistics-and-national-surveys","site":"theorempath","slug":"official-statistics-and-national-surveys","title":"Official Statistics and National Surveys","layer":"3","tier":3,"module":"methodology","url":"https://theorempath.com/topics/official-statistics-and-national-surveys","prerequisites":["survey-sampling-methods","prasad-rao-mse-correction","small-area-estimation"],"leadsTo":["small-area-estimation","nonresponse-and-missing-data","design-based-vs-model-based-inference"]},{"id":"theorempath:offline-reinforcement-learning","site":"theorempath","slug":"offline-reinforcement-learning","title":"Offline Reinforcement Learning","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/offline-reinforcement-learning","prerequisites":["q-learning"],"leadsTo":["policy-optimization-ppo-trpo","agentic-rl-and-tool-use"]},{"id":"theorempath:online-convex-optimization","site":"theorempath","slug":"online-convex-optimization","title":"Online Convex Optimization","layer":"3","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/online-convex-optimization","prerequisites":["convex-optimization-basics","no-regret-learning"],"leadsTo":["multi-armed-bandits-theory","stochastic-gradient-descent-convergence","mirror-descent-and-frank-wolfe"]},{"id":"theorempath:online-learning-and-bandits","site":"theorempath","slug":"online-learning-and-bandits","title":"Online Learning and Bandits","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/online-learning-and-bandits","prerequisites":["no-regret-learning","adaptive-learning-is-not-iid","test-time-training"],"leadsTo":["markov-decision-processes","policy-gradient-theorem"]},{"id":"theorempath:open-problems-in-matrix-computation","site":"theorempath","slug":"open-problems-in-matrix-computation","title":"Open Problems in Matrix Computation","layer":"3","tier":3,"module":"algorithms-foundations","url":"https://theorempath.com/topics/open-problems-in-matrix-computation","prerequisites":["matrix-multiplication-algorithms","eigenvalues-and-eigenvectors"],"leadsTo":["unsolved-problems-in-computer-science"]},{"id":"theorempath:open-problems-in-ml-theory","site":"theorempath","slug":"open-problems-in-ml-theory","title":"Open Problems in ML Theory","layer":"5","tier":3,"module":"modern-generalization","url":"https://theorempath.com/topics/open-problems-in-ml-theory","prerequisites":["implicit-bias-and-modern-generalization","scaling-laws","continuous-thought-machines","grokking","unsolved-problems-in-computer-science"],"leadsTo":[]},{"id":"theorempath:optimal-brain-surgery-and-pruning-theory","site":"theorempath","slug":"optimal-brain-surgery-and-pruning-theory","title":"Optimal Brain Surgeon and Pruning Theory","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/optimal-brain-surgery-and-pruning-theory","prerequisites":["the-hessian-matrix","feedforward-networks-and-backpropagation","iterative-magnitude-pruning-and-lottery-ticket-hypothesis"],"leadsTo":[]},{"id":"theorempath:optimal-transport-and-earth-movers-distance","site":"theorempath","slug":"optimal-transport-and-earth-movers-distance","title":"Optimal Transport and Earth Mover's Distance","layer":"3","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/optimal-transport-and-earth-movers-distance","prerequisites":["convex-duality","wasserstein-distances"],"leadsTo":[]},{"id":"theorempath:optimizer-theory-sgd-adam-muon","site":"theorempath","slug":"optimizer-theory-sgd-adam-muon","title":"Optimizer Theory: SGD, Adam, and Muon","layer":"3","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/optimizer-theory-sgd-adam-muon","prerequisites":["convex-optimization-basics","adam-optimizer","automatic-differentiation","gradient-descent-variants","information-geometry","preconditioned-optimizers","riemannian-optimization","training-dynamics-and-loss-landscapes"],"leadsTo":["scaling-laws","continual-learning-and-forgetting","distributed-training-theory","federated-learning"]},{"id":"theorempath:options-and-temporal-abstraction","site":"theorempath","slug":"options-and-temporal-abstraction","title":"Options and Temporal Abstraction","layer":"3","tier":3,"module":"rl-theory","url":"https://theorempath.com/topics/options-and-temporal-abstraction","prerequisites":["markov-decision-processes","value-iteration-and-policy-iteration","policy-representations"],"leadsTo":[]},{"id":"theorempath:order-statistics","site":"theorempath","slug":"order-statistics","title":"Order Statistics","layer":"1","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/order-statistics","prerequisites":["common-probability-distributions","triangular-distribution"],"leadsTo":["bootstrap-methods","extreme-value-theory","knn","split-conformal-prediction","winsorization"]},{"id":"theorempath:out-of-distribution-detection","site":"theorempath","slug":"out-of-distribution-detection","title":"Out-of-Distribution Detection","layer":"3","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/out-of-distribution-detection","prerequisites":["calibration-and-uncertainty","anomaly-detection-gravitational-waves","cnns-for-medical-imaging"],"leadsTo":["mechanistic-interpretability","hallucination-theory"]},{"id":"theorempath:overfitting-and-underfitting","site":"theorempath","slug":"overfitting-and-underfitting","title":"Overfitting and Underfitting","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/overfitting-and-underfitting","prerequisites":["empirical-risk-minimization","bias-variance-tradeoff"],"leadsTo":["cross-validation-theory","regularization-theory"]},{"id":"theorempath:p-hacking-and-multiple-testing","site":"theorempath","slug":"p-hacking-and-multiple-testing","title":"P-Hacking and Multiple Testing","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/p-hacking-and-multiple-testing","prerequisites":["hypothesis-testing-for-ml","meta-analysis"],"leadsTo":[]},{"id":"theorempath:pac-bayes-bounds","site":"theorempath","slug":"pac-bayes-bounds","title":"PAC-Bayes Bounds","layer":"3","tier":1,"module":"modern-generalization","url":"https://theorempath.com/topics/pac-bayes-bounds","prerequisites":["rademacher-complexity","bayesian-estimation","pac-learning-framework","sample-complexity-bounds"],"leadsTo":["algorithmic-stability","implicit-bias-and-modern-generalization"]},{"id":"theorempath:pac-learning-framework","site":"theorempath","slug":"pac-learning-framework","title":"PAC Learning Framework","layer":"1","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/pac-learning-framework","prerequisites":["concentration-inequalities","uniform-convergence","counting-and-combinatorics","hypothesis-classes-and-function-spaces","realizability-assumption","understanding-machine-learning-book","basic-logic-and-proof-techniques","sets-functions-and-relations","loss-functions","sluds-inequality"],"leadsTo":["empirical-risk-minimization","vc-dimension","glivenko-cantelli-theorem","pac-bayes-bounds","bias-complexity-tradeoff","no-free-lunch-theorem"]},{"id":"theorempath:paddleocr-and-practical-ocr","site":"theorempath","slug":"paddleocr-and-practical-ocr","title":"PaddleOCR and Practical OCR","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/paddleocr-and-practical-ocr","prerequisites":["document-intelligence","hough-transform-and-circle-detection"],"leadsTo":["donut-and-ocr-free-document-understanding","table-extraction-and-structure-recognition"]},{"id":"theorempath:pagerank-algorithm","site":"theorempath","slug":"pagerank-algorithm","title":"PageRank Algorithm","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/pagerank-algorithm","prerequisites":["eigenvalues-and-eigenvectors","graph-algorithms-essentials"],"leadsTo":["spectral-clustering","graph-neural-networks","markov-chains-and-steady-state"]},{"id":"theorempath:pandas-and-numpy-fundamentals","site":"theorempath","slug":"pandas-and-numpy-fundamentals","title":"Pandas and NumPy Fundamentals","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/pandas-and-numpy-fundamentals","prerequisites":[],"leadsTo":["tensors-and-tensor-operations","exploratory-data-analysis"]},{"id":"theorempath:parallel-processing-fundamentals","site":"theorempath","slug":"parallel-processing-fundamentals","title":"Parallel Processing Fundamentals","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/parallel-processing-fundamentals","prerequisites":["stochastic-gradient-descent-convergence","broadcast-joins-distributed-compute","dask-parallel-python","ray-distributed-python"],"leadsTo":["distributed-training-theory","nvidia-gpu-architectures"]},{"id":"theorempath:pareto-distribution","site":"theorempath","slug":"pareto-distribution","title":"Pareto Distribution","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/pareto-distribution","prerequisites":["common-probability-distributions","central-limit-theorem","law-of-large-numbers","distributions-atlas"],"leadsTo":["fat-tails","lln-failures-heavy-tails","extreme-value-theory"]},{"id":"theorempath:particle-filters","site":"theorempath","slug":"particle-filters","title":"Particle Filters","layer":"3","tier":3,"module":"applied-math","url":"https://theorempath.com/topics/particle-filters","prerequisites":["metropolis-hastings","importance-sampling","graphslam-and-factor-graphs","kalman-filter","state-space-models"],"leadsTo":[]},{"id":"theorempath:pde-fundamentals-for-ml","site":"theorempath","slug":"pde-fundamentals-for-ml","title":"PDE Fundamentals for Machine Learning","layer":"1","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/pde-fundamentals-for-ml","prerequisites":["fast-fourier-transform","eigenvalues-and-eigenvectors","stochastic-differential-equations","measure-theoretic-probability","functional-analysis-core","divergence-curl-and-line-integrals"],"leadsTo":["physics-informed-neural-networks","diffusion-models","flow-matching","neural-odes","fokker-planck-equation","navier-stokes-for-ml"]},{"id":"theorempath:peano-axioms","site":"theorempath","slug":"peano-axioms","title":"Peano Axioms","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/peano-axioms","prerequisites":[],"leadsTo":["number-theory-and-ml","foundational-dependencies"]},{"id":"theorempath:perceptron","site":"theorempath","slug":"perceptron","title":"Perceptron","layer":"1","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/perceptron","prerequisites":[],"leadsTo":["support-vector-machines","feedforward-networks-and-backpropagation","hebbian-learning"]},{"id":"theorempath:perfect-sampling","site":"theorempath","slug":"perfect-sampling","title":"Perfect Sampling","layer":"3","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/perfect-sampling","prerequisites":["metropolis-hastings","gibbs-sampling"],"leadsTo":["burn-in-convergence-diagnostics","mcmc-for-markov-random-fields"]},{"id":"theorempath:permutation-tests","site":"theorempath","slug":"permutation-tests","title":"Permutation Tests","layer":"2","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/permutation-tests","prerequisites":["hypothesis-testing-for-ml","bootstrap-methods","neyman-pearson-and-hypothesis-testing-theory"],"leadsTo":["kernel-two-sample-tests","p-hacking-and-multiple-testing","e-values-and-anytime-valid-inference"]},{"id":"theorempath:perplexity-and-language-model-evaluation","site":"theorempath","slug":"perplexity-and-language-model-evaluation","title":"Perplexity and Language Model Evaluation","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/perplexity-and-language-model-evaluation","prerequisites":["information-theory-foundations","bits-nats-perplexity-bpb","log-probability-computation"],"leadsTo":[]},{"id":"theorempath:physics-informed-neural-networks","site":"theorempath","slug":"physics-informed-neural-networks","title":"Physics-Informed Neural Networks","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/physics-informed-neural-networks","prerequisites":["the-jacobian-matrix","automatic-differentiation","feedforward-networks-and-backpropagation","gradient-descent-variants","classical-odes","divergence-curl-and-line-integrals","kolmogorov-arnold-networks","pde-fundamentals-for-ml","symbolic-regression-and-equation-discovery"],"leadsTo":["deep-bsde-method","lyapunov-based-machine-learning-for-chaos","navier-stokes-for-ml"]},{"id":"theorempath:plan-then-generate","site":"theorempath","slug":"plan-then-generate","title":"Plan-then-Generate","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/plan-then-generate","prerequisites":["transformer-architecture"],"leadsTo":[]},{"id":"theorempath:poisson-distribution","site":"theorempath","slug":"poisson-distribution","title":"Poisson Distribution","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/poisson-distribution","prerequisites":["common-probability-distributions","distributions-atlas","exponential-distribution"],"leadsTo":["chi-squared-distribution-and-tests","naive-bayes","gamma-distribution","bayesian-estimation"]},{"id":"theorempath:poisson-limit-theorem","site":"theorempath","slug":"poisson-limit-theorem","title":"Poisson Limit Theorem and Le Cam's Bound","layer":"1","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/poisson-limit-theorem","prerequisites":["common-probability-distributions","characteristic-functions","moment-generating-functions"],"leadsTo":["central-limit-theorem","de-moivre-laplace-theorem","characteristic-functions"]},{"id":"theorempath:policy-gradient-theorem","site":"theorempath","slug":"policy-gradient-theorem","title":"Policy Gradient Theorem","layer":"3","tier":1,"module":"rl-theory","url":"https://theorempath.com/topics/policy-gradient-theorem","prerequisites":["markov-decision-processes","convex-optimization-basics","multi-armed-bandits-theory","online-learning-and-bandits","q-learning","td-learning","value-iteration-and-policy-iteration"],"leadsTo":["actor-critic-methods","policy-optimization-ppo-trpo","rlhf-and-alignment","agentic-rl-and-tool-use","ddpg","deep-rl-for-control","dpo-vs-grpo-vs-rl-reasoning","multi-agent-collaboration","reinforcement-learning-for-drug-discovery","reinforcement-learning-for-synthesis-planning","reinforcement-learning-from-human-feedback-deep-dive","reward-systems-and-reinforcement-learning-neuroscience","td3"]},{"id":"theorempath:policy-optimization-ppo-trpo","site":"theorempath","slug":"policy-optimization-ppo-trpo","title":"Policy Optimization: PPO and TRPO","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/policy-optimization-ppo-trpo","prerequisites":["policy-gradient-theorem","actor-critic-methods","ddpg","offline-reinforcement-learning","td3"],"leadsTo":["dpo-vs-grpo-vs-rl-reasoning","post-training-overview"]},{"id":"theorempath:policy-representations","site":"theorempath","slug":"policy-representations","title":"Policy Representations","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/policy-representations","prerequisites":["markov-decision-processes"],"leadsTo":["options-and-temporal-abstraction"]},{"id":"theorempath:positional-encoding","site":"theorempath","slug":"positional-encoding","title":"Positional Encoding","layer":"4","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/positional-encoding","prerequisites":["attention-mechanism-theory","attention-is-all-you-need-paper","attention-mechanisms-history"],"leadsTo":[]},{"id":"theorempath:positive-semidefinite-matrices","site":"theorempath","slug":"positive-semidefinite-matrices","title":"Positive Semidefinite Matrices","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/positive-semidefinite-matrices","prerequisites":["eigenvalues-and-eigenvectors"],"leadsTo":["convex-optimization-basics","principal-component-analysis","fisher-information","gaussian-splatting","multivariate-normal-distribution"]},{"id":"theorempath:post-training-overview","site":"theorempath","slug":"post-training-overview","title":"Post-Training Overview","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/post-training-overview","prerequisites":["rlhf-and-alignment","transformer-architecture","agentic-rl-and-tool-use","bert-and-pretrain-finetune-paradigm","policy-optimization-ppo-trpo","test-time-compute-and-search"],"leadsTo":["dpo-vs-grpo-vs-rl-reasoning","reward-models-and-verifiers","test-time-compute-and-search","gpt-series-evolution","llama-and-open-weight-models","reasoning-data-curation"]},{"id":"theorempath:prasad-rao-mse-correction","site":"theorempath","slug":"prasad-rao-mse-correction","title":"Prasad-Rao MSE Correction","layer":"4","tier":2,"module":"methodology","url":"https://theorempath.com/topics/prasad-rao-mse-correction","prerequisites":["small-area-estimation","expectation-variance-covariance-moments","reml-and-variance-component-estimation"],"leadsTo":["reml-and-variance-component-estimation","adjusted-density-maximization","official-statistics-and-national-surveys"]},{"id":"theorempath:preconditioned-optimizers","site":"theorempath","slug":"preconditioned-optimizers","title":"Preconditioned Optimizers: Shampoo, K-FAC, and Natural Gradient","layer":"3","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/preconditioned-optimizers","prerequisites":["convex-optimization-basics","fisher-information","the-hessian-matrix","conjugate-gradient-methods"],"leadsTo":["riemannian-optimization","optimizer-theory-sgd-adam-muon"]},{"id":"theorempath:predictive-coding-and-autoencoders-in-the-brain","site":"theorempath","slug":"predictive-coding-and-autoencoders-in-the-brain","title":"Predictive Coding and Autoencoders in the Brain","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/predictive-coding-and-autoencoders-in-the-brain","prerequisites":["autoencoders","variational-autoencoders","kl-divergence","reward-systems-and-reinforcement-learning-neuroscience","sparse-coding-and-efficient-coding","spiking-neural-networks"],"leadsTo":["hebbian-learning","spiking-neural-networks","reward-systems-and-reinforcement-learning-neuroscience"]},{"id":"theorempath:prefix-caching","site":"theorempath","slug":"prefix-caching","title":"Prefix Caching","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/prefix-caching","prerequisites":["kv-cache","kv-cache-optimization"],"leadsTo":[]},{"id":"theorempath:principal-component-analysis","site":"theorempath","slug":"principal-component-analysis","title":"Principal Component Analysis","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/principal-component-analysis","prerequisites":["eigenvalues-and-eigenvectors","singular-value-decomposition","gram-matrices-and-kernel-matrices","high-dimensional-covariance-estimation","nmf-nonnegative-matrix-factorization","positive-semidefinite-matrices","tensors-and-tensor-operations"],"leadsTo":["random-matrix-theory-overview","autoencoders-for-low-dimensional-dynamical-structures","dimensionality-reduction-theory","mechanistic-interpretability","tsne-and-umap","whitening-and-decorrelation"]},{"id":"theorempath:probability-flow-ode","site":"theorempath","slug":"probability-flow-ode","title":"Probability Flow ODE","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/probability-flow-ode","prerequisites":["stochastic-differential-equations","fokker-planck-equation","score-matching","time-reversal-of-sdes"],"leadsTo":["diffusion-models","score-matching","time-reversal-of-sdes"]},{"id":"theorempath:projected-gradient-descent","site":"theorempath","slug":"projected-gradient-descent","title":"Projected Gradient Descent","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/projected-gradient-descent","prerequisites":["convex-optimization-basics"],"leadsTo":["mirror-descent-and-frank-wolfe","augmented-lagrangian-and-admm"]},{"id":"theorempath:prompt-engineering-and-in-context-learning","site":"theorempath","slug":"prompt-engineering-and-in-context-learning","title":"Prompt Engineering and In-Context Learning","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/prompt-engineering-and-in-context-learning","prerequisites":["transformer-architecture"],"leadsTo":["context-engineering","hallucination-theory","chain-of-thought-and-reasoning","gpt-series-evolution","tabular-foundation-models-bayesian-inference","tool-augmented-reasoning"]},{"id":"theorempath:proof-theory-and-cut-elimination","site":"theorempath","slug":"proof-theory-and-cut-elimination","title":"Proof Theory and Cut-Elimination","layer":"2","tier":3,"module":"foundations","url":"https://theorempath.com/topics/proof-theory-and-cut-elimination","prerequisites":["basic-logic-and-proof-techniques","tactics-vs-proof-terms","theorem-proving-in-coq","theorem-proving-in-lean","type-theory"],"leadsTo":["dependent-type-theory"]},{"id":"theorempath:proper-scoring-rules","site":"theorempath","slug":"proper-scoring-rules","title":"Proper Scoring Rules","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/proper-scoring-rules","prerequisites":["evaluation-metrics-and-properties","roc-curve-and-auc"],"leadsTo":["cross-validation-theory"]},{"id":"theorempath:prospect-theory","site":"theorempath","slug":"prospect-theory","title":"Prospect Theory","layer":"3","tier":2,"module":"decision-theory","url":"https://theorempath.com/topics/prospect-theory","prerequisites":["expected-utility","common-probability-distributions"],"leadsTo":[]},{"id":"theorempath:proximal-gradient-methods","site":"theorempath","slug":"proximal-gradient-methods","title":"Proximal Gradient Methods","layer":"2","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/proximal-gradient-methods","prerequisites":["convex-optimization-basics","quasi-newton-methods","subgradients-and-subdifferentials"],"leadsTo":["coordinate-descent","stochastic-gradient-descent-convergence"]},{"id":"theorempath:public-key-cryptography","site":"theorempath","slug":"public-key-cryptography","title":"Public-Key Cryptography","layer":"2","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/public-key-cryptography","prerequisites":["sets-functions-and-relations","common-probability-distributions","hash-functions"],"leadsTo":["zero-knowledge-proofs"]},{"id":"theorempath:python-for-ml-research","site":"theorempath","slug":"python-for-ml-research","title":"Python for ML Research","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/python-for-ml-research","prerequisites":[],"leadsTo":["reproducibility-and-experimental-rigor"]},{"id":"theorempath:q-learning","site":"theorempath","slug":"q-learning","title":"Q-Learning","layer":"2","tier":1,"module":"rl-theory","url":"https://theorempath.com/topics/q-learning","prerequisites":["value-iteration-and-policy-iteration","bellman-equations","stochastic-approximation-theory","td-learning"],"leadsTo":["policy-gradient-theorem","actor-critic-methods","ddpg","offline-reinforcement-learning","td3"]},{"id":"theorempath:quantization-theory","site":"theorempath","slug":"quantization-theory","title":"Quantization Theory","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/quantization-theory","prerequisites":["matrix-operations-and-properties","eigenvalues-and-eigenvectors","matrix-calculus","feedforward-networks-and-backpropagation","softmax-and-numerical-stability","iterative-magnitude-pruning-and-lottery-ticket-hypothesis"],"leadsTo":[]},{"id":"theorempath:quantum-machine-learning-overview","site":"theorempath","slug":"quantum-machine-learning-overview","title":"Quantum Machine Learning Overview","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/quantum-machine-learning-overview","prerequisites":[],"leadsTo":[]},{"id":"theorempath:quasi-newton-methods","site":"theorempath","slug":"quasi-newton-methods","title":"Quasi-Newton Methods","layer":"2","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/quasi-newton-methods","prerequisites":["newtons-method","line-search-methods","secant-method"],"leadsTo":["proximal-gradient-methods"]},{"id":"theorempath:qwen-and-chinese-models","site":"theorempath","slug":"qwen-and-chinese-models","title":"Qwen and Chinese Models","layer":"5","tier":3,"module":"model-timeline","url":"https://theorempath.com/topics/qwen-and-chinese-models","prerequisites":["transformer-architecture"],"leadsTo":["model-comparison-table"]},{"id":"theorempath:rademacher-complexity","site":"theorempath","slug":"rademacher-complexity","title":"Rademacher Complexity","layer":"3","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/rademacher-complexity","prerequisites":["empirical-risk-minimization","vc-dimension","concentration-inequalities","glivenko-cantelli-theorem","hypothesis-classes-and-function-spaces","mcdiarmids-inequality","subgaussian-random-variables","understanding-machine-learning-book","uniform-convergence"],"leadsTo":["algorithmic-stability","contraction-inequality","empirical-processes-and-chaining","implicit-bias-and-modern-generalization","kernels-and-rkhs","pac-bayes-bounds","symmetrization-inequality"]},{"id":"theorempath:radon-nikodym-and-conditional-expectation","site":"theorempath","slug":"radon-nikodym-and-conditional-expectation","title":"Radon-Nikodym and Conditional Expectation","layer":"0B","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/radon-nikodym-and-conditional-expectation","prerequisites":["measure-theoretic-probability"],"leadsTo":["maximum-likelihood-estimation","importance-sampling","concentration-inequalities","adaptive-learning-is-not-iid","weighted-conformal-prediction"]},{"id":"theorempath:random-forests","site":"theorempath","slug":"random-forests","title":"Random Forests","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/random-forests","prerequisites":["decision-trees-and-ensembles","bootstrap-methods","bagging"],"leadsTo":["gradient-boosting","cross-validation-theory"]},{"id":"theorempath:random-matrix-theory-overview","site":"theorempath","slug":"random-matrix-theory-overview","title":"Random Matrix Theory Overview","layer":"4","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/random-matrix-theory-overview","prerequisites":["matrix-concentration","epsilon-nets-and-covering-numbers","measure-theoretic-probability","inner-product-spaces-and-orthogonality","hanson-wright-inequality","principal-component-analysis"],"leadsTo":["implicit-bias-and-modern-generalization","double-descent","benign-overfitting"]},{"id":"theorempath:random-variables","site":"theorempath","slug":"random-variables","title":"Random Variables","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/random-variables","prerequisites":["kolmogorov-probability-axioms","sets-functions-and-relations"],"leadsTo":["expectation-variance-covariance-moments","common-probability-distributions","triangular-distribution","joint-marginal-conditional-distributions","measure-theoretic-probability","adaptive-learning-is-not-iid","law-of-large-numbers","loss-functions"]},{"id":"theorempath:rao-blackwellization","site":"theorempath","slug":"rao-blackwellization","title":"Rao-Blackwellization","layer":"2","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/rao-blackwellization","prerequisites":["sufficient-statistics-and-exponential-families","importance-sampling"],"leadsTo":[]},{"id":"theorempath:ray-distributed-python","site":"theorempath","slug":"ray-distributed-python","title":"Ray Distributed Python","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/ray-distributed-python","prerequisites":[],"leadsTo":["distributed-training-theory","parallel-processing-fundamentals"]},{"id":"theorempath:realizability-assumption","site":"theorempath","slug":"realizability-assumption","title":"Realizability Assumption","layer":"2","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/realizability-assumption","prerequisites":["empirical-risk-minimization","hypothesis-classes-and-function-spaces"],"leadsTo":["pac-learning-framework","uniform-convergence","sample-complexity-bounds"]},{"id":"theorempath:reasoning-data-curation","site":"theorempath","slug":"reasoning-data-curation","title":"Reasoning Data Curation","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/reasoning-data-curation","prerequisites":["post-training-overview","alphaproof-and-ai-theorem-proving","synthetic-data-distillation"],"leadsTo":["dpo-vs-grpo-vs-rl-reasoning","reward-models-and-verifiers"]},{"id":"theorempath:recommender-systems","site":"theorempath","slug":"recommender-systems","title":"Recommender Systems","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/recommender-systems","prerequisites":["eigenvalues-and-eigenvectors"],"leadsTo":[]},{"id":"theorempath:recurrent-neural-networks","site":"theorempath","slug":"recurrent-neural-networks","title":"Recurrent Neural Networks","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/recurrent-neural-networks","prerequisites":["feedforward-networks-and-backpropagation","convolutional-neural-networks","macroeconomic-time-series-forecasting"],"leadsTo":["transformer-architecture","attention-mechanisms-history","deep-learning-time-series","fox-forget-gate","mamba-and-state-space-models","reservoir-computing-and-echo-state-networks","rnns-for-signal-sequences","speech-and-audio-ml","test-time-training"]},{"id":"theorempath:red-teaming-and-adversarial-eval","site":"theorempath","slug":"red-teaming-and-adversarial-eval","title":"Red-Teaming and Adversarial Evaluation","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/red-teaming-and-adversarial-eval","prerequisites":["rlhf-and-alignment","calibration-and-uncertainty"],"leadsTo":[]},{"id":"theorempath:regularization-in-practice","site":"theorempath","slug":"regularization-in-practice","title":"Regularization in Practice","layer":"2","tier":1,"module":"training-techniques","url":"https://theorempath.com/topics/regularization-in-practice","prerequisites":["regularization-theory","cross-entropy-loss-deep-dive"],"leadsTo":["batch-normalization","data-augmentation-theory"]},{"id":"theorempath:regularization-theory","site":"theorempath","slug":"regularization-theory","title":"Regularization Theory","layer":"2","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/regularization-theory","prerequisites":["convex-optimization-basics","bias-variance-tradeoff","adaboost","convex-duality","elastic-net","gradient-boosting","overfitting-and-underfitting","xgboost","bias-complexity-tradeoff","maximum-a-posteriori-estimation"],"leadsTo":["algorithmic-stability","kernels-and-rkhs","grokking","regularization-in-practice"]},{"id":"theorempath:reinforcement-learning-environments-and-benchmarks","site":"theorempath","slug":"reinforcement-learning-environments-and-benchmarks","title":"Reinforcement Learning Environments and Benchmarks","layer":"3","tier":3,"module":"rl-theory","url":"https://theorempath.com/topics/reinforcement-learning-environments-and-benchmarks","prerequisites":["markov-decision-processes","deep-rl-for-control"],"leadsTo":[]},{"id":"theorempath:reinforcement-learning-for-auction-design","site":"theorempath","slug":"reinforcement-learning-for-auction-design","title":"Reinforcement Learning for Auction Design","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/reinforcement-learning-for-auction-design","prerequisites":["auction-theory","mechanism-design"],"leadsTo":["markov-games-and-self-play","policy-gradient-theorem"]},{"id":"theorempath:reinforcement-learning-for-drug-discovery","site":"theorempath","slug":"reinforcement-learning-for-drug-discovery","title":"Reinforcement Learning for Drug Discovery","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/reinforcement-learning-for-drug-discovery","prerequisites":["policy-gradient-theorem","markov-decision-processes"],"leadsTo":["exploration-vs-exploitation","reward-design"]},{"id":"theorempath:reinforcement-learning-for-synthesis-planning","site":"theorempath","slug":"reinforcement-learning-for-synthesis-planning","title":"Reinforcement Learning for Synthesis Planning","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/reinforcement-learning-for-synthesis-planning","prerequisites":["markov-decision-processes","policy-gradient-theorem"],"leadsTo":["reinforcement-learning-from-human-feedback-deep-dive"]},{"id":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","site":"theorempath","slug":"reinforcement-learning-from-human-feedback-deep-dive","title":"Reinforcement Learning from Human Feedback","layer":"5","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/reinforcement-learning-from-human-feedback-deep-dive","prerequisites":["policy-gradient-theorem","rlhf-and-alignment","reinforcement-learning-for-synthesis-planning","reward-design"],"leadsTo":["dpo-vs-grpo-vs-rl-reasoning","constitutional-ai","hallucination-theory","ineffable-intelligence"]},{"id":"theorempath:rejection-sampling","site":"theorempath","slug":"rejection-sampling","title":"Rejection Sampling","layer":"1","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/rejection-sampling","prerequisites":["monte-carlo-methods"],"leadsTo":["adaptive-rejection-sampling","importance-sampling","squeezed-rejection-sampling"]},{"id":"theorempath:relational-algebra","site":"theorempath","slug":"relational-algebra","title":"Relational Algebra","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/relational-algebra","prerequisites":["sets-functions-and-relations","basic-logic-and-proof-techniques"],"leadsTo":[]},{"id":"theorempath:reml-and-variance-component-estimation","site":"theorempath","slug":"reml-and-variance-component-estimation","title":"REML and Variance Component Estimation","layer":"2","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/reml-and-variance-component-estimation","prerequisites":["maximum-likelihood-estimation","linear-regression","expectation-variance-covariance-moments"],"leadsTo":["small-area-estimation","meta-analysis","prasad-rao-mse-correction","adjusted-density-maximization"]},{"id":"theorempath:representation-learning-in-cosmology","site":"theorempath","slug":"representation-learning-in-cosmology","title":"Representation Learning in Cosmology","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/representation-learning-in-cosmology","prerequisites":["contrastive-learning","self-supervised-vision"],"leadsTo":["representation-learning-theory","transfer-learning"]},{"id":"theorempath:representation-learning-theory","site":"theorempath","slug":"representation-learning-theory","title":"Representation Learning Theory","layer":"3","tier":2,"module":"modern-generalization","url":"https://theorempath.com/topics/representation-learning-theory","prerequisites":["information-theory-foundations","variational-autoencoders","equivariant-deep-learning","hyperbolic-embeddings-for-graphs","representation-learning-in-cosmology"],"leadsTo":[]},{"id":"theorempath:reproducibility-and-experimental-rigor","site":"theorempath","slug":"reproducibility-and-experimental-rigor","title":"Reproducibility and Experimental Rigor","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/reproducibility-and-experimental-rigor","prerequisites":["git-and-gitlab-for-ml-research","python-for-ml-research","weights-and-biases-experiment-tracking"],"leadsTo":["ablation-study-design","hypothesis-testing-for-ml","benchmarking-methodology","experiment-tracking-and-tooling"]},{"id":"theorempath:reservoir-computing-and-echo-state-networks","site":"theorempath","slug":"reservoir-computing-and-echo-state-networks","title":"Reservoir Computing and Echo State Networks","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/reservoir-computing-and-echo-state-networks","prerequisites":["recurrent-neural-networks","autoencoders-for-low-dimensional-dynamical-structures","lyapunov-based-machine-learning-for-chaos","nonlinear-dynamics-and-chaos-fundamentals","symbolic-regression-and-equation-discovery"],"leadsTo":["mamba-and-state-space-models"]},{"id":"theorempath:residual-stream-and-transformer-internals","site":"theorempath","slug":"residual-stream-and-transformer-internals","title":"Residual Stream and Transformer Internals","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/residual-stream-and-transformer-internals","prerequisites":["transformer-architecture","fox-forget-gate","gradient-flow-and-vanishing-gradients"],"leadsTo":["mechanistic-interpretability","induction-heads","sparse-autoencoders","truth-directions-and-linear-probes"]},{"id":"theorempath:restricted-isometry-property","site":"theorempath","slug":"restricted-isometry-property","title":"Restricted Isometry Property","layer":"3","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/restricted-isometry-property","prerequisites":["subgaussian-random-variables"],"leadsTo":[]},{"id":"theorempath:reversible-jump-mcmc","site":"theorempath","slug":"reversible-jump-mcmc","title":"Reversible Jump MCMC","layer":"3","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/reversible-jump-mcmc","prerequisites":["metropolis-hastings"],"leadsTo":[]},{"id":"theorempath:reward-design","site":"theorempath","slug":"reward-design","title":"Reward Design and Reward Misspecification","layer":"3","tier":1,"module":"rl-theory","url":"https://theorempath.com/topics/reward-design","prerequisites":["markov-decision-processes","bellman-equations","reinforcement-learning-for-drug-discovery"],"leadsTo":["reward-hacking","reinforcement-learning-from-human-feedback-deep-dive"]},{"id":"theorempath:reward-hacking","site":"theorempath","slug":"reward-hacking","title":"Reward Hacking","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/reward-hacking","prerequisites":["reward-models-and-verifiers","rlhf-and-alignment","hallucination-theory","reward-design"],"leadsTo":["constitutional-ai"]},{"id":"theorempath:reward-models-and-verifiers","site":"theorempath","slug":"reward-models-and-verifiers","title":"Reward Models and Verifiers","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/reward-models-and-verifiers","prerequisites":["rlhf-and-alignment","post-training-overview","reasoning-data-curation","test-time-compute-and-search"],"leadsTo":["test-time-compute-and-search","dpo-vs-grpo-vs-rl-reasoning","reward-hacking","verifier-design-and-process-reward"]},{"id":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","site":"theorempath","slug":"reward-systems-and-reinforcement-learning-neuroscience","title":"Reward Systems and Reinforcement Learning Neuroscience","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/reward-systems-and-reinforcement-learning-neuroscience","prerequisites":["td-learning","markov-decision-processes","policy-gradient-theorem"],"leadsTo":["predictive-coding-and-autoencoders-in-the-brain","model-based-rl","actor-critic-methods"]},{"id":"theorempath:ridge-regression","site":"theorempath","slug":"ridge-regression","title":"Ridge Regression","layer":"1","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/ridge-regression","prerequisites":["linear-regression","convex-optimization-basics","shrinkage-estimation-james-stein","elements-of-statistical-learning-book","gauss-markov-theorem","maximum-a-posteriori-estimation"],"leadsTo":["lasso-regression","elastic-net","kernels-and-rkhs","neural-tangent-kernel","double-descent","benign-overfitting","bayesian-linear-regression","gaussian-processes-for-ml","gaussian-processes-regression","kernel-trick"]},{"id":"theorempath:riemannian-optimization","site":"theorempath","slug":"riemannian-optimization","title":"Riemannian Optimization and Manifold Constraints","layer":"3","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/riemannian-optimization","prerequisites":["convex-optimization-basics","the-hessian-matrix","eigenvalues-and-eigenvectors","equivariant-deep-learning","hyperbolic-embeddings-for-graphs","non-euclidean-and-hyperbolic-geometry","preconditioned-optimizers","tsne-and-umap"],"leadsTo":["optimizer-theory-sgd-adam-muon","second-order-optimization-methods"]},{"id":"theorempath:rl-for-wargaming-simulations","site":"theorempath","slug":"rl-for-wargaming-simulations","title":"RL for Wargaming and Simulations","layer":"3","tier":3,"module":"ml-applications","url":"https://theorempath.com/topics/rl-for-wargaming-simulations","prerequisites":[],"leadsTo":[]},{"id":"theorempath:rlhf-and-alignment","site":"theorempath","slug":"rlhf-and-alignment","title":"RLHF and Alignment","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/rlhf-and-alignment","prerequisites":["policy-gradient-theorem","markov-decision-processes","actor-critic-methods","fine-tuning-and-adaptation","transformer-architecture"],"leadsTo":["hallucination-theory","mechanistic-interpretability","constitutional-ai","dpo-vs-grpo-vs-rl-reasoning","gpt-series-evolution","llm-application-security","post-training-overview","red-teaming-and-adversarial-eval","reinforcement-learning-from-human-feedback-deep-dive","reward-hacking","reward-models-and-verifiers"]},{"id":"theorempath:rnns-for-signal-sequences","site":"theorempath","slug":"rnns-for-signal-sequences","title":"RNNs for Signal Sequences","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/rnns-for-signal-sequences","prerequisites":["recurrent-neural-networks","signals-and-systems-for-ml"],"leadsTo":["transformer-architecture","signal-detection-theory"]},{"id":"theorempath:robust-adversarial-policies","site":"theorempath","slug":"robust-adversarial-policies","title":"Robust Adversarial Policies","layer":"4","tier":3,"module":"rl-theory","url":"https://theorempath.com/topics/robust-adversarial-policies","prerequisites":["markov-decision-processes","minimax-lower-bounds"],"leadsTo":[]},{"id":"theorempath:robust-statistics-and-m-estimators","site":"theorempath","slug":"robust-statistics-and-m-estimators","title":"Robust Statistics and M-Estimators","layer":"3","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/robust-statistics-and-m-estimators","prerequisites":["maximum-likelihood-estimation","minimax-saddle-points","skewness-kurtosis-and-higher-moments","winsorization"],"leadsTo":["empirical-risk-minimization","hypothesis-testing-for-ml"]},{"id":"theorempath:roc-curve-and-auc","site":"theorempath","slug":"roc-curve-and-auc","title":"ROC Curve and AUC","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/roc-curve-and-auc","prerequisites":["confusion-matrices-and-classification-metrics","common-probability-distributions"],"leadsTo":["proper-scoring-rules","calibration-and-uncertainty"]},{"id":"theorempath:running-ml-workloads-on-gpus","site":"theorempath","slug":"running-ml-workloads-on-gpus","title":"Running ML Workloads on GPUs","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/running-ml-workloads-on-gpus","prerequisites":["gpu-compute-model"],"leadsTo":["distributed-training-theory","nvidia-gpu-architectures","mixed-precision-training"]},{"id":"theorempath:sample-complexity-bounds","site":"theorempath","slug":"sample-complexity-bounds","title":"Sample Complexity Bounds","layer":"2","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/sample-complexity-bounds","prerequisites":["vc-dimension","realizability-assumption"],"leadsTo":["algorithmic-stability","pac-bayes-bounds"]},{"id":"theorempath:sample-size-determination","site":"theorempath","slug":"sample-size-determination","title":"Sample Size Determination","layer":"2","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/sample-size-determination","prerequisites":["hypothesis-testing-for-ml","common-probability-distributions","survey-sampling-methods"],"leadsTo":["survey-sampling-methods","types-of-bias-in-statistics"]},{"id":"theorempath:scale-location-shape-parameters","site":"theorempath","slug":"scale-location-shape-parameters","title":"Scale, Location, and Shape Parameters","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/scale-location-shape-parameters","prerequisites":["common-probability-distributions","expectation-variance-covariance-moments"],"leadsTo":["moment-generating-functions","method-of-moments","sufficient-statistics-and-exponential-families","multivariate-distributions-atlas"]},{"id":"theorempath:scaling-compute-optimal-training","site":"theorempath","slug":"scaling-compute-optimal-training","title":"Scaling Compute-Optimal Training","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/scaling-compute-optimal-training","prerequisites":["scaling-laws"],"leadsTo":[]},{"id":"theorempath:scaling-laws","site":"theorempath","slug":"scaling-laws","title":"Scaling Laws","layer":"4","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/scaling-laws","prerequisites":["convex-optimization-basics","data-contamination-and-evaluation","distributed-training-theory","history-of-ai","ineffable-intelligence","inference-systems-overview","lazy-vs-feature-learning","optimizer-theory-sgd-adam-muon"],"leadsTo":["chain-of-thought-and-reasoning","scaling-compute-optimal-training","gpt-series-evolution","inference-time-scaling-laws","llama-and-open-weight-models","open-problems-in-ml-theory","test-time-compute-and-search"]},{"id":"theorempath:score-matching","site":"theorempath","slug":"score-matching","title":"Score Matching","layer":"3","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/score-matching","prerequisites":["stochastic-differential-equations","fokker-planck-equation","expectation-variance-covariance-moments","fisher-information","deep-generative-models-for-cosmic-structures","stochastic-calculus-for-ml","time-reversal-of-sdes"],"leadsTo":["diffusion-models","time-reversal-of-sdes","langevin-dynamics","energy-based-models","probability-flow-ode"]},{"id":"theorempath:secant-method","site":"theorempath","slug":"secant-method","title":"Secant Method","layer":"1","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/secant-method","prerequisites":["newtons-method"],"leadsTo":["quasi-newton-methods"]},{"id":"theorempath:second-order-optimization-methods","site":"theorempath","slug":"second-order-optimization-methods","title":"Second-Order Optimization Methods","layer":"3","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/second-order-optimization-methods","prerequisites":["newtons-method","the-hessian-matrix","conjugate-gradient-methods","equilibrium-and-implicit-models","riemannian-optimization","trust-region-methods"],"leadsTo":[]},{"id":"theorempath:self-organizing-maps","site":"theorempath","slug":"self-organizing-maps","title":"Self-Organizing Maps","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/self-organizing-maps","prerequisites":[],"leadsTo":["tsne-and-umap","k-means-clustering"]},{"id":"theorempath:self-play-and-multi-agent-rl","site":"theorempath","slug":"self-play-and-multi-agent-rl","title":"Self-Play and Multi-Agent RL","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/self-play-and-multi-agent-rl","prerequisites":["markov-decision-processes","agent-based-modeling-with-ml","no-regret-learning"],"leadsTo":[]},{"id":"theorempath:self-supervised-vision","site":"theorempath","slug":"self-supervised-vision","title":"Self-Supervised Vision","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/self-supervised-vision","prerequisites":["vision-transformer-lineage","attention-for-protein-structure-alphafold","cnns-for-signal-feature-extraction"],"leadsTo":["jepa-and-joint-embedding","data-augmentation-theory","florence-and-vision-foundation-models","representation-learning-in-cosmology"]},{"id":"theorempath:semantic-search-and-embeddings","site":"theorempath","slug":"semantic-search-and-embeddings","title":"Semantic Search and Embeddings","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/semantic-search-and-embeddings","prerequisites":["word-embeddings","inner-product-spaces-and-orthogonality","information-retrieval","fuzzy-matching-and-record-linkage","knn"],"leadsTo":["multimodal-rag","context-engineering"]},{"id":"theorempath:sequences-and-series-of-functions","site":"theorempath","slug":"sequences-and-series-of-functions","title":"Sequences and Series of Functions","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/sequences-and-series-of-functions","prerequisites":["metric-spaces-convergence-completeness"],"leadsTo":["empirical-risk-minimization","uniform-convergence"]},{"id":"theorempath:sets-functions-and-relations","site":"theorempath","slug":"sets-functions-and-relations","title":"Sets, Functions, and Relations","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/sets-functions-and-relations","prerequisites":["basic-logic-and-proof-techniques"],"leadsTo":["vectors-matrices-and-linear-maps","metric-spaces-convergence-completeness","measure-theoretic-probability","cardinality-and-countability","arrows-impossibility","category-theory","common-probability-distributions","differentiation-in-rn","dynamic-programming","graph-algorithms-essentials","hash-functions","kolmogorov-probability-axioms","matrix-operations-and-properties","public-key-cryptography","random-variables","relational-algebra","concentration-inequalities","hoeffdings-lemma","pac-learning-framework","uniform-convergence","vc-dimension"]},{"id":"theorempath:sgd-as-sde","site":"theorempath","slug":"sgd-as-sde","title":"SGD as a Stochastic Differential Equation","layer":"3","tier":2,"module":"optimization","url":"https://theorempath.com/topics/sgd-as-sde","prerequisites":["stochastic-differential-equations","stochastic-gradient-descent-convergence","fokker-planck-equation","stochastic-calculus-for-ml"],"leadsTo":["langevin-dynamics","implicit-bias-and-modern-generalization","fokker-planck-equation"]},{"id":"theorempath:shrinkage-estimation-james-stein","site":"theorempath","slug":"shrinkage-estimation-james-stein","title":"Shrinkage Estimation and the James-Stein Estimator: Inadmissibility, SURE, and Brown's Characterization","layer":"0B","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/shrinkage-estimation-james-stein","prerequisites":["maximum-likelihood-estimation","cramer-rao-bound","minimax-lower-bounds"],"leadsTo":["bayesian-estimation","ridge-regression","minimax-lower-bounds","empirical-bayes-vs-hierarchical-bayes","steins-paradox"]},{"id":"theorempath:signal-detection-theory","site":"theorempath","slug":"signal-detection-theory","title":"Signal Detection Theory","layer":"2","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/signal-detection-theory","prerequisites":["common-probability-distributions","hypothesis-testing-for-ml","rnns-for-signal-sequences"],"leadsTo":["confusion-matrices-and-classification-metrics","anomaly-detection-gravitational-waves"]},{"id":"theorempath:signals-and-systems-for-ml","site":"theorempath","slug":"signals-and-systems-for-ml","title":"Signals and Systems for ML","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/signals-and-systems-for-ml","prerequisites":[],"leadsTo":["convolutional-neural-networks","cnns-for-signal-feature-extraction","hough-transform-and-circle-detection","rnns-for-signal-sequences","speech-and-audio-ml","svm-for-rf-classification","wavelet-smoothing"]},{"id":"theorempath:simpsons-paradox","site":"theorempath","slug":"simpsons-paradox","title":"Simpson's Paradox","layer":"1","tier":2,"module":"methodology","url":"https://theorempath.com/topics/simpsons-paradox","prerequisites":["causal-inference-basics"],"leadsTo":["base-rate-fallacy","statistical-paradoxes-collection"]},{"id":"theorempath:singular-value-decomposition","site":"theorempath","slug":"singular-value-decomposition","title":"Singular Value Decomposition","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/singular-value-decomposition","prerequisites":["eigenvalues-and-eigenvectors","linear-independence","matrix-norms","matrix-operations-and-properties"],"leadsTo":["principal-component-analysis","conditioning-and-condition-number","distributional-semantics","word-embeddings"]},{"id":"theorempath:skewness-kurtosis-and-higher-moments","site":"theorempath","slug":"skewness-kurtosis-and-higher-moments","title":"Skewness, Kurtosis, and Higher Moments","layer":"1","tier":1,"module":"foundations","url":"https://theorempath.com/topics/skewness-kurtosis-and-higher-moments","prerequisites":["common-probability-distributions","expectation-variance-covariance-moments"],"leadsTo":["subgaussian-random-variables","concentration-inequalities","robust-statistics-and-m-estimators"]},{"id":"theorempath:skip-connections-and-resnets","site":"theorempath","slug":"skip-connections-and-resnets","title":"Skip Connections and ResNets","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/skip-connections-and-resnets","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["batch-normalization","convolutional-neural-networks","equilibrium-and-implicit-models","neural-odes"]},{"id":"theorempath:slice-sampling","site":"theorempath","slug":"slice-sampling","title":"Slice Sampling","layer":"2","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/slice-sampling","prerequisites":["metropolis-hastings"],"leadsTo":["burn-in-convergence-diagnostics"]},{"id":"theorempath:sluds-inequality","site":"theorempath","slug":"sluds-inequality","title":"Slud's Inequality","layer":"2","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/sluds-inequality","prerequisites":["common-probability-distributions","concentration-inequalities"],"leadsTo":["vc-dimension","pac-learning-framework"]},{"id":"theorempath:small-area-estimation","site":"theorempath","slug":"small-area-estimation","title":"Small Area Estimation","layer":"3","tier":3,"module":"statistical-foundations","url":"https://theorempath.com/topics/small-area-estimation","prerequisites":["bayesian-estimation","linear-regression","reml-and-variance-component-estimation","survey-weight-calibration-and-raking"],"leadsTo":["longitudinal-surveys-and-panel-data","official-statistics-and-national-surveys","adjusted-density-maximization","prasad-rao-mse-correction"]},{"id":"theorempath:snowflake-data-warehouse","site":"theorempath","slug":"snowflake-data-warehouse","title":"Snowflake Data Warehouse","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/snowflake-data-warehouse","prerequisites":[],"leadsTo":[]},{"id":"theorempath:softmax-and-numerical-stability","site":"theorempath","slug":"softmax-and-numerical-stability","title":"Softmax and Numerical Stability","layer":"1","tier":1,"module":"numerical-optimization","url":"https://theorempath.com/topics/softmax-and-numerical-stability","prerequisites":[],"leadsTo":["conditioning-and-condition-number","attention-mechanism-theory","decoding-strategies","flash-attention","log-probability-computation","quantization-theory","token-prediction-and-language-modeling","transformer-architecture"]},{"id":"theorempath:sorting-algorithms","site":"theorempath","slug":"sorting-algorithms","title":"Sorting Algorithms","layer":"0A","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/sorting-algorithms","prerequisites":[],"leadsTo":[]},{"id":"theorempath:sparse-attention-and-long-context","site":"theorempath","slug":"sparse-attention-and-long-context","title":"Sparse Attention and Long Context","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/sparse-attention-and-long-context","prerequisites":["attention-mechanism-theory","gemini-and-google-models"],"leadsTo":["context-engineering","fox-forget-gate"]},{"id":"theorempath:sparse-autoencoders","site":"theorempath","slug":"sparse-autoencoders","title":"Sparse Autoencoders for Interpretability: TopK, JumpReLU, Matryoshka, and Scaling","layer":"4","tier":1,"module":"llm-construction","url":"https://theorempath.com/topics/sparse-autoencoders","prerequisites":["autoencoders","mechanistic-interpretability","lasso-regression","residual-stream-and-transformer-internals","sparse-coding-and-efficient-coding","truth-directions-and-linear-probes"],"leadsTo":["induction-heads","residual-stream-and-transformer-internals","feature-importance-and-interpretability"]},{"id":"theorempath:sparse-recovery-and-compressed-sensing","site":"theorempath","slug":"sparse-recovery-and-compressed-sensing","title":"Sparse Recovery and Compressed Sensing","layer":"4","tier":3,"module":"modern-generalization","url":"https://theorempath.com/topics/sparse-recovery-and-compressed-sensing","prerequisites":["lasso-regression","subgaussian-random-variables","sparse-coding-and-efficient-coding"],"leadsTo":["minimax-lower-bounds","symbolic-regression-and-equation-discovery"]},{"id":"theorempath:spectral-clustering","site":"theorempath","slug":"spectral-clustering","title":"Spectral Clustering","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/spectral-clustering","prerequisites":["eigenvalues-and-eigenvectors","k-means-clustering","pagerank-algorithm"],"leadsTo":["kernels-and-rkhs","principal-component-analysis","clustering-for-gene-expression"]},{"id":"theorempath:spectral-theory-of-operators","site":"theorempath","slug":"spectral-theory-of-operators","title":"Spectral Theory of Operators","layer":"0B","tier":3,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/spectral-theory-of-operators","prerequisites":["eigenvalues-and-eigenvectors","complex-numbers-for-fourier","functional-analysis-core"],"leadsTo":["deeponet","fourier-neural-operator"]},{"id":"theorempath:speculative-decoding-and-quantization","site":"theorempath","slug":"speculative-decoding-and-quantization","title":"Speculative Decoding and Quantization","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/speculative-decoding-and-quantization","prerequisites":["transformer-architecture","kv-cache","megakernels","multi-token-prediction"],"leadsTo":["context-engineering","mixture-of-experts","edge-and-on-device-ml","inference-systems-overview"]},{"id":"theorempath:speech-and-audio-ml","site":"theorempath","slug":"speech-and-audio-ml","title":"Speech and Audio ML","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/speech-and-audio-ml","prerequisites":["signals-and-systems-for-ml","recurrent-neural-networks","cnns-for-signal-feature-extraction"],"leadsTo":["audio-language-models"]},{"id":"theorempath:spiking-neural-networks","site":"theorempath","slug":"spiking-neural-networks","title":"Spiking Neural Networks","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/spiking-neural-networks","prerequisites":["feedforward-networks-and-backpropagation","convolutional-neural-networks"],"leadsTo":["hebbian-learning","predictive-coding-and-autoencoders-in-the-brain"]},{"id":"theorempath:split-conformal-prediction","site":"theorempath","slug":"split-conformal-prediction","title":"Split Conformal Prediction","layer":"2","tier":1,"module":"predictive-uncertainty","url":"https://theorempath.com/topics/split-conformal-prediction","prerequisites":["order-statistics","hypothesis-testing-for-ml","cross-validation-theory","tabular-foundation-models-bayesian-inference"],"leadsTo":["weighted-conformal-prediction","calibration-and-uncertainty"]},{"id":"theorempath:squeezed-rejection-sampling","site":"theorempath","slug":"squeezed-rejection-sampling","title":"Squeezed Rejection Sampling","layer":"2","tier":3,"module":"sampling-mcmc","url":"https://theorempath.com/topics/squeezed-rejection-sampling","prerequisites":["rejection-sampling"],"leadsTo":["adaptive-rejection-sampling","importance-sampling"]},{"id":"theorempath:stability-and-optimization-dynamics","site":"theorempath","slug":"stability-and-optimization-dynamics","title":"Stability and Optimization Dynamics","layer":"2","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/stability-and-optimization-dynamics","prerequisites":["convex-optimization-basics","invariants-and-monovariants"],"leadsTo":["training-dynamics-and-loss-landscapes","implicit-bias-and-modern-generalization"]},{"id":"theorempath:state-space-models","site":"theorempath","slug":"state-space-models","title":"State Space Models","layer":"2","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/state-space-models","prerequisites":["time-series-foundations","markov-chains-and-steady-state","kalman-filter","expectation-variance-covariance-moments"],"leadsTo":["deep-learning-time-series","particle-filters","mamba-and-state-space-models"]},{"id":"theorempath:statistical-paradoxes-collection","site":"theorempath","slug":"statistical-paradoxes-collection","title":"Statistical Paradoxes Collection","layer":"2","tier":3,"module":"methodology","url":"https://theorempath.com/topics/statistical-paradoxes-collection","prerequisites":["simpsons-paradox","base-rate-fallacy","anthropic-bias-and-observation-selection","steins-paradox"],"leadsTo":[]},{"id":"theorempath:statistical-significance-and-multiple-comparisons","site":"theorempath","slug":"statistical-significance-and-multiple-comparisons","title":"Statistical Significance and Multiple Comparisons","layer":"2","tier":2,"module":"methodology","url":"https://theorempath.com/topics/statistical-significance-and-multiple-comparisons","prerequisites":["hypothesis-testing-for-ml"],"leadsTo":["bootstrap-methods","cross-validation-theory"]},{"id":"theorempath:steins-paradox","site":"theorempath","slug":"steins-paradox","title":"Stein's Paradox","layer":"0B","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/steins-paradox","prerequisites":["maximum-likelihood-estimation","shrinkage-estimation-james-stein"],"leadsTo":["statistical-paradoxes-collection"]},{"id":"theorempath:stochastic-approximation-theory","site":"theorempath","slug":"stochastic-approximation-theory","title":"Stochastic Approximation Theory","layer":"2","tier":2,"module":"optimization-function-classes","url":"https://theorempath.com/topics/stochastic-approximation-theory","prerequisites":["convex-optimization-basics","martingale-theory","adaptive-learning-is-not-iid","borel-cantelli-lemmas","stochastic-gradient-descent-convergence"],"leadsTo":["stochastic-gradient-descent-convergence","td-learning","q-learning"]},{"id":"theorempath:stochastic-calculus-for-ml","site":"theorempath","slug":"stochastic-calculus-for-ml","title":"Stochastic Calculus for ML","layer":"3","tier":3,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/stochastic-calculus-for-ml","prerequisites":["martingale-theory","measure-theoretic-probability","classical-odes"],"leadsTo":["diffusion-models","langevin-dynamics","sgd-as-sde","score-matching","ito-lemma","neural-sdes","stochastic-differential-equations"]},{"id":"theorempath:stochastic-differential-equations","site":"theorempath","slug":"stochastic-differential-equations","title":"Stochastic Differential Equations","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/stochastic-differential-equations","prerequisites":["brownian-motion","ito-lemma","stochastic-calculus-for-ml"],"leadsTo":["deep-bsde-method","neural-sdes","backward-sde-theory","feynman-kac-formula","fokker-planck-equation","hamilton-jacobi-bellman-equation","langevin-dynamics","pde-fundamentals-for-ml","probability-flow-ode","score-matching","sgd-as-sde","time-reversal-of-sdes"]},{"id":"theorempath:stochastic-gradient-descent-convergence","site":"theorempath","slug":"stochastic-gradient-descent-convergence","title":"Stochastic Gradient Descent Convergence","layer":"2","tier":1,"module":"optimization-function-classes","url":"https://theorempath.com/topics/stochastic-gradient-descent-convergence","prerequisites":["gradient-descent-variants","concentration-inequalities","coordinate-descent","invariants-and-monovariants","online-convex-optimization","proximal-gradient-methods"],"leadsTo":["stochastic-approximation-theory","adam-optimizer","batch-size-and-learning-dynamics","grokking","learning-rate-scheduling","parallel-processing-fundamentals","sgd-as-sde","test-time-training"]},{"id":"theorempath:stochastic-processes-ml","site":"theorempath","slug":"stochastic-processes-ml","title":"Stochastic Processes for ML","layer":"2","tier":2,"module":"concentration-probability","url":"https://theorempath.com/topics/stochastic-processes-ml","prerequisites":["measure-theoretic-probability","expectation-variance-covariance-moments","concentration-inequalities"],"leadsTo":["empirical-processes-and-chaining","neural-tangent-kernel","martingale-theory","markov-chain-monte-carlo","langevin-dynamics","time-series-foundations"]},{"id":"theorempath:structured-output-and-constrained-generation","site":"theorempath","slug":"structured-output-and-constrained-generation","title":"Structured Output and Constrained Generation","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/structured-output-and-constrained-generation","prerequisites":["transformer-architecture","tool-augmented-reasoning"],"leadsTo":["tool-augmented-reasoning"]},{"id":"theorempath:student-t-distribution-and-t-test","site":"theorempath","slug":"student-t-distribution-and-t-test","title":"Student-t Distribution and t-Test","layer":"1","tier":1,"module":"statistical-estimation","url":"https://theorempath.com/topics/student-t-distribution-and-t-test","prerequisites":["distributions-atlas","normal-distribution","chi-squared-distribution-and-tests","central-limit-theorem","hypothesis-testing-for-ml"],"leadsTo":["f-distribution-and-anova","permutation-tests","likelihood-ratio-wald-score-tests","bootstrap-methods"]},{"id":"theorempath:subexponential-random-variables","site":"theorempath","slug":"subexponential-random-variables","title":"Sub-Exponential Random Variables","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/subexponential-random-variables","prerequisites":["subgaussian-random-variables","concentration-inequalities","bernstein-inequality","chernoff-bounds","bennetts-inequality","chi-squared-concentration"],"leadsTo":["matrix-concentration","epsilon-nets-and-covering-numbers"]},{"id":"theorempath:subgaussian-random-variables","site":"theorempath","slug":"subgaussian-random-variables","title":"Sub-Gaussian Random Variables","layer":"2","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/subgaussian-random-variables","prerequisites":["concentration-inequalities","chernoff-bounds","skewness-kurtosis-and-higher-moments","hoeffdings-lemma"],"leadsTo":["subexponential-random-variables","epsilon-nets-and-covering-numbers","hanson-wright-inequality","matrix-concentration","mcdiarmids-inequality","measure-concentration-and-geometric-fa","restricted-isometry-property","sparse-recovery-and-compressed-sensing","rademacher-complexity"]},{"id":"theorempath:subgradients-and-subdifferentials","site":"theorempath","slug":"subgradients-and-subdifferentials","title":"Subgradients and Subdifferentials","layer":"1","tier":1,"module":"optimization-function-classes","url":"https://theorempath.com/topics/subgradients-and-subdifferentials","prerequisites":["convex-optimization-basics"],"leadsTo":["proximal-gradient-methods","lasso-regression","convex-duality"]},{"id":"theorempath:submodular-optimization","site":"theorempath","slug":"submodular-optimization","title":"Submodular Optimization","layer":"3","tier":3,"module":"numerical-optimization","url":"https://theorempath.com/topics/submodular-optimization","prerequisites":["greedy-algorithms"],"leadsTo":["convex-optimization-basics"]},{"id":"theorempath:sufficient-statistics-and-exponential-families","site":"theorempath","slug":"sufficient-statistics-and-exponential-families","title":"Sufficient Statistics and Exponential Families","layer":"0B","tier":2,"module":"statistical-estimation","url":"https://theorempath.com/topics/sufficient-statistics-and-exponential-families","prerequisites":["maximum-likelihood-estimation"],"leadsTo":["fisher-information","hypothesis-testing-for-ml","em-algorithm","basu-theorem","rao-blackwellization","conjugate-priors"]},{"id":"theorempath:support-vector-machines","site":"theorempath","slug":"support-vector-machines","title":"Support Vector Machines","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/support-vector-machines","prerequisites":["convex-optimization-basics","convex-duality","logistic-regression","perceptron","loss-functions"],"leadsTo":["kernels-and-rkhs","svm-for-rf-classification","kernel-trick"]},{"id":"theorempath:survey-sampling-methods","site":"theorempath","slug":"survey-sampling-methods","title":"Survey Sampling Methods","layer":"2","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/survey-sampling-methods","prerequisites":["common-probability-distributions","expectation-variance-covariance-moments","types-of-bias-in-statistics"],"leadsTo":["sample-size-determination","design-based-vs-model-based-inference","nonresponse-and-missing-data","greg-estimator","official-statistics-and-national-surveys","survey-weight-calibration-and-raking"]},{"id":"theorempath:survival-analysis","site":"theorempath","slug":"survival-analysis","title":"Survival Analysis","layer":"3","tier":2,"module":"statistical-foundations","url":"https://theorempath.com/topics/survival-analysis","prerequisites":["maximum-likelihood-estimation"],"leadsTo":["hypothesis-testing-for-ml","causal-inference-basics"]},{"id":"theorempath:svm-for-rf-classification","site":"theorempath","slug":"svm-for-rf-classification","title":"SVM for RF Classification","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/svm-for-rf-classification","prerequisites":["support-vector-machines","signals-and-systems-for-ml"],"leadsTo":["kernels-and-rkhs","convolutional-neural-networks"]},{"id":"theorempath:symbolic-regression-and-equation-discovery","site":"theorempath","slug":"symbolic-regression-and-equation-discovery","title":"Symbolic Regression and Equation Discovery","layer":"4","tier":3,"module":"applied-ml","url":"https://theorempath.com/topics/symbolic-regression-and-equation-discovery","prerequisites":["lasso-regression","sparse-recovery-and-compressed-sensing"],"leadsTo":["physics-informed-neural-networks","reservoir-computing-and-echo-state-networks"]},{"id":"theorempath:symmetrization-inequality","site":"theorempath","slug":"symmetrization-inequality","title":"Symmetrization Inequality","layer":"3","tier":1,"module":"concentration-probability","url":"https://theorempath.com/topics/symmetrization-inequality","prerequisites":["rademacher-complexity","concentration-inequalities"],"leadsTo":["algorithmic-stability","epsilon-nets-and-covering-numbers"]},{"id":"theorempath:synthetic-data-distillation","site":"theorempath","slug":"synthetic-data-distillation","title":"Synthetic Data Distillation","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/synthetic-data-distillation","prerequisites":["knowledge-distillation","synthetic-data-generation"],"leadsTo":["reasoning-data-curation","curriculum-learning"]},{"id":"theorempath:synthetic-data-generation","site":"theorempath","slug":"synthetic-data-generation","title":"Synthetic Data Generation","layer":"3","tier":2,"module":"methodology","url":"https://theorempath.com/topics/synthetic-data-generation","prerequisites":["common-probability-distributions"],"leadsTo":["data-augmentation-theory","data-contamination-and-evaluation","model-collapse-and-data-quality","synthetic-data-distillation"]},{"id":"theorempath:table-extraction-and-structure-recognition","site":"theorempath","slug":"table-extraction-and-structure-recognition","title":"Table Extraction and Structure Recognition","layer":"5","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/table-extraction-and-structure-recognition","prerequisites":["document-intelligence","paddleocr-and-practical-ocr"],"leadsTo":[]},{"id":"theorempath:tabu-search","site":"theorempath","slug":"tabu-search","title":"Tabu Search","layer":"2","tier":3,"module":"numerical-optimization","url":"https://theorempath.com/topics/tabu-search","prerequisites":["greedy-algorithms","ascent-algorithms"],"leadsTo":[]},{"id":"theorempath:tabular-foundation-models-bayesian-inference","site":"theorempath","slug":"tabular-foundation-models-bayesian-inference","title":"Tabular Foundation Models as Bayesian Inference Engines","layer":"3","tier":1,"module":"bayesian-ml-frontier","url":"https://theorempath.com/topics/tabular-foundation-models-bayesian-inference","prerequisites":["bayesian-estimation","transformer-architecture","prompt-engineering-and-in-context-learning"],"leadsTo":["e-values-and-anytime-valid-inference","split-conformal-prediction"]},{"id":"theorempath:taylor-expansion","site":"theorempath","slug":"taylor-expansion","title":"Taylor Expansion","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/taylor-expansion","prerequisites":["continuity-in-rn","differentiation-in-rn"],"leadsTo":["convex-optimization-basics","newtons-method","automatic-differentiation"]},{"id":"theorempath:td-learning","site":"theorempath","slug":"td-learning","title":"Temporal Difference Learning","layer":"2","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/td-learning","prerequisites":["markov-decision-processes","value-iteration-and-policy-iteration","bellman-equations","stochastic-approximation-theory"],"leadsTo":["q-learning","actor-critic-methods","policy-gradient-theorem","reward-systems-and-reinforcement-learning-neuroscience"]},{"id":"theorempath:td3","site":"theorempath","slug":"td3","title":"TD3: Twin Delayed Deep Deterministic Policy Gradient","layer":"3","tier":2,"module":"rl-theory","url":"https://theorempath.com/topics/td3","prerequisites":["ddpg","q-learning","policy-gradient-theorem"],"leadsTo":["policy-optimization-ppo-trpo"]},{"id":"theorempath:tensors-and-tensor-operations","site":"theorempath","slug":"tensors-and-tensor-operations","title":"Tensors and Tensor Operations","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/tensors-and-tensor-operations","prerequisites":["eigenvalues-and-eigenvectors","pandas-and-numpy-fundamentals"],"leadsTo":["feedforward-networks-and-backpropagation","principal-component-analysis"]},{"id":"theorempath:test-time-compute-and-search","site":"theorempath","slug":"test-time-compute-and-search","title":"Test-Time Compute and Search","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/test-time-compute-and-search","prerequisites":["scaling-laws","agentic-rl-and-tool-use"],"leadsTo":["reward-models-and-verifiers","post-training-overview","inference-time-scaling-laws","latent-reasoning"]},{"id":"theorempath:test-time-training","site":"theorempath","slug":"test-time-training","title":"Test-Time Training and Adaptive Inference","layer":"5","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/test-time-training","prerequisites":["stochastic-gradient-descent-convergence","recurrent-neural-networks","continuous-thought-machines"],"leadsTo":["online-learning-and-bandits","meta-learning"]},{"id":"theorempath:the-hessian-matrix","site":"theorempath","slug":"the-hessian-matrix","title":"The Hessian Matrix","layer":"0A","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/the-hessian-matrix","prerequisites":["matrix-operations-and-properties","eigenvalues-and-eigenvectors","differentiation-in-rn","the-jacobian-matrix","vector-calculus-chain-rule"],"leadsTo":["newtons-method","convex-optimization-basics","automatic-differentiation","neural-network-optimization-landscape","matrix-calculus","optimal-brain-surgery-and-pruning-theory","preconditioned-optimizers","riemannian-optimization","second-order-optimization-methods","training-dynamics-and-loss-landscapes","trust-region-methods"]},{"id":"theorempath:the-jacobian-matrix","site":"theorempath","slug":"the-jacobian-matrix","title":"The Jacobian Matrix","layer":"0A","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/the-jacobian-matrix","prerequisites":["differentiation-in-rn"],"leadsTo":["automatic-differentiation","the-hessian-matrix","classical-odes","continuous-normalizing-flows","divergence-curl-and-line-integrals","gradient-flow-and-vanishing-gradients","implicit-differentiation","inverse-and-implicit-function-theorem","matrix-calculus","normalization-flows","physics-informed-neural-networks","vector-calculus-chain-rule","multivariate-normal-distribution"]},{"id":"theorempath:time-reversal-of-sdes","site":"theorempath","slug":"time-reversal-of-sdes","title":"Time Reversal of SDEs","layer":"3","tier":2,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/time-reversal-of-sdes","prerequisites":["stochastic-differential-equations","fokker-planck-equation"],"leadsTo":["score-matching","diffusion-models","probability-flow-ode"]},{"id":"theorempath:time-series-forecasting-basics","site":"theorempath","slug":"time-series-forecasting-basics","title":"Time Series Forecasting Basics","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/time-series-forecasting-basics","prerequisites":["linear-regression","time-series-foundations"],"leadsTo":["gaussian-processes-for-ml","macroeconomic-time-series-forecasting"]},{"id":"theorempath:time-series-foundations","site":"theorempath","slug":"time-series-foundations","title":"Time Series Foundations","layer":"2","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/time-series-foundations","prerequisites":["kolmogorov-probability-axioms","expectation-variance-covariance-moments","stochastic-processes-ml"],"leadsTo":["state-space-models","time-series-forecasting-basics","deep-learning-time-series"]},{"id":"theorempath:token-prediction-and-language-modeling","site":"theorempath","slug":"token-prediction-and-language-modeling","title":"Token Prediction and Language Modeling","layer":"3","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/token-prediction-and-language-modeling","prerequisites":["information-theory-foundations","softmax-and-numerical-stability","feedforward-networks-and-backpropagation","common-probability-distributions"],"leadsTo":["bert-and-pretrain-finetune-paradigm","transformer-architecture","llama-and-open-weight-models"]},{"id":"theorempath:tokenization-and-information-theory","site":"theorempath","slug":"tokenization-and-information-theory","title":"Tokenization and Information Theory","layer":"4","tier":3,"module":"llm-construction","url":"https://theorempath.com/topics/tokenization-and-information-theory","prerequisites":["information-theory-foundations","common-probability-distributions","morphology-and-subword-modeling"],"leadsTo":["distributed-training-theory","byte-level-language-models","cohere-models","gpt-series-evolution","llama-and-open-weight-models","mistral-models"]},{"id":"theorempath:tool-augmented-reasoning","site":"theorempath","slug":"tool-augmented-reasoning","title":"Tool-Augmented Reasoning","layer":"5","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/tool-augmented-reasoning","prerequisites":["transformer-architecture","chain-of-thought-and-reasoning","prompt-engineering-and-in-context-learning","agentic-rl-and-tool-use"],"leadsTo":["agent-protocols-mcp-a2a","structured-output-and-constrained-generation"]},{"id":"theorempath:total-variation-distance","site":"theorempath","slug":"total-variation-distance","title":"Total Variation Distance","layer":"1","tier":1,"module":"foundations","url":"https://theorempath.com/topics/total-variation-distance","prerequisites":["common-probability-distributions","measure-theoretic-probability"],"leadsTo":["kl-divergence","wasserstein-distances","coupling-arguments-and-mixing-time"]},{"id":"theorempath:train-test-split-and-data-leakage","site":"theorempath","slug":"train-test-split-and-data-leakage","title":"Train-Test Split and Data Leakage","layer":"1","tier":1,"module":"methodology","url":"https://theorempath.com/topics/train-test-split-and-data-leakage","prerequisites":["ml-project-lifecycle"],"leadsTo":["cross-validation-theory","exploratory-data-analysis"]},{"id":"theorempath:training-dynamics-and-loss-landscapes","site":"theorempath","slug":"training-dynamics-and-loss-landscapes","title":"Training Dynamics and Loss Landscapes","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/training-dynamics-and-loss-landscapes","prerequisites":["convex-optimization-basics","the-hessian-matrix","stability-and-optimization-dynamics"],"leadsTo":["implicit-bias-and-modern-generalization","optimizer-theory-sgd-adam-muon","neural-network-optimization-landscape"]},{"id":"theorempath:transfer-learning","site":"theorempath","slug":"transfer-learning","title":"Transfer Learning","layer":"3","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/transfer-learning","prerequisites":["feedforward-networks-and-backpropagation","representation-learning-in-cosmology"],"leadsTo":[]},{"id":"theorempath:transformer-architecture","site":"theorempath","slug":"transformer-architecture","title":"Transformer Architecture","layer":"4","tier":2,"module":"llm-construction","url":"https://theorempath.com/topics/transformer-architecture","prerequisites":["attention-mechanism-theory","feedforward-networks-and-backpropagation","softmax-and-numerical-stability","adam-optimizer","attention-mechanisms-history","byte-level-language-models","convolutional-neural-networks","deep-learning-goodfellow-book","distributional-semantics","linear-layer-shapes-memory","macroeconomic-time-series-forecasting","recurrent-neural-networks","rnns-for-signal-sequences","syntax-and-parsing","token-prediction-and-language-modeling","word-embeddings"],"leadsTo":["mechanistic-interpretability","hallucination-theory","rlhf-and-alignment","attention-for-protein-structure-alphafold","attention-is-all-you-need-paper","audio-language-models","bert-and-pretrain-finetune-paradigm","chain-of-thought-and-reasoning","claude-model-family","cohere-models","deep-learning-time-series","deepseek-models","donut-and-ocr-free-document-understanding","fox-forget-gate","gemini-and-google-models","gpt-series-evolution","induction-heads","llama-and-open-weight-models","mistral-models","mixture-of-experts","model-comparison-table","model-merging-and-weight-averaging","multi-token-prediction","plan-then-generate","post-training-overview","prompt-engineering-and-in-context-learning","qwen-and-chinese-models","residual-stream-and-transformer-internals","speculative-decoding-and-quantization","structured-output-and-constrained-generation","tabular-foundation-models-bayesian-inference","tool-augmented-reasoning","vision-transformer-lineage"]},{"id":"theorempath:triangular-distribution","site":"theorempath","slug":"triangular-distribution","title":"Triangular Distribution","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/triangular-distribution","prerequisites":["common-probability-distributions","random-variables"],"leadsTo":["expectation-variance-covariance-moments","order-statistics","common-probability-distributions"]},{"id":"theorempath:trust-region-methods","site":"theorempath","slug":"trust-region-methods","title":"Trust Region Methods","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/trust-region-methods","prerequisites":["newtons-method","the-hessian-matrix","line-search-methods","augmented-lagrangian-and-admm","conjugate-gradient-methods"],"leadsTo":["second-order-optimization-methods","interior-point-methods"]},{"id":"theorempath:truth-directions-and-linear-probes","site":"theorempath","slug":"truth-directions-and-linear-probes","title":"Truth Directions and Linear Probes","layer":"4","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/truth-directions-and-linear-probes","prerequisites":["mechanistic-interpretability","residual-stream-and-transformer-internals"],"leadsTo":["sparse-autoencoders","residual-stream-and-transformer-internals","mechanistic-interpretability"]},{"id":"theorempath:tsne-and-umap","site":"theorempath","slug":"tsne-and-umap","title":"t-SNE and UMAP","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/tsne-and-umap","prerequisites":["principal-component-analysis","self-organizing-maps"],"leadsTo":["autoencoders","k-means-clustering","riemannian-optimization"]},{"id":"theorempath:tweedie-distribution","site":"theorempath","slug":"tweedie-distribution","title":"Tweedie Distribution","layer":"1","tier":2,"module":"statistics","url":"https://theorempath.com/topics/tweedie-distribution","prerequisites":["common-probability-distributions","sufficient-statistics-and-exponential-families","maximum-likelihood-estimation"],"leadsTo":["maximum-likelihood-estimation","common-probability-distributions"]},{"id":"theorempath:type-theory","site":"theorempath","slug":"type-theory","title":"Type Theory","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/type-theory","prerequisites":["lambda-calculus","basic-logic-and-proof-techniques"],"leadsTo":["proof-theory-and-cut-elimination"]},{"id":"theorempath:types-of-bias-in-statistics","site":"theorempath","slug":"types-of-bias-in-statistics","title":"Types of Bias in Statistics","layer":"1","tier":1,"module":"methodology","url":"https://theorempath.com/topics/types-of-bias-in-statistics","prerequisites":["anthropic-bias-and-observation-selection"],"leadsTo":["survey-sampling-methods","nonresponse-and-missing-data"]},{"id":"theorempath:understanding-machine-learning-book","site":"theorempath","slug":"understanding-machine-learning-book","title":"Understanding Machine Learning (Shalev-Shwartz, Ben-David)","layer":"1","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/understanding-machine-learning-book","prerequisites":[],"leadsTo":["empirical-risk-minimization","pac-learning-framework","vc-dimension","rademacher-complexity"]},{"id":"theorempath:uniform-convergence","site":"theorempath","slug":"uniform-convergence","title":"Uniform Convergence","layer":"2","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/uniform-convergence","prerequisites":["empirical-risk-minimization","adaptive-learning-is-not-iid","bernstein-inequality","realizability-assumption","sequences-and-series-of-functions","basic-logic-and-proof-techniques","sets-functions-and-relations"],"leadsTo":["vc-dimension","rademacher-complexity","glivenko-cantelli-theorem","pac-learning-framework"]},{"id":"theorempath:universal-approximation-theorem","site":"theorempath","slug":"universal-approximation-theorem","title":"Universal Approximation Theorem","layer":"2","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/universal-approximation-theorem","prerequisites":["feedforward-networks-and-backpropagation"],"leadsTo":["kolmogorov-arnold-networks"]},{"id":"theorempath:unsolved-problems-in-computer-science","site":"theorempath","slug":"unsolved-problems-in-computer-science","title":"Unsolved Problems in Computer Science","layer":"3","tier":2,"module":"algorithms-foundations","url":"https://theorempath.com/topics/unsolved-problems-in-computer-science","prerequisites":["p-vs-np","open-problems-in-matrix-computation"],"leadsTo":["open-problems-in-ml-theory"]},{"id":"theorempath:value-iteration-and-policy-iteration","site":"theorempath","slug":"value-iteration-and-policy-iteration","title":"Value Iteration and Policy Iteration","layer":"2","tier":1,"module":"rl-theory","url":"https://theorempath.com/topics/value-iteration-and-policy-iteration","prerequisites":["markov-decision-processes","bellman-equations"],"leadsTo":["q-learning","policy-gradient-theorem","options-and-temporal-abstraction","td-learning"]},{"id":"theorempath:variance-reduction-techniques","site":"theorempath","slug":"variance-reduction-techniques","title":"Variance Reduction Techniques","layer":"2","tier":2,"module":"sampling-mcmc","url":"https://theorempath.com/topics/variance-reduction-techniques","prerequisites":["importance-sampling"],"leadsTo":["burn-in-convergence-diagnostics","hamiltonian-monte-carlo"]},{"id":"theorempath:variance-stabilizing-transformations","site":"theorempath","slug":"variance-stabilizing-transformations","title":"Variance-Stabilizing Transformations","layer":"1","tier":1,"module":"statistics","url":"https://theorempath.com/topics/variance-stabilizing-transformations","prerequisites":["delta-method","central-limit-theorem","common-probability-distributions","expectation-variance-covariance-moments"],"leadsTo":["analysis-of-variance","common-probability-distributions","bootstrap-methods"]},{"id":"theorempath:variational-autoencoders","site":"theorempath","slug":"variational-autoencoders","title":"Variational Autoencoders","layer":"3","tier":1,"module":"ml-methods","url":"https://theorempath.com/topics/variational-autoencoders","prerequisites":["autoencoders","maximum-likelihood-estimation","autoencoders-for-low-dimensional-dynamical-structures","bayesian-estimation","gaussian-mixture-models-and-em","information-theory-foundations","kl-divergence"],"leadsTo":["diffusion-models","normalization-flows","autoencoders-for-single-cell-rna-seq","deep-generative-models-for-molecules","jepa-and-joint-embedding","predictive-coding-and-autoencoders-in-the-brain","representation-learning-theory"]},{"id":"theorempath:vc-dimension","site":"theorempath","slug":"vc-dimension","title":"VC Dimension","layer":"2","tier":1,"module":"learning-theory-core","url":"https://theorempath.com/topics/vc-dimension","prerequisites":["empirical-risk-minimization","concentration-inequalities","counting-and-combinatorics","hypothesis-classes-and-function-spaces","pac-learning-framework","understanding-machine-learning-book","uniform-convergence","basic-logic-and-proof-techniques","sets-functions-and-relations","bias-complexity-tradeoff","no-free-lunch-theorem","sluds-inequality"],"leadsTo":["rademacher-complexity","algorithmic-stability","glivenko-cantelli-theorem","implicit-bias-and-modern-generalization","sample-complexity-bounds"]},{"id":"theorempath:vector-calculus-chain-rule","site":"theorempath","slug":"vector-calculus-chain-rule","title":"Vector Calculus Chain Rule","layer":"0A","tier":1,"module":"mathematical-infrastructure","url":"https://theorempath.com/topics/vector-calculus-chain-rule","prerequisites":["the-jacobian-matrix","vectors-matrices-and-linear-maps","differentiation-in-rn"],"leadsTo":["automatic-differentiation","feedforward-networks-and-backpropagation","the-hessian-matrix","divergence-curl-and-line-integrals"]},{"id":"theorempath:vectors-matrices-and-linear-maps","site":"theorempath","slug":"vectors-matrices-and-linear-maps","title":"Vectors, Matrices, and Linear Maps","layer":"0A","tier":1,"module":"foundations","url":"https://theorempath.com/topics/vectors-matrices-and-linear-maps","prerequisites":["sets-functions-and-relations"],"leadsTo":["matrix-norms","inner-product-spaces-and-orthogonality","eigenvalues-and-eigenvectors","autoencoders","complex-numbers-for-fourier","convolutional-neural-networks","differentiation-in-rn","hough-transform-and-circle-detection","linear-independence","matrix-multiplication-algorithms","non-euclidean-and-hyperbolic-geometry","vector-calculus-chain-rule"]},{"id":"theorempath:verifier-design-and-process-reward","site":"theorempath","slug":"verifier-design-and-process-reward","title":"Verifier Design and Process Reward","layer":"5","tier":2,"module":"ai-safety","url":"https://theorempath.com/topics/verifier-design-and-process-reward","prerequisites":["reward-models-and-verifiers"],"leadsTo":["test-time-compute-and-search"]},{"id":"theorempath:video-world-models","site":"theorempath","slug":"video-world-models","title":"Video World Models","layer":"5","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/video-world-models","prerequisites":["world-models-and-planning","diffusion-models"],"leadsTo":["world-models-and-planning","agentic-rl-and-tool-use","diffusion-models"]},{"id":"theorempath:vieta-jumping","site":"theorempath","slug":"vieta-jumping","title":"Vieta Jumping","layer":"0A","tier":3,"module":"foundations","url":"https://theorempath.com/topics/vieta-jumping","prerequisites":[],"leadsTo":[]},{"id":"theorempath:vision-transformer-lineage","site":"theorempath","slug":"vision-transformer-lineage","title":"Vision Transformer Lineage: ViT, DeiT, Swin, MAE, DINOv2, SAM","layer":"4","tier":1,"module":"beyond-llms","url":"https://theorempath.com/topics/vision-transformer-lineage","prerequisites":["transformer-architecture","convolutional-neural-networks","cnns-for-medical-imaging"],"leadsTo":["clip-and-openclip-in-practice","florence-and-vision-foundation-models","jepa-and-joint-embedding","diffusion-models","self-supervised-vision"]},{"id":"theorempath:visual-semantic-slam","site":"theorempath","slug":"visual-semantic-slam","title":"Visual and Semantic SLAM","layer":"4","tier":3,"module":"applied-math","url":"https://theorempath.com/topics/visual-semantic-slam","prerequisites":["graphslam-and-factor-graphs"],"leadsTo":["active-slam-and-pomdps"]},{"id":"theorempath:wasserstein-distances","site":"theorempath","slug":"wasserstein-distances","title":"Wasserstein Distances","layer":"4","tier":3,"module":"modern-generalization","url":"https://theorempath.com/topics/wasserstein-distances","prerequisites":["common-probability-distributions","measure-theoretic-probability","convex-duality","distance-metrics-compared","total-variation-distance"],"leadsTo":["optimal-transport-and-earth-movers-distance"]},{"id":"theorempath:wave-based-neural-networks","site":"theorempath","slug":"wave-based-neural-networks","title":"Wave-Based Neural Networks","layer":"3","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/wave-based-neural-networks","prerequisites":["complex-numbers-for-fourier"],"leadsTo":[]},{"id":"theorempath:wavelet-smoothing","site":"theorempath","slug":"wavelet-smoothing","title":"Wavelet Smoothing","layer":"2","tier":3,"module":"ml-methods","url":"https://theorempath.com/topics/wavelet-smoothing","prerequisites":["signals-and-systems-for-ml"],"leadsTo":[]},{"id":"theorempath:webgpu-for-ml","site":"theorempath","slug":"webgpu-for-ml","title":"WebGPU for Machine Learning","layer":"0B","tier":2,"module":"infrastructure","url":"https://theorempath.com/topics/webgpu-for-ml","prerequisites":["computer-architecture-for-ml","automatic-differentiation"],"leadsTo":["fused-kernels","mixed-precision-training","gaussian-splatting"]},{"id":"theorempath:weibull-distribution","site":"theorempath","slug":"weibull-distribution","title":"Weibull Distribution","layer":"1","tier":2,"module":"foundations","url":"https://theorempath.com/topics/weibull-distribution","prerequisites":["common-probability-distributions","exponential-distribution","gamma-distribution","distributions-atlas"],"leadsTo":["survival-analysis","extreme-value-theory"]},{"id":"theorempath:weight-initialization","site":"theorempath","slug":"weight-initialization","title":"Weight Initialization","layer":"2","tier":1,"module":"training-techniques","url":"https://theorempath.com/topics/weight-initialization","prerequisites":["feedforward-networks-and-backpropagation","eigenvalues-and-eigenvectors","activation-functions"],"leadsTo":["batch-normalization"]},{"id":"theorempath:weighted-conformal-prediction","site":"theorempath","slug":"weighted-conformal-prediction","title":"Weighted Conformal Prediction Under Covariate Shift","layer":"3","tier":1,"module":"predictive-uncertainty","url":"https://theorempath.com/topics/weighted-conformal-prediction","prerequisites":["split-conformal-prediction","radon-nikodym-and-conditional-expectation","importance-sampling","causal-inference-basics"],"leadsTo":["double-debiased-machine-learning","e-values-and-anytime-valid-inference"]},{"id":"theorempath:weights-and-biases-experiment-tracking","site":"theorempath","slug":"weights-and-biases-experiment-tracking","title":"Weights and Biases for Experiment Tracking","layer":"4","tier":3,"module":"infrastructure","url":"https://theorempath.com/topics/weights-and-biases-experiment-tracking","prerequisites":[],"leadsTo":["experiment-tracking-and-tooling","reproducibility-and-experimental-rigor"]},{"id":"theorempath:whitening-and-decorrelation","site":"theorempath","slug":"whitening-and-decorrelation","title":"Whitening and Decorrelation","layer":"2","tier":2,"module":"numerical-optimization","url":"https://theorempath.com/topics/whitening-and-decorrelation","prerequisites":["eigenvalues-and-eigenvectors","principal-component-analysis","floating-point-arithmetic"],"leadsTo":["batch-normalization","information-geometry"]},{"id":"theorempath:winsorization","site":"theorempath","slug":"winsorization","title":"Winsorization","layer":"1","tier":3,"module":"numerical-optimization","url":"https://theorempath.com/topics/winsorization","prerequisites":["order-statistics","common-probability-distributions"],"leadsTo":["robust-statistics-and-m-estimators"]},{"id":"theorempath:word-embeddings","site":"theorempath","slug":"word-embeddings","title":"Word Embeddings","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/word-embeddings","prerequisites":["logistic-regression","singular-value-decomposition","maximum-likelihood-estimation","information-retrieval"],"leadsTo":["attention-mechanism-theory","transformer-architecture","natural-language-processing-foundations","nlp-for-economic-text-analysis","semantic-search-and-embeddings"]},{"id":"theorempath:world-model-evaluation","site":"theorempath","slug":"world-model-evaluation","title":"World Model Evaluation","layer":"5","tier":3,"module":"beyond-llms","url":"https://theorempath.com/topics/world-model-evaluation","prerequisites":["world-models-and-planning"],"leadsTo":[]},{"id":"theorempath:world-models-and-planning","site":"theorempath","slug":"world-models-and-planning","title":"World Models and Planning","layer":"4","tier":2,"module":"beyond-llms","url":"https://theorempath.com/topics/world-models-and-planning","prerequisites":["markov-decision-processes","era-of-experience","history-of-ai","model-based-rl"],"leadsTo":["video-world-models","jepa-and-joint-embedding","agentic-rl-and-tool-use","world-model-evaluation"]},{"id":"theorempath:xgboost","site":"theorempath","slug":"xgboost","title":"XGBoost","layer":"2","tier":2,"module":"ml-methods","url":"https://theorempath.com/topics/xgboost","prerequisites":["gradient-boosting"],"leadsTo":["regularization-theory","cross-validation-theory"]},{"id":"theorempath:zermelo-fraenkel-set-theory","site":"theorempath","slug":"zermelo-fraenkel-set-theory","title":"Zermelo-Fraenkel Set Theory","layer":"0A","tier":2,"module":"foundations","url":"https://theorempath.com/topics/zermelo-fraenkel-set-theory","prerequisites":[],"leadsTo":["cantors-theorem-and-uncountability","measure-theoretic-probability","foundational-dependencies"]},{"id":"theorempath:zero-knowledge-proofs","site":"theorempath","slug":"zero-knowledge-proofs","title":"Zero-Knowledge Proofs","layer":"3","tier":2,"module":"applied-math","url":"https://theorempath.com/topics/zero-knowledge-proofs","prerequisites":["public-key-cryptography","p-vs-np"],"leadsTo":[]}],"edges":[{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:ablation-study-design","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:ablation-study-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:benchmarking-methodology--prerequisite-of--theorempath:ablation-study-design","from":"theorempath:benchmarking-methodology","to":"theorempath:ablation-study-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:experiment-tracking-and-tooling--prerequisite-of--theorempath:ablation-study-design","from":"theorempath:experiment-tracking-and-tooling","to":"theorempath:ablation-study-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reproducibility-and-experimental-rigor--prerequisite-of--theorempath:ablation-study-design","from":"theorempath:reproducibility-and-experimental-rigor","to":"theorempath:ablation-study-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:activation-checkpointing","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:activation-checkpointing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mixed-precision-training--prerequisite-of--theorempath:activation-checkpointing","from":"theorempath:mixed-precision-training","to":"theorempath:activation-checkpointing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:activation-functions","from":"theorempath:differentiation-in-rn","to":"theorempath:activation-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:activation-functions","from":"theorempath:convex-optimization-basics","to":"theorempath:activation-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graphslam-and-factor-graphs--prerequisite-of--theorempath:active-slam-and-pomdps","from":"theorempath:graphslam-and-factor-graphs","to":"theorempath:active-slam-and-pomdps","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:active-slam-and-pomdps","from":"theorempath:markov-decision-processes","to":"theorempath:active-slam-and-pomdps","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:visual-semantic-slam--prerequisite-of--theorempath:active-slam-and-pomdps","from":"theorempath:visual-semantic-slam","to":"theorempath:active-slam-and-pomdps","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:actor-critic-methods","from":"theorempath:policy-gradient-theorem","to":"theorempath:actor-critic-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:q-learning--prerequisite-of--theorempath:actor-critic-methods","from":"theorempath:q-learning","to":"theorempath:actor-critic-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-systems-and-reinforcement-learning-neuroscience--prerequisite-of--theorempath:actor-critic-methods","from":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","to":"theorempath:actor-critic-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:td-learning--prerequisite-of--theorempath:actor-critic-methods","from":"theorempath:td-learning","to":"theorempath:actor-critic-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:adaboost","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:adaboost","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:adam-optimizer","from":"theorempath:gradient-descent-variants","to":"theorempath:adam-optimizer","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:adam-optimizer","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:adam-optimizer","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:adaptive-learning-is-not-iid","from":"theorempath:random-variables","to":"theorempath:adaptive-learning-is-not-iid","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:radon-nikodym-and-conditional-expectation--prerequisite-of--theorempath:adaptive-learning-is-not-iid","from":"theorempath:radon-nikodym-and-conditional-expectation","to":"theorempath:adaptive-learning-is-not-iid","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:adaptive-learning-is-not-iid","from":"theorempath:martingale-theory","to":"theorempath:adaptive-learning-is-not-iid","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:adaptive-learning-is-not-iid","from":"theorempath:concentration-inequalities","to":"theorempath:adaptive-learning-is-not-iid","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rejection-sampling--prerequisite-of--theorempath:adaptive-rejection-sampling","from":"theorempath:rejection-sampling","to":"theorempath:adaptive-rejection-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:griddy-gibbs--prerequisite-of--theorempath:adaptive-rejection-sampling","from":"theorempath:griddy-gibbs","to":"theorempath:adaptive-rejection-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:squeezed-rejection-sampling--prerequisite-of--theorempath:adaptive-rejection-sampling","from":"theorempath:squeezed-rejection-sampling","to":"theorempath:adaptive-rejection-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-odes--prerequisite-of--theorempath:adjoint-sensitivity-method","from":"theorempath:neural-odes","to":"theorempath:adjoint-sensitivity-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:classical-odes--prerequisite-of--theorempath:adjoint-sensitivity-method","from":"theorempath:classical-odes","to":"theorempath:adjoint-sensitivity-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:adjoint-sensitivity-method","from":"theorempath:automatic-differentiation","to":"theorempath:adjoint-sensitivity-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:small-area-estimation--prerequisite-of--theorempath:adjusted-density-maximization","from":"theorempath:small-area-estimation","to":"theorempath:adjusted-density-maximization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reml-and-variance-component-estimation--prerequisite-of--theorempath:adjusted-density-maximization","from":"theorempath:reml-and-variance-component-estimation","to":"theorempath:adjusted-density-maximization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prasad-rao-mse-correction--prerequisite-of--theorempath:adjusted-density-maximization","from":"theorempath:prasad-rao-mse-correction","to":"theorempath:adjusted-density-maximization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:adversarial-machine-learning","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:adversarial-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:minimax-saddle-points--prerequisite-of--theorempath:adversarial-machine-learning","from":"theorempath:minimax-saddle-points","to":"theorempath:adversarial-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:minimax-theorem--prerequisite-of--theorempath:adversarial-machine-learning","from":"theorempath:minimax-theorem","to":"theorempath:adversarial-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-armed-bandits-theory--prerequisite-of--theorempath:agent-based-modeling-with-ml","from":"theorempath:multi-armed-bandits-theory","to":"theorempath:agent-based-modeling-with-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-games-and-self-play--prerequisite-of--theorempath:agent-based-modeling-with-ml","from":"theorempath:markov-games-and-self-play","to":"theorempath:agent-based-modeling-with-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agentic-rl-and-tool-use--prerequisite-of--theorempath:agent-protocols-mcp-a2a","from":"theorempath:agentic-rl-and-tool-use","to":"theorempath:agent-protocols-mcp-a2a","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tool-augmented-reasoning--prerequisite-of--theorempath:agent-protocols-mcp-a2a","from":"theorempath:tool-augmented-reasoning","to":"theorempath:agent-protocols-mcp-a2a","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:agentic-rl-and-tool-use","from":"theorempath:markov-decision-processes","to":"theorempath:agentic-rl-and-tool-use","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:agentic-rl-and-tool-use","from":"theorempath:policy-gradient-theorem","to":"theorempath:agentic-rl-and-tool-use","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:offline-reinforcement-learning--prerequisite-of--theorempath:agentic-rl-and-tool-use","from":"theorempath:offline-reinforcement-learning","to":"theorempath:agentic-rl-and-tool-use","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:video-world-models--prerequisite-of--theorempath:agentic-rl-and-tool-use","from":"theorempath:video-world-models","to":"theorempath:agentic-rl-and-tool-use","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:world-models-and-planning--prerequisite-of--theorempath:agentic-rl-and-tool-use","from":"theorempath:world-models-and-planning","to":"theorempath:agentic-rl-and-tool-use","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-timeline--prerequisite-of--theorempath:ai-labs-landscape","from":"theorempath:model-timeline","to":"theorempath:ai-labs-landscape","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:key-researchers-and-ideas--prerequisite-of--theorempath:ai-labs-landscape","from":"theorempath:key-researchers-and-ideas","to":"theorempath:ai-labs-landscape","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:aic-and-bic","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:aic-and-bic","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:aic-and-bic","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:aic-and-bic","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gauss-markov-theorem--prerequisite-of--theorempath:aic-and-bic","from":"theorempath:gauss-markov-theorem","to":"theorempath:aic-and-bic","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-complexity-and-mdl--prerequisite-of--theorempath:aic-and-bic","from":"theorempath:kolmogorov-complexity-and-mdl","to":"theorempath:aic-and-bic","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:alexnet-and-deep-learning-history","from":"theorempath:convolutional-neural-networks","to":"theorempath:alexnet-and-deep-learning-history","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:empirical-risk-minimization","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vc-dimension--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:vc-dimension","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:concentration-inequalities","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:contraction-inequality--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:contraction-inequality","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cross-validation-theory--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:cross-validation-theory","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-complexity-and-mdl--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:kolmogorov-complexity-and-mdl","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mcdiarmids-inequality--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:mcdiarmids-inequality","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-bayes-bounds--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:pac-bayes-bounds","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:rademacher-complexity","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:regularization-theory--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:regularization-theory","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sample-complexity-bounds--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:sample-complexity-bounds","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:symmetrization-inequality--prerequisite-of--theorempath:algorithmic-stability","from":"theorempath:symmetrization-inequality","to":"theorempath:algorithmic-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:theorem-proving-in-lean--prerequisite-of--theorempath:alphaproof-and-ai-theorem-proving","from":"theorempath:theorem-proving-in-lean","to":"theorempath:alphaproof-and-ai-theorem-proving","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ineffable-intelligence--prerequisite-of--theorempath:alphaproof-and-ai-theorem-proving","from":"theorempath:ineffable-intelligence","to":"theorempath:alphaproof-and-ai-theorem-proving","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:amd-competition-landscape","from":"theorempath:gpu-compute-model","to":"theorempath:amd-competition-landscape","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:analysis-of-variance","from":"theorempath:central-limit-theorem","to":"theorempath:analysis-of-variance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multivariate-normal-distribution--prerequisite-of--theorempath:analysis-of-variance","from":"theorempath:multivariate-normal-distribution","to":"theorempath:analysis-of-variance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:analysis-of-variance","from":"theorempath:linear-regression","to":"theorempath:analysis-of-variance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:analysis-of-variance","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:analysis-of-variance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:analysis-of-variance","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:analysis-of-variance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:anomaly-detection-gravitational-waves","from":"theorempath:convolutional-neural-networks","to":"theorempath:anomaly-detection-gravitational-waves","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signal-detection-theory--prerequisite-of--theorempath:anomaly-detection-gravitational-waves","from":"theorempath:signal-detection-theory","to":"theorempath:anomaly-detection-gravitational-waves","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:anomaly-detection","from":"theorempath:common-probability-distributions","to":"theorempath:anomaly-detection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:anomaly-detection-gravitational-waves--prerequisite-of--theorempath:anomaly-detection","from":"theorempath:anomaly-detection-gravitational-waves","to":"theorempath:anomaly-detection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:anthropic-bias-and-observation-selection","from":"theorempath:bayesian-estimation","to":"theorempath:anthropic-bias-and-observation-selection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:arrows-impossibility","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:arrows-impossibility","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:arrows-impossibility","from":"theorempath:sets-functions-and-relations","to":"theorempath:arrows-impossibility","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:ascent-algorithms","from":"theorempath:convex-optimization-basics","to":"theorempath:ascent-algorithms","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:asymptotic-statistics","from":"theorempath:central-limit-theorem","to":"theorempath:asymptotic-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:asymptotic-statistics","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:asymptotic-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modes-of-convergence-random-variables--prerequisite-of--theorempath:asymptotic-statistics","from":"theorempath:modes-of-convergence-random-variables","to":"theorempath:asymptotic-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cramer-rao-bound--prerequisite-of--theorempath:asymptotic-statistics","from":"theorempath:cramer-rao-bound","to":"theorempath:asymptotic-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cramer-wold-theorem--prerequisite-of--theorempath:asymptotic-statistics","from":"theorempath:cramer-wold-theorem","to":"theorempath:asymptotic-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:asymptotic-statistics","from":"theorempath:fisher-information","to":"theorempath:asymptotic-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:attention-as-kernel-regression","from":"theorempath:attention-mechanism-theory","to":"theorempath:attention-as-kernel-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:attention-as-kernel-regression","from":"theorempath:kernels-and-rkhs","to":"theorempath:attention-as-kernel-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:attention-for-protein-structure-alphafold","from":"theorempath:attention-mechanism-theory","to":"theorempath:attention-for-protein-structure-alphafold","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:attention-for-protein-structure-alphafold","from":"theorempath:transformer-architecture","to":"theorempath:attention-for-protein-structure-alphafold","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:attention-is-all-you-need-paper","from":"theorempath:transformer-architecture","to":"theorempath:attention-is-all-you-need-paper","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:attention-mechanism-theory","from":"theorempath:matrix-operations-and-properties","to":"theorempath:attention-mechanism-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:attention-mechanism-theory","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:attention-mechanism-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gram-matrices-and-kernel-matrices--prerequisite-of--theorempath:attention-mechanism-theory","from":"theorempath:gram-matrices-and-kernel-matrices","to":"theorempath:attention-mechanism-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-layer-shapes-memory--prerequisite-of--theorempath:attention-mechanism-theory","from":"theorempath:linear-layer-shapes-memory","to":"theorempath:attention-mechanism-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:word-embeddings--prerequisite-of--theorempath:attention-mechanism-theory","from":"theorempath:word-embeddings","to":"theorempath:attention-mechanism-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:attention-mechanisms-history","from":"theorempath:recurrent-neural-networks","to":"theorempath:attention-mechanisms-history","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:byte-level-language-models--prerequisite-of--theorempath:attention-mechanisms-history","from":"theorempath:byte-level-language-models","to":"theorempath:attention-mechanisms-history","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:attention-sinks-and-retrieval-decay","from":"theorempath:attention-mechanism-theory","to":"theorempath:attention-sinks-and-retrieval-decay","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fox-forget-gate--prerequisite-of--theorempath:attention-sinks-and-retrieval-decay","from":"theorempath:fox-forget-gate","to":"theorempath:attention-sinks-and-retrieval-decay","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:attention-variants-and-efficiency","from":"theorempath:attention-mechanism-theory","to":"theorempath:attention-variants-and-efficiency","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fast-fourier-transform--prerequisite-of--theorempath:attention-variants-and-efficiency","from":"theorempath:fast-fourier-transform","to":"theorempath:attention-variants-and-efficiency","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:game-theory--prerequisite-of--theorempath:auction-theory","from":"theorempath:game-theory","to":"theorempath:auction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nash-equilibrium--prerequisite-of--theorempath:auction-theory","from":"theorempath:nash-equilibrium","to":"theorempath:auction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:auction-theory","from":"theorempath:common-probability-distributions","to":"theorempath:auction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stable-matching-and-deferred-acceptance--prerequisite-of--theorempath:auction-theory","from":"theorempath:stable-matching-and-deferred-acceptance","to":"theorempath:auction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:speech-and-audio-ml--prerequisite-of--theorempath:audio-language-models","from":"theorempath:speech-and-audio-ml","to":"theorempath:audio-language-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:audio-language-models","from":"theorempath:transformer-architecture","to":"theorempath:audio-language-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:augmented-lagrangian-and-admm","from":"theorempath:convex-optimization-basics","to":"theorempath:augmented-lagrangian-and-admm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:augmented-lagrangian-and-admm","from":"theorempath:convex-duality","to":"theorempath:augmented-lagrangian-and-admm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nonlinear-gauss-seidel--prerequisite-of--theorempath:augmented-lagrangian-and-admm","from":"theorempath:nonlinear-gauss-seidel","to":"theorempath:augmented-lagrangian-and-admm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:projected-gradient-descent--prerequisite-of--theorempath:augmented-lagrangian-and-admm","from":"theorempath:projected-gradient-descent","to":"theorempath:augmented-lagrangian-and-admm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders--prerequisite-of--theorempath:autoencoders-for-low-dimensional-dynamical-structures","from":"theorempath:autoencoders","to":"theorempath:autoencoders-for-low-dimensional-dynamical-structures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:principal-component-analysis--prerequisite-of--theorempath:autoencoders-for-low-dimensional-dynamical-structures","from":"theorempath:principal-component-analysis","to":"theorempath:autoencoders-for-low-dimensional-dynamical-structures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:autoencoders-for-single-cell-rna-seq","from":"theorempath:variational-autoencoders","to":"theorempath:autoencoders-for-single-cell-rna-seq","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders--prerequisite-of--theorempath:autoencoders-for-single-cell-rna-seq","from":"theorempath:autoencoders","to":"theorempath:autoencoders-for-single-cell-rna-seq","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:autoencoders","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:autoencoders","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:boltzmann-machines-and-hopfield-networks--prerequisite-of--theorempath:autoencoders","from":"theorempath:boltzmann-machines-and-hopfield-networks","to":"theorempath:autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:dimensionality-reduction-theory--prerequisite-of--theorempath:autoencoders","from":"theorempath:dimensionality-reduction-theory","to":"theorempath:autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-maximization-variants--prerequisite-of--theorempath:autoencoders","from":"theorempath:expectation-maximization-variants","to":"theorempath:autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tsne-and-umap--prerequisite-of--theorempath:autoencoders","from":"theorempath:tsne-and-umap","to":"theorempath:autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:automatic-differentiation","from":"theorempath:the-jacobian-matrix","to":"theorempath:automatic-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:automatic-differentiation","from":"theorempath:differentiation-in-rn","to":"theorempath:automatic-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-calculus--prerequisite-of--theorempath:automatic-differentiation","from":"theorempath:matrix-calculus","to":"theorempath:automatic-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:taylor-expansion--prerequisite-of--theorempath:automatic-differentiation","from":"theorempath:taylor-expansion","to":"theorempath:automatic-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:automatic-differentiation","from":"theorempath:the-hessian-matrix","to":"theorempath:automatic-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vector-calculus-chain-rule--prerequisite-of--theorempath:automatic-differentiation","from":"theorempath:vector-calculus-chain-rule","to":"theorempath:automatic-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:backward-sde-theory","from":"theorempath:stochastic-differential-equations","to":"theorempath:backward-sde-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ito-lemma--prerequisite-of--theorempath:backward-sde-theory","from":"theorempath:ito-lemma","to":"theorempath:backward-sde-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feynman-kac-formula--prerequisite-of--theorempath:backward-sde-theory","from":"theorempath:feynman-kac-formula","to":"theorempath:backward-sde-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hamilton-jacobi-bellman-equation--prerequisite-of--theorempath:backward-sde-theory","from":"theorempath:hamilton-jacobi-bellman-equation","to":"theorempath:backward-sde-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bootstrap-methods--prerequisite-of--theorempath:bagging","from":"theorempath:bootstrap-methods","to":"theorempath:bagging","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:bagging","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:bagging","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:base-rate-fallacy","from":"theorempath:common-probability-distributions","to":"theorempath:base-rate-fallacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:birthday-paradox--prerequisite-of--theorempath:base-rate-fallacy","from":"theorempath:birthday-paradox","to":"theorempath:base-rate-fallacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrices-and-classification-metrics--prerequisite-of--theorempath:base-rate-fallacy","from":"theorempath:confusion-matrices-and-classification-metrics","to":"theorempath:base-rate-fallacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:monty-hall-problem--prerequisite-of--theorempath:base-rate-fallacy","from":"theorempath:monty-hall-problem","to":"theorempath:base-rate-fallacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:simpsons-paradox--prerequisite-of--theorempath:base-rate-fallacy","from":"theorempath:simpsons-paradox","to":"theorempath:base-rate-fallacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:basu-theorem","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:basu-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:batch-normalization","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:batch-normalization","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:activation-functions--prerequisite-of--theorempath:batch-normalization","from":"theorempath:activation-functions","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-flow-and-vanishing-gradients--prerequisite-of--theorempath:batch-normalization","from":"theorempath:gradient-flow-and-vanishing-gradients","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:regularization-in-practice--prerequisite-of--theorempath:batch-normalization","from":"theorempath:regularization-in-practice","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skip-connections-and-resnets--prerequisite-of--theorempath:batch-normalization","from":"theorempath:skip-connections-and-resnets","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:weight-initialization--prerequisite-of--theorempath:batch-normalization","from":"theorempath:weight-initialization","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:whitening-and-decorrelation--prerequisite-of--theorempath:batch-normalization","from":"theorempath:whitening-and-decorrelation","to":"theorempath:batch-normalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:batch-size-and-learning-dynamics","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:batch-size-and-learning-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adam-optimizer--prerequisite-of--theorempath:batch-size-and-learning-dynamics","from":"theorempath:adam-optimizer","to":"theorempath:batch-size-and-learning-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:bayesian-estimation","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:bayesian-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:bayesian-estimation","from":"theorempath:common-probability-distributions","to":"theorempath:bayesian-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:joint-marginal-conditional-distributions--prerequisite-of--theorempath:bayesian-estimation","from":"theorempath:joint-marginal-conditional-distributions","to":"theorempath:bayesian-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:shrinkage-estimation-james-stein--prerequisite-of--theorempath:bayesian-estimation","from":"theorempath:shrinkage-estimation-james-stein","to":"theorempath:bayesian-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:linear-regression","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:ridge-regression","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multivariate-normal-distribution--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:multivariate-normal-distribution","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:bayesian-estimation","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-priors--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:conjugate-priors","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-a-posteriori-estimation--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:maximum-a-posteriori-estimation","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:bayesian-linear-regression","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:bayesian-linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:bayesian-neural-networks","from":"theorempath:bayesian-estimation","to":"theorempath:bayesian-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:bayesian-neural-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:bayesian-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-for-ml--prerequisite-of--theorempath:bayesian-neural-networks","from":"theorempath:gaussian-processes-for-ml","to":"theorempath:bayesian-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-u-turn-sampler-and-neals-funnel--prerequisite-of--theorempath:bayesian-neural-networks","from":"theorempath:no-u-turn-sampler-and-neals-funnel","to":"theorempath:bayesian-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-regression--prerequisite-of--theorempath:bayesian-optimization-for-hyperparameters","from":"theorempath:gaussian-processes-regression","to":"theorempath:bayesian-optimization-for-hyperparameters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-for-ml--prerequisite-of--theorempath:bayesian-optimization-for-hyperparameters","from":"theorempath:gaussian-processes-for-ml","to":"theorempath:bayesian-optimization-for-hyperparameters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:bayesian-state-estimation","from":"theorempath:bayesian-estimation","to":"theorempath:bayesian-state-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:bayesian-state-estimation","from":"theorempath:common-probability-distributions","to":"theorempath:bayesian-state-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-in-astronomy--prerequisite-of--theorempath:bayesian-state-estimation","from":"theorempath:gaussian-processes-in-astronomy","to":"theorempath:bayesian-state-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kalman-filter--prerequisite-of--theorempath:bayesian-state-estimation","from":"theorempath:kalman-filter","to":"theorempath:bayesian-state-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-u-turn-sampler-and-neals-funnel--prerequisite-of--theorempath:bayesian-state-estimation","from":"theorempath:no-u-turn-sampler-and-neals-funnel","to":"theorempath:bayesian-state-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:bellman-equations","from":"theorempath:markov-decision-processes","to":"theorempath:bellman-equations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:bellman-equations","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:bellman-equations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:evaluation-metrics-and-properties--prerequisite-of--theorempath:benchmarking-methodology","from":"theorempath:evaluation-metrics-and-properties","to":"theorempath:benchmarking-methodology","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reproducibility-and-experimental-rigor--prerequisite-of--theorempath:benchmarking-methodology","from":"theorempath:reproducibility-and-experimental-rigor","to":"theorempath:benchmarking-methodology","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:benfords-law","from":"theorempath:common-probability-distributions","to":"theorempath:benfords-law","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:implicit-bias-and-modern-generalization--prerequisite-of--theorempath:benign-overfitting","from":"theorempath:implicit-bias-and-modern-generalization","to":"theorempath:benign-overfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-matrix-theory-overview--prerequisite-of--theorempath:benign-overfitting","from":"theorempath:random-matrix-theory-overview","to":"theorempath:benign-overfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:double-descent--prerequisite-of--theorempath:benign-overfitting","from":"theorempath:double-descent","to":"theorempath:benign-overfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-network-optimization-landscape--prerequisite-of--theorempath:benign-overfitting","from":"theorempath:neural-network-optimization-landscape","to":"theorempath:benign-overfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-tangent-kernel--prerequisite-of--theorempath:benign-overfitting","from":"theorempath:neural-tangent-kernel","to":"theorempath:benign-overfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:benign-overfitting","from":"theorempath:ridge-regression","to":"theorempath:benign-overfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:bennetts-inequality","from":"theorempath:concentration-inequalities","to":"theorempath:bennetts-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chernoff-bounds--prerequisite-of--theorempath:bennetts-inequality","from":"theorempath:chernoff-bounds","to":"theorempath:bennetts-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:bennetts-inequality","from":"theorempath:moment-generating-functions","to":"theorempath:bennetts-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:bennetts-inequality","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:bennetts-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:bernstein-inequality","from":"theorempath:concentration-inequalities","to":"theorempath:bernstein-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:bernstein-inequality","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:bernstein-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:bernstein-inequality","from":"theorempath:moment-generating-functions","to":"theorempath:bernstein-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bennetts-inequality--prerequisite-of--theorempath:bernstein-inequality","from":"theorempath:bennetts-inequality","to":"theorempath:bernstein-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hoeffdings-lemma--prerequisite-of--theorempath:bernstein-inequality","from":"theorempath:hoeffdings-lemma","to":"theorempath:bernstein-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:bert-and-pretrain-finetune-paradigm","from":"theorempath:transformer-architecture","to":"theorempath:bert-and-pretrain-finetune-paradigm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:token-prediction-and-language-modeling--prerequisite-of--theorempath:bert-and-pretrain-finetune-paradigm","from":"theorempath:token-prediction-and-language-modeling","to":"theorempath:bert-and-pretrain-finetune-paradigm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nlp-for-economic-text-analysis--prerequisite-of--theorempath:bert-and-pretrain-finetune-paradigm","from":"theorempath:nlp-for-economic-text-analysis","to":"theorempath:bert-and-pretrain-finetune-paradigm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:beta-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:beta-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:beta-distribution","from":"theorempath:distributions-atlas","to":"theorempath:beta-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gamma-distribution--prerequisite-of--theorempath:beta-distribution","from":"theorempath:gamma-distribution","to":"theorempath:beta-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-learning-framework--prerequisite-of--theorempath:bias-complexity-tradeoff","from":"theorempath:pac-learning-framework","to":"theorempath:bias-complexity-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:bias-complexity-tradeoff","from":"theorempath:empirical-risk-minimization","to":"theorempath:bias-complexity-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-free-lunch-theorem--prerequisite-of--theorempath:bias-complexity-tradeoff","from":"theorempath:no-free-lunch-theorem","to":"theorempath:bias-complexity-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:empirical-risk-minimization","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:elastic-net--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:elastic-net","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:elements-of-statistical-learning-book--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:elements-of-statistical-learning-book","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:generalized-additive-models--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:generalized-additive-models","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:knn--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:knn","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:linear-regression","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-complexity-tradeoff--prerequisite-of--theorempath:bias-variance-tradeoff","from":"theorempath:bias-complexity-tradeoff","to":"theorempath:bias-variance-tradeoff","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:birthday-paradox","from":"theorempath:common-probability-distributions","to":"theorempath:birthday-paradox","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:monty-hall-problem--prerequisite-of--theorempath:birthday-paradox","from":"theorempath:monty-hall-problem","to":"theorempath:birthday-paradox","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:bits-nats-perplexity-bpb","from":"theorempath:information-theory-foundations","to":"theorempath:bits-nats-perplexity-bpb","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:bits-nats-perplexity-bpb","from":"theorempath:kl-divergence","to":"theorempath:bits-nats-perplexity-bpb","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:boltzmann-machines-and-hopfield-networks","from":"theorempath:common-probability-distributions","to":"theorempath:boltzmann-machines-and-hopfield-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:common-probability-distributions","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:asymptotic-statistics--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:asymptotic-statistics","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:central-limit-theorem","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cross-validation-theory--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:cross-validation-theory","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neyman-pearson-and-hypothesis-testing-theory--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:neyman-pearson-and-hypothesis-testing-theory","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:order-statistics--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:order-statistics","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:statistical-significance-and-multiple-comparisons--prerequisite-of--theorempath:bootstrap-methods","from":"theorempath:statistical-significance-and-multiple-comparisons","to":"theorempath:bootstrap-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:borel-cantelli-lemmas","from":"theorempath:measure-theoretic-probability","to":"theorempath:borel-cantelli-lemmas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modes-of-convergence-random-variables--prerequisite-of--theorempath:borel-cantelli-lemmas","from":"theorempath:modes-of-convergence-random-variables","to":"theorempath:borel-cantelli-lemmas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-theory-foundations--prerequisite-of--theorempath:bounded-rationality","from":"theorempath:decision-theory-foundations","to":"theorempath:bounded-rationality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:bounded-rationality","from":"theorempath:convex-optimization-basics","to":"theorempath:bounded-rationality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-tinkering--prerequisite-of--theorempath:bounded-rationality","from":"theorempath:convex-tinkering","to":"theorempath:bounded-rationality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:editorial-principles--prerequisite-of--theorempath:bounded-rationality","from":"theorempath:editorial-principles","to":"theorempath:bounded-rationality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:leverage-points-systems--prerequisite-of--theorempath:bounded-rationality","from":"theorempath:leverage-points-systems","to":"theorempath:bounded-rationality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:metropolis-hastings","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chains-and-steady-state--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:markov-chains-and-steady-state","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:coupling-arguments-and-mixing-time--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:coupling-arguments-and-mixing-time","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gibbs-sampling--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:gibbs-sampling","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hamiltonian-monte-carlo--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:hamiltonian-monte-carlo","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chain-monte-carlo--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:markov-chain-monte-carlo","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mcmc-for-markov-random-fields--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:mcmc-for-markov-random-fields","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:perfect-sampling--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:perfect-sampling","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:slice-sampling--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:slice-sampling","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variance-reduction-techniques--prerequisite-of--theorempath:burn-in-convergence-diagnostics","from":"theorempath:variance-reduction-techniques","to":"theorempath:burn-in-convergence-diagnostics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tokenization-and-information-theory--prerequisite-of--theorempath:byte-level-language-models","from":"theorempath:tokenization-and-information-theory","to":"theorempath:byte-level-language-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:morphology-and-subword-modeling--prerequisite-of--theorempath:byte-level-language-models","from":"theorempath:morphology-and-subword-modeling","to":"theorempath:byte-level-language-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:calibration-and-uncertainty","from":"theorempath:logistic-regression","to":"theorempath:calibration-and-uncertainty","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bits-nats-perplexity-bpb--prerequisite-of--theorempath:calibration-and-uncertainty","from":"theorempath:bits-nats-perplexity-bpb","to":"theorempath:calibration-and-uncertainty","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decoding-strategies--prerequisite-of--theorempath:calibration-and-uncertainty","from":"theorempath:decoding-strategies","to":"theorempath:calibration-and-uncertainty","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:goodness-of-fit-tests--prerequisite-of--theorempath:calibration-and-uncertainty","from":"theorempath:goodness-of-fit-tests","to":"theorempath:calibration-and-uncertainty","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:roc-curve-and-auc--prerequisite-of--theorempath:calibration-and-uncertainty","from":"theorempath:roc-curve-and-auc","to":"theorempath:calibration-and-uncertainty","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:split-conformal-prediction--prerequisite-of--theorempath:calibration-and-uncertainty","from":"theorempath:split-conformal-prediction","to":"theorempath:calibration-and-uncertainty","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:zermelo-fraenkel-set-theory--prerequisite-of--theorempath:cantors-theorem-and-uncountability","from":"theorempath:zermelo-fraenkel-set-theory","to":"theorempath:cantors-theorem-and-uncountability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:cap-theorem","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:cap-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributed-consensus--prerequisite-of--theorempath:cap-theorem","from":"theorempath:distributed-consensus","to":"theorempath:cap-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:cardinality-and-countability","from":"theorempath:sets-functions-and-relations","to":"theorempath:cardinality-and-countability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fine-tuning-and-adaptation--prerequisite-of--theorempath:catastrophic-forgetting","from":"theorempath:fine-tuning-and-adaptation","to":"theorempath:catastrophic-forgetting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:category-theory","from":"theorempath:sets-functions-and-relations","to":"theorempath:category-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:category-theory","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:category-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:causal-inference-basics","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:causal-inference-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feature-importance-and-interpretability--prerequisite-of--theorempath:causal-inference-basics","from":"theorempath:feature-importance-and-interpretability","to":"theorempath:causal-inference-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survival-analysis--prerequisite-of--theorempath:causal-inference-basics","from":"theorempath:survival-analysis","to":"theorempath:causal-inference-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-basics--prerequisite-of--theorempath:causal-inference-for-policy-evaluation","from":"theorempath:causal-inference-basics","to":"theorempath:causal-inference-for-policy-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-pearl--prerequisite-of--theorempath:causal-inference-for-policy-evaluation","from":"theorempath:causal-inference-pearl","to":"theorempath:causal-inference-for-policy-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:causal-inference-for-policy-evaluation","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:causal-inference-for-policy-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:causal-inference-pearl","from":"theorempath:common-probability-distributions","to":"theorempath:causal-inference-pearl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:causal-inference-pearl","from":"theorempath:bayesian-estimation","to":"theorempath:causal-inference-pearl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-basics--prerequisite-of--theorempath:causal-inference-pearl","from":"theorempath:causal-inference-basics","to":"theorempath:causal-inference-pearl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:double-debiased-machine-learning--prerequisite-of--theorempath:causal-inference-pearl","from":"theorempath:double-debiased-machine-learning","to":"theorempath:causal-inference-pearl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:editorial-principles--prerequisite-of--theorempath:causal-inference-pearl","from":"theorempath:editorial-principles","to":"theorempath:causal-inference-pearl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:central-limit-theorem","from":"theorempath:law-of-large-numbers","to":"theorempath:central-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:central-limit-theorem","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:central-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:central-limit-theorem","from":"theorempath:common-probability-distributions","to":"theorempath:central-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:characteristic-functions--prerequisite-of--theorempath:central-limit-theorem","from":"theorempath:characteristic-functions","to":"theorempath:central-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modes-of-convergence-random-variables--prerequisite-of--theorempath:central-limit-theorem","from":"theorempath:modes-of-convergence-random-variables","to":"theorempath:central-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prompt-engineering-and-in-context-learning--prerequisite-of--theorempath:chain-of-thought-and-reasoning","from":"theorempath:prompt-engineering-and-in-context-learning","to":"theorempath:chain-of-thought-and-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:chain-of-thought-and-reasoning","from":"theorempath:transformer-architecture","to":"theorempath:chain-of-thought-and-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decoding-strategies--prerequisite-of--theorempath:chain-of-thought-and-reasoning","from":"theorempath:decoding-strategies","to":"theorempath:chain-of-thought-and-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:chain-of-thought-and-reasoning","from":"theorempath:scaling-laws","to":"theorempath:chain-of-thought-and-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:characteristic-functions","from":"theorempath:measure-theoretic-probability","to":"theorempath:characteristic-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:characteristic-functions","from":"theorempath:moment-generating-functions","to":"theorempath:characteristic-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:chernoff-bounds","from":"theorempath:concentration-inequalities","to":"theorempath:chernoff-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:chernoff-bounds","from":"theorempath:moment-generating-functions","to":"theorempath:chernoff-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:chi-squared-concentration","from":"theorempath:concentration-inequalities","to":"theorempath:chi-squared-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chernoff-bounds--prerequisite-of--theorempath:chi-squared-concentration","from":"theorempath:chernoff-bounds","to":"theorempath:chi-squared-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:chi-squared-concentration","from":"theorempath:common-probability-distributions","to":"theorempath:chi-squared-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:chi-squared-concentration","from":"theorempath:moment-generating-functions","to":"theorempath:chi-squared-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:chi-squared-distribution-and-tests","from":"theorempath:distributions-atlas","to":"theorempath:chi-squared-distribution-and-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normal-distribution--prerequisite-of--theorempath:chi-squared-distribution-and-tests","from":"theorempath:normal-distribution","to":"theorempath:chi-squared-distribution-and-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gamma-distribution--prerequisite-of--theorempath:chi-squared-distribution-and-tests","from":"theorempath:gamma-distribution","to":"theorempath:chi-squared-distribution-and-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:chi-squared-distribution-and-tests","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:chi-squared-distribution-and-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrices-and-classification-metrics--prerequisite-of--theorempath:class-imbalance-and-resampling","from":"theorempath:confusion-matrices-and-classification-metrics","to":"theorempath:class-imbalance-and-resampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuity-in-rn--prerequisite-of--theorempath:classical-odes","from":"theorempath:continuity-in-rn","to":"theorempath:classical-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:classical-odes","from":"theorempath:the-jacobian-matrix","to":"theorempath:classical-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:claude-model-family","from":"theorempath:transformer-architecture","to":"theorempath:claude-model-family","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:contrastive-learning--prerequisite-of--theorempath:clip-and-openclip-in-practice","from":"theorempath:contrastive-learning","to":"theorempath:clip-and-openclip-in-practice","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vision-transformer-lineage--prerequisite-of--theorempath:clip-and-openclip-in-practice","from":"theorempath:vision-transformer-lineage","to":"theorempath:clip-and-openclip-in-practice","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:clip-and-openclip-in-practice","from":"theorempath:information-theory-foundations","to":"theorempath:clip-and-openclip-in-practice","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:florence-and-vision-foundation-models--prerequisite-of--theorempath:clip-and-openclip-in-practice","from":"theorempath:florence-and-vision-foundation-models","to":"theorempath:clip-and-openclip-in-practice","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:k-means-clustering--prerequisite-of--theorempath:clustering-for-gene-expression","from":"theorempath:k-means-clustering","to":"theorempath:clustering-for-gene-expression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:spectral-clustering--prerequisite-of--theorempath:clustering-for-gene-expression","from":"theorempath:spectral-clustering","to":"theorempath:clustering-for-gene-expression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:cnns-for-medical-imaging","from":"theorempath:convolutional-neural-networks","to":"theorempath:cnns-for-medical-imaging","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:object-detection-and-segmentation--prerequisite-of--theorempath:cnns-for-medical-imaging","from":"theorempath:object-detection-and-segmentation","to":"theorempath:cnns-for-medical-imaging","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:cnns-for-signal-feature-extraction","from":"theorempath:convolutional-neural-networks","to":"theorempath:cnns-for-signal-feature-extraction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signals-and-systems-for-ml--prerequisite-of--theorempath:cnns-for-signal-feature-extraction","from":"theorempath:signals-and-systems-for-ml","to":"theorempath:cnns-for-signal-feature-extraction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:cohere-models","from":"theorempath:transformer-architecture","to":"theorempath:cohere-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tokenization-and-information-theory--prerequisite-of--theorempath:cohere-models","from":"theorempath:tokenization-and-information-theory","to":"theorempath:cohere-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-retrieval--prerequisite-of--theorempath:cohere-models","from":"theorempath:information-retrieval","to":"theorempath:cohere-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:common-inequalities","from":"theorempath:common-probability-distributions","to":"theorempath:common-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-probability-axioms--prerequisite-of--theorempath:common-inequalities","from":"theorempath:kolmogorov-probability-axioms","to":"theorempath:common-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:common-probability-distributions","from":"theorempath:sets-functions-and-relations","to":"theorempath:common-probability-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:common-probability-distributions","from":"theorempath:exponential-function-properties","to":"theorempath:common-probability-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:integration-and-change-of-variables--prerequisite-of--theorempath:common-probability-distributions","from":"theorempath:integration-and-change-of-variables","to":"theorempath:common-probability-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:common-probability-distributions","from":"theorempath:measure-theoretic-probability","to":"theorempath:common-probability-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:common-probability-distributions","from":"theorempath:random-variables","to":"theorempath:common-probability-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:game-theory--prerequisite-of--theorempath:commons-governance-ostrom","from":"theorempath:game-theory","to":"theorempath:commons-governance-ostrom","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:editorial-principles--prerequisite-of--theorempath:commons-governance-ostrom","from":"theorempath:editorial-principles","to":"theorempath:commons-governance-ostrom","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:compactness-and-heine-borel","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:compactness-and-heine-borel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:complex-numbers-for-fourier","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:complex-numbers-for-fourier","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:floating-point-arithmetic--prerequisite-of--theorempath:computer-architecture-for-ml","from":"theorempath:floating-point-arithmetic","to":"theorempath:computer-architecture-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:common-probability-distributions","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:central-limit-theorem","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-inequalities--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:common-inequalities","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:law-of-large-numbers","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:martingale-theory","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:measure-theoretic-probability","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:moment-generating-functions","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:radon-nikodym-and-conditional-expectation--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:radon-nikodym-and-conditional-expectation","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skewness-kurtosis-and-higher-moments--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:skewness-kurtosis-and-higher-moments","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:concentration-inequalities","from":"theorempath:sets-functions-and-relations","to":"theorempath:concentration-inequalities","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:conditioning-and-condition-number","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:conditioning-and-condition-number","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:conditioning-and-condition-number","from":"theorempath:matrix-operations-and-properties","to":"theorempath:conditioning-and-condition-number","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-norms--prerequisite-of--theorempath:conditioning-and-condition-number","from":"theorempath:matrix-norms","to":"theorempath:conditioning-and-condition-number","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:numerical-stability--prerequisite-of--theorempath:conditioning-and-condition-number","from":"theorempath:numerical-stability","to":"theorempath:conditioning-and-condition-number","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:singular-value-decomposition--prerequisite-of--theorempath:conditioning-and-condition-number","from":"theorempath:singular-value-decomposition","to":"theorempath:conditioning-and-condition-number","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:conditioning-and-condition-number","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:conditioning-and-condition-number","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:confusion-matrices-and-classification-metrics","from":"theorempath:common-probability-distributions","to":"theorempath:confusion-matrices-and-classification-metrics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-class-and-multi-label-classification--prerequisite-of--theorempath:confusion-matrices-and-classification-metrics","from":"theorempath:multi-class-and-multi-label-classification","to":"theorempath:confusion-matrices-and-classification-metrics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signal-detection-theory--prerequisite-of--theorempath:confusion-matrices-and-classification-metrics","from":"theorempath:signal-detection-theory","to":"theorempath:confusion-matrices-and-classification-metrics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:line-search-methods--prerequisite-of--theorempath:conjugate-gradient-methods","from":"theorempath:line-search-methods","to":"theorempath:conjugate-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:conjugate-gradient-methods","from":"theorempath:matrix-operations-and-properties","to":"theorempath:conjugate-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-norms--prerequisite-of--theorempath:conjugate-gradient-methods","from":"theorempath:matrix-norms","to":"theorempath:conjugate-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:numerical-linear-algebra--prerequisite-of--theorempath:conjugate-gradient-methods","from":"theorempath:numerical-linear-algebra","to":"theorempath:conjugate-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:conjugate-priors","from":"theorempath:bayesian-estimation","to":"theorempath:conjugate-priors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:conjugate-priors","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:conjugate-priors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:conjugate-priors","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:conjugate-priors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:conjugate-priors","from":"theorempath:common-probability-distributions","to":"theorempath:conjugate-priors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multivariate-normal-distribution--prerequisite-of--theorempath:conjugate-priors","from":"theorempath:multivariate-normal-distribution","to":"theorempath:conjugate-priors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-a-posteriori-estimation--prerequisite-of--theorempath:conjugate-priors","from":"theorempath:maximum-a-posteriori-estimation","to":"theorempath:conjugate-priors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:constitutional-ai","from":"theorempath:rlhf-and-alignment","to":"theorempath:constitutional-ai","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-from-human-feedback-deep-dive--prerequisite-of--theorempath:constitutional-ai","from":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","to":"theorempath:constitutional-ai","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-hacking--prerequisite-of--theorempath:constitutional-ai","from":"theorempath:reward-hacking","to":"theorempath:constitutional-ai","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache--prerequisite-of--theorempath:context-engineering","from":"theorempath:kv-cache","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:context-engineering","from":"theorempath:attention-mechanism-theory","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agent-protocols-mcp-a2a--prerequisite-of--theorempath:context-engineering","from":"theorempath:agent-protocols-mcp-a2a","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-sinks-and-retrieval-decay--prerequisite-of--theorempath:context-engineering","from":"theorempath:attention-sinks-and-retrieval-decay","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inference-systems-overview--prerequisite-of--theorempath:context-engineering","from":"theorempath:inference-systems-overview","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mamba-and-state-space-models--prerequisite-of--theorempath:context-engineering","from":"theorempath:mamba-and-state-space-models","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prompt-engineering-and-in-context-learning--prerequisite-of--theorempath:context-engineering","from":"theorempath:prompt-engineering-and-in-context-learning","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:semantic-search-and-embeddings--prerequisite-of--theorempath:context-engineering","from":"theorempath:semantic-search-and-embeddings","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-attention-and-long-context--prerequisite-of--theorempath:context-engineering","from":"theorempath:sparse-attention-and-long-context","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:speculative-decoding-and-quantization--prerequisite-of--theorempath:context-engineering","from":"theorempath:speculative-decoding-and-quantization","to":"theorempath:context-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:optimizer-theory-sgd-adam-muon--prerequisite-of--theorempath:continual-learning-and-forgetting","from":"theorempath:optimizer-theory-sgd-adam-muon","to":"theorempath:continual-learning-and-forgetting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:continuity-in-rn","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:continuity-in-rn","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-odes--prerequisite-of--theorempath:continuous-normalizing-flows","from":"theorempath:neural-odes","to":"theorempath:continuous-normalizing-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normalization-flows--prerequisite-of--theorempath:continuous-normalizing-flows","from":"theorempath:normalization-flows","to":"theorempath:continuous-normalizing-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:continuous-normalizing-flows","from":"theorempath:the-jacobian-matrix","to":"theorempath:continuous-normalizing-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adjoint-sensitivity-method--prerequisite-of--theorempath:continuous-normalizing-flows","from":"theorempath:adjoint-sensitivity-method","to":"theorempath:continuous-normalizing-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-odes--prerequisite-of--theorempath:continuous-thought-machines","from":"theorempath:neural-odes","to":"theorempath:continuous-thought-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:equilibrium-and-implicit-models--prerequisite-of--theorempath:continuous-thought-machines","from":"theorempath:equilibrium-and-implicit-models","to":"theorempath:continuous-thought-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:contraction-inequality","from":"theorempath:rademacher-complexity","to":"theorempath:contraction-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:contrastive-learning","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:contrastive-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:convex-duality","from":"theorempath:convex-optimization-basics","to":"theorempath:convex-duality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inverse-and-implicit-function-theorem--prerequisite-of--theorempath:convex-duality","from":"theorempath:inverse-and-implicit-function-theorem","to":"theorempath:convex-duality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgradients-and-subdifferentials--prerequisite-of--theorempath:convex-duality","from":"theorempath:subgradients-and-subdifferentials","to":"theorempath:convex-duality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:differentiation-in-rn","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:matrix-operations-and-properties","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-inequalities--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:common-inequalities","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuity-in-rn--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:continuity-in-rn","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:dynamic-programming--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:dynamic-programming","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graphslam-and-factor-graphs--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:graphslam-and-factor-graphs","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inverse-and-implicit-function-theorem--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:inverse-and-implicit-function-theorem","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:positive-semidefinite-matrices--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:positive-semidefinite-matrices","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:submodular-optimization--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:submodular-optimization","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:taylor-expansion--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:taylor-expansion","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:convex-optimization-basics","from":"theorempath:the-hessian-matrix","to":"theorempath:convex-optimization-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-inequalities--prerequisite-of--theorempath:convex-tinkering","from":"theorempath:common-inequalities","to":"theorempath:convex-tinkering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:editorial-principles--prerequisite-of--theorempath:convex-tinkering","from":"theorempath:editorial-principles","to":"theorempath:convex-tinkering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:non-probability-sampling--prerequisite-of--theorempath:convex-tinkering","from":"theorempath:non-probability-sampling","to":"theorempath:convex-tinkering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:convolutional-neural-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:convolutional-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:convolutional-neural-networks","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:convolutional-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fast-fourier-transform--prerequisite-of--theorempath:convolutional-neural-networks","from":"theorempath:fast-fourier-transform","to":"theorempath:convolutional-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signals-and-systems-for-ml--prerequisite-of--theorempath:convolutional-neural-networks","from":"theorempath:signals-and-systems-for-ml","to":"theorempath:convolutional-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skip-connections-and-resnets--prerequisite-of--theorempath:convolutional-neural-networks","from":"theorempath:skip-connections-and-resnets","to":"theorempath:convolutional-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:svm-for-rf-classification--prerequisite-of--theorempath:convolutional-neural-networks","from":"theorempath:svm-for-rf-classification","to":"theorempath:convolutional-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:coordinate-descent","from":"theorempath:convex-optimization-basics","to":"theorempath:coordinate-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mirror-descent-and-frank-wolfe--prerequisite-of--theorempath:coordinate-descent","from":"theorempath:mirror-descent-and-frank-wolfe","to":"theorempath:coordinate-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:proximal-gradient-methods--prerequisite-of--theorempath:coordinate-descent","from":"theorempath:proximal-gradient-methods","to":"theorempath:coordinate-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:copulas","from":"theorempath:common-probability-distributions","to":"theorempath:copulas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:counting-and-combinatorics","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:counting-and-combinatorics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:coupling-arguments-and-mixing-time","from":"theorempath:metropolis-hastings","to":"theorempath:coupling-arguments-and-mixing-time","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:coupling-arguments-and-mixing-time","from":"theorempath:martingale-theory","to":"theorempath:coupling-arguments-and-mixing-time","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:total-variation-distance--prerequisite-of--theorempath:coupling-arguments-and-mixing-time","from":"theorempath:total-variation-distance","to":"theorempath:coupling-arguments-and-mixing-time","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:cramer-rao-bound","from":"theorempath:fisher-information","to":"theorempath:cramer-rao-bound","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:cramer-rao-bound","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:cramer-rao-bound","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:cramer-rao-bound","from":"theorempath:kl-divergence","to":"theorempath:cramer-rao-bound","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:cramer-wold-theorem","from":"theorempath:central-limit-theorem","to":"theorempath:cramer-wold-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:cramer-wold-theorem","from":"theorempath:measure-theoretic-probability","to":"theorempath:cramer-wold-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:cross-entropy-loss-deep-dive","from":"theorempath:information-theory-foundations","to":"theorempath:cross-entropy-loss-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:cross-entropy-loss-deep-dive","from":"theorempath:logistic-regression","to":"theorempath:cross-entropy-loss-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:log-probability-computation--prerequisite-of--theorempath:cross-entropy-loss-deep-dive","from":"theorempath:log-probability-computation","to":"theorempath:cross-entropy-loss-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-class-and-multi-label-classification--prerequisite-of--theorempath:cross-entropy-loss-deep-dive","from":"theorempath:multi-class-and-multi-label-classification","to":"theorempath:cross-entropy-loss-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:empirical-risk-minimization","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-variance-tradeoff--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:bias-variance-tradeoff","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:aic-and-bic--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:aic-and-bic","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:class-imbalance-and-resampling--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:class-imbalance-and-resampling","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrices-and-classification-metrics--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:confusion-matrices-and-classification-metrics","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrix-deep-dive--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:confusion-matrix-deep-dive","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:evaluation-metrics-and-properties--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:evaluation-metrics-and-properties","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feature-importance-and-interpretability--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:feature-importance-and-interpretability","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-regression--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:gaussian-processes-regression","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-evaluation-best-practices--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:model-evaluation-best-practices","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:overfitting-and-underfitting--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:overfitting-and-underfitting","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:proper-scoring-rules--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:proper-scoring-rules","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:statistical-significance-and-multiple-comparisons--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:statistical-significance-and-multiple-comparisons","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:train-test-split-and-data-leakage--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:train-test-split-and-data-leakage","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:xgboost--prerequisite-of--theorempath:cross-validation-theory","from":"theorempath:xgboost","to":"theorempath:cross-validation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:cubist-and-model-trees","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:cubist-and-model-trees","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:cubist-and-model-trees","from":"theorempath:linear-regression","to":"theorempath:cubist-and-model-trees","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:cuda-programming-fundamentals","from":"theorempath:gpu-compute-model","to":"theorempath:cuda-programming-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:synthetic-data-distillation--prerequisite-of--theorempath:curriculum-learning","from":"theorempath:synthetic-data-distillation","to":"theorempath:curriculum-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hough-transform-and-circle-detection--prerequisite-of--theorempath:cv-for-intelligence-imagery","from":"theorempath:hough-transform-and-circle-detection","to":"theorempath:cv-for-intelligence-imagery","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:contrastive-learning--prerequisite-of--theorempath:data-augmentation-theory","from":"theorempath:contrastive-learning","to":"theorempath:data-augmentation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:regularization-in-practice--prerequisite-of--theorempath:data-augmentation-theory","from":"theorempath:regularization-in-practice","to":"theorempath:data-augmentation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:self-supervised-vision--prerequisite-of--theorempath:data-augmentation-theory","from":"theorempath:self-supervised-vision","to":"theorempath:data-augmentation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:synthetic-data-generation--prerequisite-of--theorempath:data-augmentation-theory","from":"theorempath:synthetic-data-generation","to":"theorempath:data-augmentation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:data-contamination-and-evaluation","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:data-contamination-and-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:benchmarking-methodology--prerequisite-of--theorempath:data-contamination-and-evaluation","from":"theorempath:benchmarking-methodology","to":"theorempath:data-contamination-and-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-collapse-and-data-quality--prerequisite-of--theorempath:data-contamination-and-evaluation","from":"theorempath:model-collapse-and-data-quality","to":"theorempath:data-contamination-and-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:synthetic-data-generation--prerequisite-of--theorempath:data-contamination-and-evaluation","from":"theorempath:synthetic-data-generation","to":"theorempath:data-contamination-and-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:data-preprocessing-and-feature-engineering","from":"theorempath:common-probability-distributions","to":"theorempath:data-preprocessing-and-feature-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:data-preprocessing-and-feature-engineering","from":"theorempath:linear-regression","to":"theorempath:data-preprocessing-and-feature-engineering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:ddpg","from":"theorempath:policy-gradient-theorem","to":"theorempath:ddpg","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:q-learning--prerequisite-of--theorempath:ddpg","from":"theorempath:q-learning","to":"theorempath:ddpg","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:actor-critic-methods--prerequisite-of--theorempath:ddpg","from":"theorempath:actor-critic-methods","to":"theorempath:ddpg","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:de-moivre-laplace-theorem","from":"theorempath:common-probability-distributions","to":"theorempath:de-moivre-laplace-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:de-moivre-laplace-theorem","from":"theorempath:central-limit-theorem","to":"theorempath:de-moivre-laplace-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:de-moivre-laplace-theorem","from":"theorempath:moment-generating-functions","to":"theorempath:de-moivre-laplace-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:decision-theory-foundations","from":"theorempath:common-probability-distributions","to":"theorempath:decision-theory-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:decision-theory-foundations","from":"theorempath:bayesian-estimation","to":"theorempath:decision-theory-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-pearl--prerequisite-of--theorempath:decision-theory-foundations","from":"theorempath:causal-inference-pearl","to":"theorempath:decision-theory-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:decision-trees-and-ensembles","from":"theorempath:empirical-risk-minimization","to":"theorempath:decision-trees-and-ensembles","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-variance-tradeoff--prerequisite-of--theorempath:decision-trees-and-ensembles","from":"theorempath:bias-variance-tradeoff","to":"theorempath:decision-trees-and-ensembles","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:knn--prerequisite-of--theorempath:decision-trees-and-ensembles","from":"theorempath:knn","to":"theorempath:decision-trees-and-ensembles","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:decoding-strategies","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:decoding-strategies","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:generative-adversarial-networks--prerequisite-of--theorempath:deep-generative-models-for-cosmic-structures","from":"theorempath:generative-adversarial-networks","to":"theorempath:deep-generative-models-for-cosmic-structures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normalization-flows--prerequisite-of--theorempath:deep-generative-models-for-cosmic-structures","from":"theorempath:normalization-flows","to":"theorempath:deep-generative-models-for-cosmic-structures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:deep-generative-models-for-molecules","from":"theorempath:variational-autoencoders","to":"theorempath:deep-generative-models-for-molecules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:diffusion-models--prerequisite-of--theorempath:deep-generative-models-for-molecules","from":"theorempath:diffusion-models","to":"theorempath:deep-generative-models-for-molecules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-series-foundations--prerequisite-of--theorempath:deep-learning-time-series","from":"theorempath:time-series-foundations","to":"theorempath:deep-learning-time-series","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:state-space-models--prerequisite-of--theorempath:deep-learning-time-series","from":"theorempath:state-space-models","to":"theorempath:deep-learning-time-series","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:deep-learning-time-series","from":"theorempath:recurrent-neural-networks","to":"theorempath:deep-learning-time-series","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:deep-learning-time-series","from":"theorempath:transformer-architecture","to":"theorempath:deep-learning-time-series","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:actor-critic-methods--prerequisite-of--theorempath:deep-rl-for-control","from":"theorempath:actor-critic-methods","to":"theorempath:deep-rl-for-control","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:deep-rl-for-control","from":"theorempath:policy-gradient-theorem","to":"theorempath:deep-rl-for-control","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:spectral-theory-of-operators--prerequisite-of--theorempath:deeponet","from":"theorempath:spectral-theory-of-operators","to":"theorempath:deeponet","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:navier-stokes-for-ml--prerequisite-of--theorempath:deeponet","from":"theorempath:navier-stokes-for-ml","to":"theorempath:deeponet","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fourier-neural-operator--prerequisite-of--theorempath:deeponet","from":"theorempath:fourier-neural-operator","to":"theorempath:deeponet","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:deepseek-models","from":"theorempath:transformer-architecture","to":"theorempath:deepseek-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mixture-of-experts--prerequisite-of--theorempath:deepseek-models","from":"theorempath:mixture-of-experts","to":"theorempath:deepseek-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:delta-method","from":"theorempath:central-limit-theorem","to":"theorempath:delta-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modes-of-convergence-random-variables--prerequisite-of--theorempath:delta-method","from":"theorempath:modes-of-convergence-random-variables","to":"theorempath:delta-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:delta-method","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:delta-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:asymptotic-statistics--prerequisite-of--theorempath:delta-method","from":"theorempath:asymptotic-statistics","to":"theorempath:delta-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survey-sampling-methods--prerequisite-of--theorempath:design-based-vs-model-based-inference","from":"theorempath:survey-sampling-methods","to":"theorempath:design-based-vs-model-based-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-for-policy-evaluation--prerequisite-of--theorempath:design-based-vs-model-based-inference","from":"theorempath:causal-inference-for-policy-evaluation","to":"theorempath:design-based-vs-model-based-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:official-statistics-and-national-surveys--prerequisite-of--theorempath:design-based-vs-model-based-inference","from":"theorempath:official-statistics-and-national-surveys","to":"theorempath:design-based-vs-model-based-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:detection-theory","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:detection-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:detection-theory","from":"theorempath:bayesian-estimation","to":"theorempath:detection-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:differential-privacy","from":"theorempath:common-probability-distributions","to":"theorempath:differential-privacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:federated-learning--prerequisite-of--theorempath:differential-privacy","from":"theorempath:federated-learning","to":"theorempath:differential-privacy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:differentiation-in-rn","from":"theorempath:sets-functions-and-relations","to":"theorempath:differentiation-in-rn","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:differentiation-in-rn","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:differentiation-in-rn","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuity-in-rn--prerequisite-of--theorempath:differentiation-in-rn","from":"theorempath:continuity-in-rn","to":"theorempath:differentiation-in-rn","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:diffusion-models","from":"theorempath:variational-autoencoders","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:score-matching--prerequisite-of--theorempath:diffusion-models","from":"theorempath:score-matching","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:boltzmann-machines-and-hopfield-networks--prerequisite-of--theorempath:diffusion-models","from":"theorempath:boltzmann-machines-and-hopfield-networks","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:clip-and-openclip-in-practice--prerequisite-of--theorempath:diffusion-models","from":"theorempath:clip-and-openclip-in-practice","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuous-normalizing-flows--prerequisite-of--theorempath:diffusion-models","from":"theorempath:continuous-normalizing-flows","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:contrastive-learning--prerequisite-of--theorempath:diffusion-models","from":"theorempath:contrastive-learning","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-generative-models-for-cosmic-structures--prerequisite-of--theorempath:diffusion-models","from":"theorempath:deep-generative-models-for-cosmic-structures","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:energy-based-models--prerequisite-of--theorempath:diffusion-models","from":"theorempath:energy-based-models","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-maximization-variants--prerequisite-of--theorempath:diffusion-models","from":"theorempath:expectation-maximization-variants","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fokker-planck-equation--prerequisite-of--theorempath:diffusion-models","from":"theorempath:fokker-planck-equation","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ito-lemma--prerequisite-of--theorempath:diffusion-models","from":"theorempath:ito-lemma","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:langevin-dynamics--prerequisite-of--theorempath:diffusion-models","from":"theorempath:langevin-dynamics","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-sdes--prerequisite-of--theorempath:diffusion-models","from":"theorempath:neural-sdes","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normalization-flows--prerequisite-of--theorempath:diffusion-models","from":"theorempath:normalization-flows","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pde-fundamentals-for-ml--prerequisite-of--theorempath:diffusion-models","from":"theorempath:pde-fundamentals-for-ml","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:probability-flow-ode--prerequisite-of--theorempath:diffusion-models","from":"theorempath:probability-flow-ode","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:diffusion-models","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-reversal-of-sdes--prerequisite-of--theorempath:diffusion-models","from":"theorempath:time-reversal-of-sdes","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vision-transformer-lineage--prerequisite-of--theorempath:diffusion-models","from":"theorempath:vision-transformer-lineage","to":"theorempath:diffusion-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:principal-component-analysis--prerequisite-of--theorempath:dimensionality-reduction-theory","from":"theorempath:principal-component-analysis","to":"theorempath:dimensionality-reduction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:dimensionality-reduction-theory","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:dimensionality-reduction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-concentration-and-geometric-fa--prerequisite-of--theorempath:dimensionality-reduction-theory","from":"theorempath:measure-concentration-and-geometric-fa","to":"theorempath:dimensionality-reduction-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:discrete-continuous-distribution-pairs","from":"theorempath:common-probability-distributions","to":"theorempath:discrete-continuous-distribution-pairs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:discrete-continuous-distribution-pairs","from":"theorempath:random-variables","to":"theorempath:discrete-continuous-distribution-pairs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:distance-metrics-compared","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:distance-metrics-compared","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:non-euclidean-and-hyperbolic-geometry--prerequisite-of--theorempath:distance-metrics-compared","from":"theorempath:non-euclidean-and-hyperbolic-geometry","to":"theorempath:distance-metrics-compared","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:distributed-consensus","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:distributed-consensus","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kafka-streaming-platform--prerequisite-of--theorempath:distributed-consensus","from":"theorempath:kafka-streaming-platform","to":"theorempath:distributed-consensus","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:optimizer-theory-sgd-adam-muon--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:optimizer-theory-sgd-adam-muon","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:parallel-processing-fundamentals--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:parallel-processing-fundamentals","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:batch-size-and-learning-dynamics--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:batch-size-and-learning-dynamics","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:broadcast-joins-distributed-compute--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:broadcast-joins-distributed-compute","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:dask-parallel-python--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:dask-parallel-python","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:federated-learning--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:federated-learning","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kafka-streaming-platform--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:kafka-streaming-platform","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ray-distributed-python--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:ray-distributed-python","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:running-ml-workloads-on-gpus--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:running-ml-workloads-on-gpus","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tokenization-and-information-theory--prerequisite-of--theorempath:distributed-training-theory","from":"theorempath:tokenization-and-information-theory","to":"theorempath:distributed-training-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:singular-value-decomposition--prerequisite-of--theorempath:distributional-semantics","from":"theorempath:singular-value-decomposition","to":"theorempath:distributional-semantics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:distributional-semantics","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:distributional-semantics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nlp-for-economic-text-analysis--prerequisite-of--theorempath:distributional-semantics","from":"theorempath:nlp-for-economic-text-analysis","to":"theorempath:distributional-semantics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:syntax-and-parsing--prerequisite-of--theorempath:distributional-semantics","from":"theorempath:syntax-and-parsing","to":"theorempath:distributional-semantics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:distributions-atlas","from":"theorempath:common-probability-distributions","to":"theorempath:distributions-atlas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:distributions-atlas","from":"theorempath:random-variables","to":"theorempath:distributions-atlas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:distributions-atlas","from":"theorempath:moment-generating-functions","to":"theorempath:distributions-atlas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:divergence-curl-and-line-integrals","from":"theorempath:the-jacobian-matrix","to":"theorempath:divergence-curl-and-line-integrals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vector-calculus-chain-rule--prerequisite-of--theorempath:divergence-curl-and-line-integrals","from":"theorempath:vector-calculus-chain-rule","to":"theorempath:divergence-curl-and-line-integrals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multimodal-rag--prerequisite-of--theorempath:document-intelligence","from":"theorempath:multimodal-rag","to":"theorempath:document-intelligence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:donut-and-ocr-free-document-understanding","from":"theorempath:transformer-architecture","to":"theorempath:donut-and-ocr-free-document-understanding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:document-intelligence--prerequisite-of--theorempath:donut-and-ocr-free-document-understanding","from":"theorempath:document-intelligence","to":"theorempath:donut-and-ocr-free-document-understanding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:paddleocr-and-practical-ocr--prerequisite-of--theorempath:donut-and-ocr-free-document-understanding","from":"theorempath:paddleocr-and-practical-ocr","to":"theorempath:donut-and-ocr-free-document-understanding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:asymptotic-statistics--prerequisite-of--theorempath:double-debiased-machine-learning","from":"theorempath:asymptotic-statistics","to":"theorempath:double-debiased-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:double-debiased-machine-learning","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:double-debiased-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cross-validation-theory--prerequisite-of--theorempath:double-debiased-machine-learning","from":"theorempath:cross-validation-theory","to":"theorempath:double-debiased-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-basics--prerequisite-of--theorempath:double-debiased-machine-learning","from":"theorempath:causal-inference-basics","to":"theorempath:double-debiased-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:double-debiased-machine-learning","from":"theorempath:central-limit-theorem","to":"theorempath:double-debiased-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:weighted-conformal-prediction--prerequisite-of--theorempath:double-debiased-machine-learning","from":"theorempath:weighted-conformal-prediction","to":"theorempath:double-debiased-machine-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:implicit-bias-and-modern-generalization--prerequisite-of--theorempath:double-descent","from":"theorempath:implicit-bias-and-modern-generalization","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-matrix-theory-overview--prerequisite-of--theorempath:double-descent","from":"theorempath:random-matrix-theory-overview","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-variance-tradeoff--prerequisite-of--theorempath:double-descent","from":"theorempath:bias-variance-tradeoff","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:grokking--prerequisite-of--theorempath:double-descent","from":"theorempath:grokking","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lazy-vs-feature-learning--prerequisite-of--theorempath:double-descent","from":"theorempath:lazy-vs-feature-learning","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-tangent-kernel--prerequisite-of--theorempath:double-descent","from":"theorempath:neural-tangent-kernel","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:double-descent","from":"theorempath:ridge-regression","to":"theorempath:double-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:rlhf-and-alignment","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:policy-gradient-theorem","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:actor-critic-methods--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:actor-critic-methods","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chain-of-thought-and-reasoning--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:chain-of-thought-and-reasoning","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-optimization-ppo-trpo--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:policy-optimization-ppo-trpo","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:post-training-overview--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:post-training-overview","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reasoning-data-curation--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:reasoning-data-curation","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-from-human-feedback-deep-dive--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-models-and-verifiers--prerequisite-of--theorempath:dpo-vs-grpo-vs-rl-reasoning","from":"theorempath:reward-models-and-verifiers","to":"theorempath:dpo-vs-grpo-vs-rl-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:dropout","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:dropout","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:dropout","from":"theorempath:common-probability-distributions","to":"theorempath:dropout","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:dynamic-programming","from":"theorempath:sets-functions-and-relations","to":"theorempath:dynamic-programming","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graph-algorithms-essentials--prerequisite-of--theorempath:dynamic-programming","from":"theorempath:graph-algorithms-essentials","to":"theorempath:dynamic-programming","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:greedy-algorithms--prerequisite-of--theorempath:dynamic-programming","from":"theorempath:greedy-algorithms","to":"theorempath:dynamic-programming","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:measure-theoretic-probability","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:martingale-theory","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neyman-pearson-and-hypothesis-testing-theory--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:neyman-pearson-and-hypothesis-testing-theory","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tabular-foundation-models-bayesian-inference--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:tabular-foundation-models-bayesian-inference","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:weighted-conformal-prediction--prerequisite-of--theorempath:e-values-and-anytime-valid-inference","from":"theorempath:weighted-conformal-prediction","to":"theorempath:e-values-and-anytime-valid-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:speculative-decoding-and-quantization--prerequisite-of--theorempath:edge-and-on-device-ml","from":"theorempath:speculative-decoding-and-quantization","to":"theorempath:edge-and-on-device-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-variants-and-efficiency--prerequisite-of--theorempath:efficient-transformers-survey","from":"theorempath:attention-variants-and-efficiency","to":"theorempath:efficient-transformers-survey","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:eigenvalues-and-eigenvectors","from":"theorempath:matrix-operations-and-properties","to":"theorempath:eigenvalues-and-eigenvectors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inner-product-spaces-and-orthogonality--prerequisite-of--theorempath:eigenvalues-and-eigenvectors","from":"theorempath:inner-product-spaces-and-orthogonality","to":"theorempath:eigenvalues-and-eigenvectors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-independence--prerequisite-of--theorempath:eigenvalues-and-eigenvectors","from":"theorempath:linear-independence","to":"theorempath:eigenvalues-and-eigenvectors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-norms--prerequisite-of--theorempath:eigenvalues-and-eigenvectors","from":"theorempath:matrix-norms","to":"theorempath:eigenvalues-and-eigenvectors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:eigenvalues-and-eigenvectors","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:eigenvalues-and-eigenvectors","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:elastic-net","from":"theorempath:ridge-regression","to":"theorempath:elastic-net","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lasso-regression--prerequisite-of--theorempath:elastic-net","from":"theorempath:lasso-regression","to":"theorempath:elastic-net","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:em-algorithm","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:em-algorithm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:em-algorithm","from":"theorempath:convex-optimization-basics","to":"theorempath:em-algorithm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:em-algorithm","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:em-algorithm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-priors--prerequisite-of--theorempath:em-algorithm","from":"theorempath:conjugate-priors","to":"theorempath:em-algorithm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:empirical-bayes-vs-hierarchical-bayes","from":"theorempath:bayesian-estimation","to":"theorempath:empirical-bayes-vs-hierarchical-bayes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:shrinkage-estimation-james-stein--prerequisite-of--theorempath:empirical-bayes-vs-hierarchical-bayes","from":"theorempath:shrinkage-estimation-james-stein","to":"theorempath:empirical-bayes-vs-hierarchical-bayes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adjusted-density-maximization--prerequisite-of--theorempath:empirical-bayes-vs-hierarchical-bayes","from":"theorempath:adjusted-density-maximization","to":"theorempath:empirical-bayes-vs-hierarchical-bayes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-linear-regression--prerequisite-of--theorempath:empirical-bayes-vs-hierarchical-bayes","from":"theorempath:bayesian-linear-regression","to":"theorempath:empirical-bayes-vs-hierarchical-bayes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-priors--prerequisite-of--theorempath:empirical-bayes-vs-hierarchical-bayes","from":"theorempath:conjugate-priors","to":"theorempath:empirical-bayes-vs-hierarchical-bayes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:empirical-processes-and-chaining","from":"theorempath:rademacher-complexity","to":"theorempath:empirical-processes-and-chaining","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:epsilon-nets-and-covering-numbers--prerequisite-of--theorempath:empirical-processes-and-chaining","from":"theorempath:epsilon-nets-and-covering-numbers","to":"theorempath:empirical-processes-and-chaining","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:asymptotic-statistics--prerequisite-of--theorempath:empirical-processes-and-chaining","from":"theorempath:asymptotic-statistics","to":"theorempath:empirical-processes-and-chaining","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:glivenko-cantelli-theorem--prerequisite-of--theorempath:empirical-processes-and-chaining","from":"theorempath:glivenko-cantelli-theorem","to":"theorempath:empirical-processes-and-chaining","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-concentration-and-geometric-fa--prerequisite-of--theorempath:empirical-processes-and-chaining","from":"theorempath:measure-concentration-and-geometric-fa","to":"theorempath:empirical-processes-and-chaining","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-processes-ml--prerequisite-of--theorempath:empirical-processes-and-chaining","from":"theorempath:stochastic-processes-ml","to":"theorempath:empirical-processes-and-chaining","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:concentration-inequalities","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:common-probability-distributions","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-inequalities--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:common-inequalities","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:high-dimensional-probability-book--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:high-dimensional-probability-book","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:law-of-large-numbers","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:loss-functions-catalog--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:loss-functions-catalog","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:robust-statistics-and-m-estimators--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:robust-statistics-and-m-estimators","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sequences-and-series-of-functions--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:sequences-and-series-of-functions","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:understanding-machine-learning-book--prerequisite-of--theorempath:empirical-risk-minimization","from":"theorempath:understanding-machine-learning-book","to":"theorempath:empirical-risk-minimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:energy-based-models","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:energy-based-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:energy-based-models","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:energy-based-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-sdes--prerequisite-of--theorempath:energy-based-models","from":"theorempath:neural-sdes","to":"theorempath:energy-based-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normalization-flows--prerequisite-of--theorempath:energy-based-models","from":"theorempath:normalization-flows","to":"theorempath:energy-based-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:score-matching--prerequisite-of--theorempath:energy-based-models","from":"theorempath:score-matching","to":"theorempath:energy-based-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bagging--prerequisite-of--theorempath:ensemble-methods-theory","from":"theorempath:bagging","to":"theorempath:ensemble-methods-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-boosting--prerequisite-of--theorempath:ensemble-methods-theory","from":"theorempath:gradient-boosting","to":"theorempath:ensemble-methods-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:epsilon-nets-and-covering-numbers","from":"theorempath:subgaussian-random-variables","to":"theorempath:epsilon-nets-and-covering-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:epsilon-nets-and-covering-numbers","from":"theorempath:concentration-inequalities","to":"theorempath:epsilon-nets-and-covering-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:contraction-inequality--prerequisite-of--theorempath:epsilon-nets-and-covering-numbers","from":"theorempath:contraction-inequality","to":"theorempath:epsilon-nets-and-covering-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subexponential-random-variables--prerequisite-of--theorempath:epsilon-nets-and-covering-numbers","from":"theorempath:subexponential-random-variables","to":"theorempath:epsilon-nets-and-covering-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:symmetrization-inequality--prerequisite-of--theorempath:epsilon-nets-and-covering-numbers","from":"theorempath:symmetrization-inequality","to":"theorempath:epsilon-nets-and-covering-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skip-connections-and-resnets--prerequisite-of--theorempath:equilibrium-and-implicit-models","from":"theorempath:skip-connections-and-resnets","to":"theorempath:equilibrium-and-implicit-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:implicit-differentiation--prerequisite-of--theorempath:equilibrium-and-implicit-models","from":"theorempath:implicit-differentiation","to":"theorempath:equilibrium-and-implicit-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:equivariant-deep-learning","from":"theorempath:convolutional-neural-networks","to":"theorempath:equivariant-deep-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graph-neural-networks--prerequisite-of--theorempath:equivariant-deep-learning","from":"theorempath:graph-neural-networks","to":"theorempath:equivariant-deep-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-for-protein-structure-alphafold--prerequisite-of--theorempath:equivariant-deep-learning","from":"theorempath:attention-for-protein-structure-alphafold","to":"theorempath:equivariant-deep-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bitter-lesson--prerequisite-of--theorempath:era-of-experience","from":"theorempath:bitter-lesson","to":"theorempath:era-of-experience","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:era-of-experience","from":"theorempath:markov-decision-processes","to":"theorempath:era-of-experience","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:em-algorithm--prerequisite-of--theorempath:expectation-maximization-variants","from":"theorempath:em-algorithm","to":"theorempath:expectation-maximization-variants","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:expectation-variance-covariance-moments","from":"theorempath:random-variables","to":"theorempath:expectation-variance-covariance-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:expectation-variance-covariance-moments","from":"theorempath:common-probability-distributions","to":"theorempath:expectation-variance-covariance-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:joint-marginal-conditional-distributions--prerequisite-of--theorempath:expectation-variance-covariance-moments","from":"theorempath:joint-marginal-conditional-distributions","to":"theorempath:expectation-variance-covariance-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:triangular-distribution--prerequisite-of--theorempath:expectation-variance-covariance-moments","from":"theorempath:triangular-distribution","to":"theorempath:expectation-variance-covariance-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:expected-utility","from":"theorempath:common-probability-distributions","to":"theorempath:expected-utility","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:expected-utility","from":"theorempath:convex-optimization-basics","to":"theorempath:expected-utility","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bounded-rationality--prerequisite-of--theorempath:expected-utility","from":"theorempath:bounded-rationality","to":"theorempath:expected-utility","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-theory-foundations--prerequisite-of--theorempath:expected-utility","from":"theorempath:decision-theory-foundations","to":"theorempath:expected-utility","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reproducibility-and-experimental-rigor--prerequisite-of--theorempath:experiment-tracking-and-tooling","from":"theorempath:reproducibility-and-experimental-rigor","to":"theorempath:experiment-tracking-and-tooling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hardware-for-ml-practitioners--prerequisite-of--theorempath:experiment-tracking-and-tooling","from":"theorempath:hardware-for-ml-practitioners","to":"theorempath:experiment-tracking-and-tooling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ml-project-lifecycle--prerequisite-of--theorempath:experiment-tracking-and-tooling","from":"theorempath:ml-project-lifecycle","to":"theorempath:experiment-tracking-and-tooling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:weights-and-biases-experiment-tracking--prerequisite-of--theorempath:experiment-tracking-and-tooling","from":"theorempath:weights-and-biases-experiment-tracking","to":"theorempath:experiment-tracking-and-tooling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-armed-bandits-theory--prerequisite-of--theorempath:exploration-vs-exploitation","from":"theorempath:multi-armed-bandits-theory","to":"theorempath:exploration-vs-exploitation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:exploration-vs-exploitation","from":"theorempath:markov-decision-processes","to":"theorempath:exploration-vs-exploitation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bitter-lesson--prerequisite-of--theorempath:exploration-vs-exploitation","from":"theorempath:bitter-lesson","to":"theorempath:exploration-vs-exploitation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-for-drug-discovery--prerequisite-of--theorempath:exploration-vs-exploitation","from":"theorempath:reinforcement-learning-for-drug-discovery","to":"theorempath:exploration-vs-exploitation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ml-project-lifecycle--prerequisite-of--theorempath:exploratory-data-analysis","from":"theorempath:ml-project-lifecycle","to":"theorempath:exploratory-data-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pandas-and-numpy-fundamentals--prerequisite-of--theorempath:exploratory-data-analysis","from":"theorempath:pandas-and-numpy-fundamentals","to":"theorempath:exploratory-data-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:train-test-split-and-data-leakage--prerequisite-of--theorempath:exploratory-data-analysis","from":"theorempath:train-test-split-and-data-leakage","to":"theorempath:exploratory-data-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:exponential-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:exponential-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:exponential-distribution","from":"theorempath:distributions-atlas","to":"theorempath:exponential-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:exponential-distribution","from":"theorempath:exponential-function-properties","to":"theorempath:exponential-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:extreme-value-theory","from":"theorempath:common-probability-distributions","to":"theorempath:extreme-value-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:order-statistics--prerequisite-of--theorempath:extreme-value-theory","from":"theorempath:order-statistics","to":"theorempath:extreme-value-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fat-tails--prerequisite-of--theorempath:extreme-value-theory","from":"theorempath:fat-tails","to":"theorempath:extreme-value-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:f-distribution-and-anova","from":"theorempath:distributions-atlas","to":"theorempath:f-distribution-and-anova","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chi-squared-distribution-and-tests--prerequisite-of--theorempath:f-distribution-and-anova","from":"theorempath:chi-squared-distribution-and-tests","to":"theorempath:f-distribution-and-anova","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:f-distribution-and-anova","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:f-distribution-and-anova","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:student-t-distribution-and-t-test--prerequisite-of--theorempath:f-distribution-and-anova","from":"theorempath:student-t-distribution-and-t-test","to":"theorempath:f-distribution-and-anova","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:minimax-lower-bounds--prerequisite-of--theorempath:fanos-inequality","from":"theorempath:minimax-lower-bounds","to":"theorempath:fanos-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:fanos-inequality","from":"theorempath:information-theory-foundations","to":"theorempath:fanos-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:fast-fourier-transform","from":"theorempath:exponential-function-properties","to":"theorempath:fast-fourier-transform","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:complex-numbers-for-fourier--prerequisite-of--theorempath:fast-fourier-transform","from":"theorempath:complex-numbers-for-fourier","to":"theorempath:fast-fourier-transform","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:fat-tails","from":"theorempath:common-probability-distributions","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:fat-tails","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:fat-tails","from":"theorempath:law-of-large-numbers","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:characteristic-functions--prerequisite-of--theorempath:fat-tails","from":"theorempath:characteristic-functions","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-tinkering--prerequisite-of--theorempath:fat-tails","from":"theorempath:convex-tinkering","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:editorial-principles--prerequisite-of--theorempath:fat-tails","from":"theorempath:editorial-principles","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kelly-criterion--prerequisite-of--theorempath:fat-tails","from":"theorempath:kelly-criterion","to":"theorempath:fat-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:feature-importance-and-interpretability","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:feature-importance-and-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:feature-importance-and-interpretability","from":"theorempath:linear-regression","to":"theorempath:feature-importance-and-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exploratory-data-analysis--prerequisite-of--theorempath:feature-importance-and-interpretability","from":"theorempath:exploratory-data-analysis","to":"theorempath:feature-importance-and-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mechanistic-interpretability--prerequisite-of--theorempath:feature-importance-and-interpretability","from":"theorempath:mechanistic-interpretability","to":"theorempath:feature-importance-and-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-autoencoders--prerequisite-of--theorempath:feature-importance-and-interpretability","from":"theorempath:sparse-autoencoders","to":"theorempath:feature-importance-and-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:optimizer-theory-sgd-adam-muon--prerequisite-of--theorempath:federated-learning","from":"theorempath:optimizer-theory-sgd-adam-muon","to":"theorempath:federated-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:differentiation-in-rn","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-calculus--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:matrix-calculus","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:activation-functions--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:activation-functions","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:automatic-differentiation","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-learning-goodfellow-book--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:deep-learning-goodfellow-book","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-boosting--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:gradient-boosting","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mars-multivariate-adaptive-regression-splines--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:mars-multivariate-adaptive-regression-splines","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:perceptron--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:perceptron","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tensors-and-tensor-operations--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:tensors-and-tensor-operations","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vector-calculus-chain-rule--prerequisite-of--theorempath:feedforward-networks-and-backpropagation","from":"theorempath:vector-calculus-chain-rule","to":"theorempath:feedforward-networks-and-backpropagation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:feynman-kac-formula","from":"theorempath:stochastic-differential-equations","to":"theorempath:feynman-kac-formula","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ito-lemma--prerequisite-of--theorempath:feynman-kac-formula","from":"theorempath:ito-lemma","to":"theorempath:feynman-kac-formula","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:fine-tuning-and-adaptation","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:fine-tuning-and-adaptation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:fisher-information","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:fisher-information","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:fisher-information","from":"theorempath:kl-divergence","to":"theorempath:fisher-information","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basu-theorem--prerequisite-of--theorempath:fisher-information","from":"theorempath:basu-theorem","to":"theorempath:fisher-information","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:positive-semidefinite-matrices--prerequisite-of--theorempath:fisher-information","from":"theorempath:positive-semidefinite-matrices","to":"theorempath:fisher-information","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:fisher-information","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:fisher-information","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:flash-attention","from":"theorempath:attention-mechanism-theory","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:flash-attention","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-is-all-you-need-paper--prerequisite-of--theorempath:flash-attention","from":"theorempath:attention-is-all-you-need-paper","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:computer-architecture-for-ml--prerequisite-of--theorempath:flash-attention","from":"theorempath:computer-architecture-for-ml","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cuda-programming-fundamentals--prerequisite-of--theorempath:flash-attention","from":"theorempath:cuda-programming-fundamentals","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:flash-attention","from":"theorempath:gpu-compute-model","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nvidia-gpu-architectures--prerequisite-of--theorempath:flash-attention","from":"theorempath:nvidia-gpu-architectures","to":"theorempath:flash-attention","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vision-transformer-lineage--prerequisite-of--theorempath:florence-and-vision-foundation-models","from":"theorempath:vision-transformer-lineage","to":"theorempath:florence-and-vision-foundation-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:self-supervised-vision--prerequisite-of--theorempath:florence-and-vision-foundation-models","from":"theorempath:self-supervised-vision","to":"theorempath:florence-and-vision-foundation-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:diffusion-models--prerequisite-of--theorempath:flow-matching","from":"theorempath:diffusion-models","to":"theorempath:flow-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ito-lemma--prerequisite-of--theorempath:flow-matching","from":"theorempath:ito-lemma","to":"theorempath:flow-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pde-fundamentals-for-ml--prerequisite-of--theorempath:flow-matching","from":"theorempath:pde-fundamentals-for-ml","to":"theorempath:flow-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:fokker-planck-equation","from":"theorempath:stochastic-differential-equations","to":"theorempath:fokker-planck-equation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pde-fundamentals-for-ml--prerequisite-of--theorempath:fokker-planck-equation","from":"theorempath:pde-fundamentals-for-ml","to":"theorempath:fokker-planck-equation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:divergence-curl-and-line-integrals--prerequisite-of--theorempath:fokker-planck-equation","from":"theorempath:divergence-curl-and-line-integrals","to":"theorempath:fokker-planck-equation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feynman-kac-formula--prerequisite-of--theorempath:fokker-planck-equation","from":"theorempath:feynman-kac-formula","to":"theorempath:fokker-planck-equation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:zermelo-fraenkel-set-theory--prerequisite-of--theorempath:foundational-dependencies","from":"theorempath:zermelo-fraenkel-set-theory","to":"theorempath:foundational-dependencies","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:peano-axioms--prerequisite-of--theorempath:foundational-dependencies","from":"theorempath:peano-axioms","to":"theorempath:foundational-dependencies","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fast-fourier-transform--prerequisite-of--theorempath:fourier-neural-operator","from":"theorempath:fast-fourier-transform","to":"theorempath:fourier-neural-operator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:navier-stokes-for-ml--prerequisite-of--theorempath:fourier-neural-operator","from":"theorempath:navier-stokes-for-ml","to":"theorempath:fourier-neural-operator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:spectral-theory-of-operators--prerequisite-of--theorempath:fourier-neural-operator","from":"theorempath:spectral-theory-of-operators","to":"theorempath:fourier-neural-operator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:complex-numbers-for-fourier--prerequisite-of--theorempath:fourier-neural-operator","from":"theorempath:complex-numbers-for-fourier","to":"theorempath:fourier-neural-operator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:fox-forget-gate","from":"theorempath:attention-mechanism-theory","to":"theorempath:fox-forget-gate","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:fox-forget-gate","from":"theorempath:recurrent-neural-networks","to":"theorempath:fox-forget-gate","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:fox-forget-gate","from":"theorempath:transformer-architecture","to":"theorempath:fox-forget-gate","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-variants-and-efficiency--prerequisite-of--theorempath:fox-forget-gate","from":"theorempath:attention-variants-and-efficiency","to":"theorempath:fox-forget-gate","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-attention-and-long-context--prerequisite-of--theorempath:fox-forget-gate","from":"theorempath:sparse-attention-and-long-context","to":"theorempath:fox-forget-gate","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:functional-analysis-core","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:functional-analysis-core","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inner-product-spaces-and-orthogonality--prerequisite-of--theorempath:functional-analysis-core","from":"theorempath:inner-product-spaces-and-orthogonality","to":"theorempath:functional-analysis-core","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:functional-analysis-core","from":"theorempath:measure-theoretic-probability","to":"theorempath:functional-analysis-core","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:fused-kernels","from":"theorempath:gpu-compute-model","to":"theorempath:fused-kernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cuda-programming-fundamentals--prerequisite-of--theorempath:fused-kernels","from":"theorempath:cuda-programming-fundamentals","to":"theorempath:fused-kernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:flash-attention--prerequisite-of--theorempath:fused-kernels","from":"theorempath:flash-attention","to":"theorempath:fused-kernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nvidia-gpu-architectures--prerequisite-of--theorempath:fused-kernels","from":"theorempath:nvidia-gpu-architectures","to":"theorempath:fused-kernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:webgpu-for-ml--prerequisite-of--theorempath:fused-kernels","from":"theorempath:webgpu-for-ml","to":"theorempath:fused-kernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:game-theory","from":"theorempath:common-probability-distributions","to":"theorempath:game-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:game-theory","from":"theorempath:convex-optimization-basics","to":"theorempath:game-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:arrows-impossibility--prerequisite-of--theorempath:game-theory","from":"theorempath:arrows-impossibility","to":"theorempath:game-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bounded-rationality--prerequisite-of--theorempath:game-theory","from":"theorempath:bounded-rationality","to":"theorempath:game-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-theory-foundations--prerequisite-of--theorempath:game-theory","from":"theorempath:decision-theory-foundations","to":"theorempath:game-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expected-utility--prerequisite-of--theorempath:game-theory","from":"theorempath:expected-utility","to":"theorempath:game-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:gamma-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:gamma-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:gamma-distribution","from":"theorempath:distributions-atlas","to":"theorempath:gamma-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-distribution--prerequisite-of--theorempath:gamma-distribution","from":"theorempath:exponential-distribution","to":"theorempath:gamma-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:gamma-distribution","from":"theorempath:exponential-function-properties","to":"theorempath:gamma-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:gauss-markov-theorem","from":"theorempath:linear-regression","to":"theorempath:gauss-markov-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multivariate-normal-distribution--prerequisite-of--theorempath:gauss-markov-theorem","from":"theorempath:multivariate-normal-distribution","to":"theorempath:gauss-markov-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:k-means-clustering--prerequisite-of--theorempath:gaussian-mixture-models-and-em","from":"theorempath:k-means-clustering","to":"theorempath:gaussian-mixture-models-and-em","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:em-algorithm--prerequisite-of--theorempath:gaussian-mixture-models-and-em","from":"theorempath:em-algorithm","to":"theorempath:gaussian-mixture-models-and-em","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:gaussian-mixture-models-and-em","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:gaussian-mixture-models-and-em","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:kernels-and-rkhs","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:joint-marginal-conditional-distributions--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:joint-marginal-conditional-distributions","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:ridge-regression","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gram-matrices-and-kernel-matrices--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:gram-matrices-and-kernel-matrices","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:bayesian-estimation","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-linear-regression--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:bayesian-linear-regression","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-priors--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:conjugate-priors","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernel-trick--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:kernel-trick","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multivariate-normal-distribution--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:multivariate-normal-distribution","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-series-forecasting-basics--prerequisite-of--theorempath:gaussian-processes-for-ml","from":"theorempath:time-series-forecasting-basics","to":"theorempath:gaussian-processes-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-for-ml--prerequisite-of--theorempath:gaussian-processes-in-astronomy","from":"theorempath:gaussian-processes-for-ml","to":"theorempath:gaussian-processes-in-astronomy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-regression--prerequisite-of--theorempath:gaussian-processes-in-astronomy","from":"theorempath:gaussian-processes-regression","to":"theorempath:gaussian-processes-in-astronomy","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:kernels-and-rkhs","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:joint-marginal-conditional-distributions--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:joint-marginal-conditional-distributions","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:ridge-regression","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gram-matrices-and-kernel-matrices--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:gram-matrices-and-kernel-matrices","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-for-ml--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:gaussian-processes-for-ml","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-linear-regression--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:bayesian-linear-regression","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernel-methods-for-molecules--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:kernel-methods-for-molecules","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernel-trick--prerequisite-of--theorempath:gaussian-processes-regression","from":"theorempath:kernel-trick","to":"theorempath:gaussian-processes-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:occupancy-networks-and-neural-fields--prerequisite-of--theorempath:gaussian-splatting","from":"theorempath:occupancy-networks-and-neural-fields","to":"theorempath:gaussian-splatting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:positive-semidefinite-matrices--prerequisite-of--theorempath:gaussian-splatting","from":"theorempath:positive-semidefinite-matrices","to":"theorempath:gaussian-splatting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:diffusion-models--prerequisite-of--theorempath:gaussian-splatting","from":"theorempath:diffusion-models","to":"theorempath:gaussian-splatting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:webgpu-for-ml--prerequisite-of--theorempath:gaussian-splatting","from":"theorempath:webgpu-for-ml","to":"theorempath:gaussian-splatting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:gemini-and-google-models","from":"theorempath:transformer-architecture","to":"theorempath:gemini-and-google-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:generalized-additive-models","from":"theorempath:linear-regression","to":"theorempath:generalized-additive-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mars-multivariate-adaptive-regression-splines--prerequisite-of--theorempath:generalized-additive-models","from":"theorempath:mars-multivariate-adaptive-regression-splines","to":"theorempath:generalized-additive-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:generative-adversarial-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:generative-adversarial-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:gibbs-sampling","from":"theorempath:metropolis-hastings","to":"theorempath:gibbs-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chain-monte-carlo--prerequisite-of--theorempath:gibbs-sampling","from":"theorempath:markov-chain-monte-carlo","to":"theorempath:gibbs-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:glivenko-cantelli-theorem","from":"theorempath:concentration-inequalities","to":"theorempath:glivenko-cantelli-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:uniform-convergence--prerequisite-of--theorempath:glivenko-cantelli-theorem","from":"theorempath:uniform-convergence","to":"theorempath:glivenko-cantelli-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vc-dimension--prerequisite-of--theorempath:glivenko-cantelli-theorem","from":"theorempath:vc-dimension","to":"theorempath:glivenko-cantelli-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-learning-framework--prerequisite-of--theorempath:glivenko-cantelli-theorem","from":"theorempath:pac-learning-framework","to":"theorempath:glivenko-cantelli-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:goodness-of-fit-tests","from":"theorempath:common-probability-distributions","to":"theorempath:goodness-of-fit-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:benfords-law--prerequisite-of--theorempath:goodness-of-fit-tests","from":"theorempath:benfords-law","to":"theorempath:goodness-of-fit-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:goodness-of-fit-tests","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:goodness-of-fit-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:transformer-architecture","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:attention-mechanism-theory","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:scaling-laws","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bert-and-pretrain-finetune-paradigm--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:bert-and-pretrain-finetune-paradigm","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tokenization-and-information-theory--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:tokenization-and-information-theory","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:post-training-overview--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:post-training-overview","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prompt-engineering-and-in-context-learning--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:prompt-engineering-and-in-context-learning","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:gpt-series-evolution","from":"theorempath:rlhf-and-alignment","to":"theorempath:gpt-series-evolution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:asml-and-chip-manufacturing--prerequisite-of--theorempath:gpu-compute-model","from":"theorempath:asml-and-chip-manufacturing","to":"theorempath:gpu-compute-model","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:docker-and-containers-for-ml--prerequisite-of--theorempath:gpu-compute-model","from":"theorempath:docker-and-containers-for-ml","to":"theorempath:gpu-compute-model","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kubernetes-for-ml-workloads--prerequisite-of--theorempath:gpu-compute-model","from":"theorempath:kubernetes-for-ml-workloads","to":"theorempath:gpu-compute-model","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modal-serverless-gpu-platform--prerequisite-of--theorempath:gpu-compute-model","from":"theorempath:modal-serverless-gpu-platform","to":"theorempath:gpu-compute-model","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:gradient-boosting","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:gradient-boosting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:gradient-boosting","from":"theorempath:gradient-descent-variants","to":"theorempath:gradient-boosting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adaboost--prerequisite-of--theorempath:gradient-boosting","from":"theorempath:adaboost","to":"theorempath:gradient-boosting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cubist-and-model-trees--prerequisite-of--theorempath:gradient-boosting","from":"theorempath:cubist-and-model-trees","to":"theorempath:gradient-boosting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:elements-of-statistical-learning-book--prerequisite-of--theorempath:gradient-boosting","from":"theorempath:elements-of-statistical-learning-book","to":"theorempath:gradient-boosting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:gradient-descent-variants","from":"theorempath:convex-optimization-basics","to":"theorempath:gradient-descent-variants","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:gradient-descent-variants","from":"theorempath:differentiation-in-rn","to":"theorempath:gradient-descent-variants","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:gradient-flow-and-vanishing-gradients","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:gradient-flow-and-vanishing-gradients","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:gradient-flow-and-vanishing-gradients","from":"theorempath:the-jacobian-matrix","to":"theorempath:gradient-flow-and-vanishing-gradients","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inner-product-spaces-and-orthogonality--prerequisite-of--theorempath:gram-matrices-and-kernel-matrices","from":"theorempath:inner-product-spaces-and-orthogonality","to":"theorempath:gram-matrices-and-kernel-matrices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:gram-matrices-and-kernel-matrices","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:gram-matrices-and-kernel-matrices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distance-metrics-compared--prerequisite-of--theorempath:gram-matrices-and-kernel-matrices","from":"theorempath:distance-metrics-compared","to":"theorempath:gram-matrices-and-kernel-matrices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-multiplication-algorithms--prerequisite-of--theorempath:gram-matrices-and-kernel-matrices","from":"theorempath:matrix-multiplication-algorithms","to":"theorempath:gram-matrices-and-kernel-matrices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernel-trick--prerequisite-of--theorempath:gram-matrices-and-kernel-matrices","from":"theorempath:kernel-trick","to":"theorempath:gram-matrices-and-kernel-matrices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:graph-algorithms-essentials","from":"theorempath:sets-functions-and-relations","to":"theorempath:graph-algorithms-essentials","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graph-neural-networks--prerequisite-of--theorempath:graph-neural-networks-for-molecules","from":"theorempath:graph-neural-networks","to":"theorempath:graph-neural-networks-for-molecules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:equivariant-deep-learning--prerequisite-of--theorempath:graph-neural-networks-for-molecules","from":"theorempath:equivariant-deep-learning","to":"theorempath:graph-neural-networks-for-molecules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:graph-neural-networks","from":"theorempath:convolutional-neural-networks","to":"theorempath:graph-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:graph-neural-networks","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:graph-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:clustering-for-gene-expression--prerequisite-of--theorempath:graph-neural-networks","from":"theorempath:clustering-for-gene-expression","to":"theorempath:graph-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pagerank-algorithm--prerequisite-of--theorempath:graph-neural-networks","from":"theorempath:pagerank-algorithm","to":"theorempath:graph-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:greg-estimator","from":"theorempath:linear-regression","to":"theorempath:greg-estimator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survey-sampling-methods--prerequisite-of--theorempath:greg-estimator","from":"theorempath:survey-sampling-methods","to":"theorempath:greg-estimator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:design-based-vs-model-based-inference--prerequisite-of--theorempath:greg-estimator","from":"theorempath:design-based-vs-model-based-inference","to":"theorempath:greg-estimator","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gibbs-sampling--prerequisite-of--theorempath:griddy-gibbs","from":"theorempath:gibbs-sampling","to":"theorempath:griddy-gibbs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:regularization-theory--prerequisite-of--theorempath:grokking","from":"theorempath:regularization-theory","to":"theorempath:grokking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:grokking","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:grokking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:implicit-bias-and-modern-generalization--prerequisite-of--theorempath:grokking","from":"theorempath:implicit-bias-and-modern-generalization","to":"theorempath:grokking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:history-of-ai--prerequisite-of--theorempath:grokking","from":"theorempath:history-of-ai","to":"theorempath:grokking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:empirical-risk-minimization","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:transformer-architecture","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-from-human-feedback-deep-dive--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agent-protocols-mcp-a2a--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:agent-protocols-mcp-a2a","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chain-of-thought-and-reasoning--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:chain-of-thought-and-reasoning","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:context-engineering--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:context-engineering","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:data-contamination-and-evaluation--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:data-contamination-and-evaluation","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multimodal-rag--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:multimodal-rag","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:out-of-distribution-detection--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:out-of-distribution-detection","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prompt-engineering-and-in-context-learning--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:prompt-engineering-and-in-context-learning","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:hallucination-theory","from":"theorempath:rlhf-and-alignment","to":"theorempath:hallucination-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:hamilton-jacobi-bellman-equation","from":"theorempath:stochastic-differential-equations","to":"theorempath:hamilton-jacobi-bellman-equation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feynman-kac-formula--prerequisite-of--theorempath:hamilton-jacobi-bellman-equation","from":"theorempath:feynman-kac-formula","to":"theorempath:hamilton-jacobi-bellman-equation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:hamiltonian-monte-carlo","from":"theorempath:metropolis-hastings","to":"theorempath:hamiltonian-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chain-monte-carlo--prerequisite-of--theorempath:hamiltonian-monte-carlo","from":"theorempath:markov-chain-monte-carlo","to":"theorempath:hamiltonian-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gibbs-sampling--prerequisite-of--theorempath:hamiltonian-monte-carlo","from":"theorempath:gibbs-sampling","to":"theorempath:hamiltonian-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:griddy-gibbs--prerequisite-of--theorempath:hamiltonian-monte-carlo","from":"theorempath:griddy-gibbs","to":"theorempath:hamiltonian-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variance-reduction-techniques--prerequisite-of--theorempath:hamiltonian-monte-carlo","from":"theorempath:variance-reduction-techniques","to":"theorempath:hamiltonian-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:hanson-wright-inequality","from":"theorempath:subgaussian-random-variables","to":"theorempath:hanson-wright-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-concentration--prerequisite-of--theorempath:hanson-wright-inequality","from":"theorempath:matrix-concentration","to":"theorempath:hanson-wright-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chi-squared-concentration--prerequisite-of--theorempath:hanson-wright-inequality","from":"theorempath:chi-squared-concentration","to":"theorempath:hanson-wright-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:hash-functions","from":"theorempath:common-probability-distributions","to":"theorempath:hash-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:hash-functions","from":"theorempath:sets-functions-and-relations","to":"theorempath:hash-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:perceptron--prerequisite-of--theorempath:hebbian-learning","from":"theorempath:perceptron","to":"theorempath:hebbian-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:hebbian-learning","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:hebbian-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:predictive-coding-and-autoencoders-in-the-brain--prerequisite-of--theorempath:hebbian-learning","from":"theorempath:predictive-coding-and-autoencoders-in-the-brain","to":"theorempath:hebbian-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:spiking-neural-networks--prerequisite-of--theorempath:hebbian-learning","from":"theorempath:spiking-neural-networks","to":"theorempath:hebbian-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-concentration--prerequisite-of--theorempath:high-dimensional-covariance-estimation","from":"theorempath:matrix-concentration","to":"theorempath:high-dimensional-covariance-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lasso-regression--prerequisite-of--theorempath:high-dimensional-covariance-estimation","from":"theorempath:lasso-regression","to":"theorempath:high-dimensional-covariance-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cramer-wold-theorem--prerequisite-of--theorempath:high-dimensional-probability-book","from":"theorempath:cramer-wold-theorem","to":"theorempath:high-dimensional-probability-book","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:hoeffdings-lemma","from":"theorempath:concentration-inequalities","to":"theorempath:hoeffdings-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:hoeffdings-lemma","from":"theorempath:moment-generating-functions","to":"theorempath:hoeffdings-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chernoff-bounds--prerequisite-of--theorempath:hoeffdings-lemma","from":"theorempath:chernoff-bounds","to":"theorempath:hoeffdings-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:hoeffdings-lemma","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:hoeffdings-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:hoeffdings-lemma","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:hoeffdings-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:hoeffdings-lemma","from":"theorempath:sets-functions-and-relations","to":"theorempath:hoeffdings-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:non-euclidean-and-hyperbolic-geometry--prerequisite-of--theorempath:hyperbolic-embeddings-for-graphs","from":"theorempath:non-euclidean-and-hyperbolic-geometry","to":"theorempath:hyperbolic-embeddings-for-graphs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:hyperbolic-embeddings-for-graphs","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:hyperbolic-embeddings-for-graphs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:hypergeometric-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:hypergeometric-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:hypergeometric-distribution","from":"theorempath:distributions-atlas","to":"theorempath:hypergeometric-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:hypothesis-classes-and-function-spaces","from":"theorempath:empirical-risk-minimization","to":"theorempath:hypothesis-classes-and-function-spaces","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:benfords-law--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:benfords-law","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrix-deep-dive--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:confusion-matrix-deep-dive","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differential-privacy--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:differential-privacy","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:evaluation-metrics-and-properties--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:evaluation-metrics-and-properties","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:fisher-information","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:method-of-moments--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:method-of-moments","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neyman-pearson-and-hypothesis-testing-theory--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:neyman-pearson-and-hypothesis-testing-theory","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reproducibility-and-experimental-rigor--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:reproducibility-and-experimental-rigor","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:robust-statistics-and-m-estimators--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:robust-statistics-and-m-estimators","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survival-analysis--prerequisite-of--theorempath:hypothesis-testing-for-ml","from":"theorempath:survival-analysis","to":"theorempath:hypothesis-testing-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:gradient-descent-variants","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:linear-regression","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vc-dimension--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:vc-dimension","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:rademacher-complexity","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:algorithmic-stability--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:algorithmic-stability","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-variance-tradeoff--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:bias-variance-tradeoff","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-bottleneck--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:information-bottleneck","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:kernels-and-rkhs","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-network-optimization-landscape--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:neural-network-optimization-landscape","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-bayes-bounds--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:pac-bayes-bounds","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-matrix-theory-overview--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:random-matrix-theory-overview","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sgd-as-sde--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:sgd-as-sde","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stability-and-optimization-dynamics--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:stability-and-optimization-dynamics","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:training-dynamics-and-loss-landscapes--prerequisite-of--theorempath:implicit-bias-and-modern-generalization","from":"theorempath:training-dynamics-and-loss-landscapes","to":"theorempath:implicit-bias-and-modern-generalization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:implicit-differentiation","from":"theorempath:the-jacobian-matrix","to":"theorempath:implicit-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:implicit-differentiation","from":"theorempath:automatic-differentiation","to":"theorempath:implicit-differentiation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:importance-sampling","from":"theorempath:common-probability-distributions","to":"theorempath:importance-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:monte-carlo-methods--prerequisite-of--theorempath:importance-sampling","from":"theorempath:monte-carlo-methods","to":"theorempath:importance-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:number-theory-and-ml--prerequisite-of--theorempath:importance-sampling","from":"theorempath:number-theory-and-ml","to":"theorempath:importance-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:radon-nikodym-and-conditional-expectation--prerequisite-of--theorempath:importance-sampling","from":"theorempath:radon-nikodym-and-conditional-expectation","to":"theorempath:importance-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rejection-sampling--prerequisite-of--theorempath:importance-sampling","from":"theorempath:rejection-sampling","to":"theorempath:importance-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:squeezed-rejection-sampling--prerequisite-of--theorempath:importance-sampling","from":"theorempath:squeezed-rejection-sampling","to":"theorempath:importance-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:induction-heads","from":"theorempath:attention-mechanism-theory","to":"theorempath:induction-heads","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:induction-heads","from":"theorempath:transformer-architecture","to":"theorempath:induction-heads","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mechanistic-interpretability--prerequisite-of--theorempath:induction-heads","from":"theorempath:mechanistic-interpretability","to":"theorempath:induction-heads","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:residual-stream-and-transformer-internals--prerequisite-of--theorempath:induction-heads","from":"theorempath:residual-stream-and-transformer-internals","to":"theorempath:induction-heads","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-autoencoders--prerequisite-of--theorempath:induction-heads","from":"theorempath:sparse-autoencoders","to":"theorempath:induction-heads","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-from-human-feedback-deep-dive--prerequisite-of--theorempath:ineffable-intelligence","from":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","to":"theorempath:ineffable-intelligence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ai-labs-landscape--prerequisite-of--theorempath:ineffable-intelligence","from":"theorempath:ai-labs-landscape","to":"theorempath:ineffable-intelligence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:kv-cache","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:speculative-decoding-and-quantization--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:speculative-decoding-and-quantization","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:docker-and-containers-for-ml--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:docker-and-containers-for-ml","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:edge-and-on-device-ml--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:edge-and-on-device-ml","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kubernetes-for-ml-workloads--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:kubernetes-for-ml-workloads","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:megakernels--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:megakernels","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-compression-and-pruning--prerequisite-of--theorempath:inference-systems-overview","from":"theorempath:model-compression-and-pruning","to":"theorempath:inference-systems-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:inference-time-scaling-laws","from":"theorempath:scaling-laws","to":"theorempath:inference-time-scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:test-time-compute-and-search--prerequisite-of--theorempath:inference-time-scaling-laws","from":"theorempath:test-time-compute-and-search","to":"theorempath:inference-time-scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:information-bottleneck","from":"theorempath:information-theory-foundations","to":"theorempath:information-bottleneck","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:information-geometry","from":"theorempath:fisher-information","to":"theorempath:information-geometry","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:information-geometry","from":"theorempath:convex-duality","to":"theorempath:information-geometry","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:non-euclidean-and-hyperbolic-geometry--prerequisite-of--theorempath:information-geometry","from":"theorempath:non-euclidean-and-hyperbolic-geometry","to":"theorempath:information-geometry","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:whitening-and-decorrelation--prerequisite-of--theorempath:information-geometry","from":"theorempath:whitening-and-decorrelation","to":"theorempath:information-geometry","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:information-retrieval","from":"theorempath:common-probability-distributions","to":"theorempath:information-retrieval","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:information-retrieval","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:information-retrieval","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fuzzy-matching-and-record-linkage--prerequisite-of--theorempath:information-retrieval","from":"theorempath:fuzzy-matching-and-record-linkage","to":"theorempath:information-retrieval","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:inner-product-spaces-and-orthogonality","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:inner-product-spaces-and-orthogonality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:interior-point-methods","from":"theorempath:convex-optimization-basics","to":"theorempath:interior-point-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:interior-point-methods","from":"theorempath:newtons-method","to":"theorempath:interior-point-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:augmented-lagrangian-and-admm--prerequisite-of--theorempath:interior-point-methods","from":"theorempath:augmented-lagrangian-and-admm","to":"theorempath:interior-point-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:trust-region-methods--prerequisite-of--theorempath:interior-point-methods","from":"theorempath:trust-region-methods","to":"theorempath:interior-point-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:inverse-and-implicit-function-theorem","from":"theorempath:the-jacobian-matrix","to":"theorempath:inverse-and-implicit-function-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-compression-and-pruning--prerequisite-of--theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","from":"theorempath:model-compression-and-pruning","to":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:ito-lemma","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:ito-lemma","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders--prerequisite-of--theorempath:jepa-and-joint-embedding","from":"theorempath:autoencoders","to":"theorempath:jepa-and-joint-embedding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:jepa-and-joint-embedding","from":"theorempath:variational-autoencoders","to":"theorempath:jepa-and-joint-embedding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:history-of-ai--prerequisite-of--theorempath:jepa-and-joint-embedding","from":"theorempath:history-of-ai","to":"theorempath:jepa-and-joint-embedding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:self-supervised-vision--prerequisite-of--theorempath:jepa-and-joint-embedding","from":"theorempath:self-supervised-vision","to":"theorempath:jepa-and-joint-embedding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vision-transformer-lineage--prerequisite-of--theorempath:jepa-and-joint-embedding","from":"theorempath:vision-transformer-lineage","to":"theorempath:jepa-and-joint-embedding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:world-models-and-planning--prerequisite-of--theorempath:jepa-and-joint-embedding","from":"theorempath:world-models-and-planning","to":"theorempath:jepa-and-joint-embedding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:joint-marginal-conditional-distributions","from":"theorempath:random-variables","to":"theorempath:joint-marginal-conditional-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:joint-marginal-conditional-distributions","from":"theorempath:common-probability-distributions","to":"theorempath:joint-marginal-conditional-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-probability-axioms--prerequisite-of--theorempath:joint-marginal-conditional-distributions","from":"theorempath:kolmogorov-probability-axioms","to":"theorempath:joint-marginal-conditional-distributions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:k-means-clustering","from":"theorempath:common-probability-distributions","to":"theorempath:k-means-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:k-means-clustering","from":"theorempath:convex-optimization-basics","to":"theorempath:k-means-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nmf-nonnegative-matrix-factorization--prerequisite-of--theorempath:k-means-clustering","from":"theorempath:nmf-nonnegative-matrix-factorization","to":"theorempath:k-means-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:self-organizing-maps--prerequisite-of--theorempath:k-means-clustering","from":"theorempath:self-organizing-maps","to":"theorempath:k-means-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tsne-and-umap--prerequisite-of--theorempath:k-means-clustering","from":"theorempath:tsne-and-umap","to":"theorempath:k-means-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:kalman-filter","from":"theorempath:common-probability-distributions","to":"theorempath:kalman-filter","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:kalman-filter","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:kalman-filter","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:kelly-criterion","from":"theorempath:common-probability-distributions","to":"theorempath:kelly-criterion","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:kelly-criterion","from":"theorempath:information-theory-foundations","to":"theorempath:kelly-criterion","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-tinkering--prerequisite-of--theorempath:kelly-criterion","from":"theorempath:convex-tinkering","to":"theorempath:kelly-criterion","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expected-utility--prerequisite-of--theorempath:kelly-criterion","from":"theorempath:expected-utility","to":"theorempath:kelly-criterion","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:kernel-methods-for-molecules","from":"theorempath:kernels-and-rkhs","to":"theorempath:kernel-methods-for-molecules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-for-ml--prerequisite-of--theorempath:kernel-methods-for-molecules","from":"theorempath:gaussian-processes-for-ml","to":"theorempath:kernel-methods-for-molecules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:support-vector-machines--prerequisite-of--theorempath:kernel-trick","from":"theorempath:support-vector-machines","to":"theorempath:kernel-trick","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:kernel-trick","from":"theorempath:ridge-regression","to":"theorempath:kernel-trick","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-linear-regression--prerequisite-of--theorempath:kernel-trick","from":"theorempath:bayesian-linear-regression","to":"theorempath:kernel-trick","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:kernel-trick","from":"theorempath:convex-optimization-basics","to":"theorempath:kernel-trick","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:kernel-trick","from":"theorempath:common-probability-distributions","to":"theorempath:kernel-trick","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:kernel-two-sample-tests","from":"theorempath:kernels-and-rkhs","to":"theorempath:kernel-two-sample-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:convex-optimization-basics","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:rademacher-complexity","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:characteristic-functions--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:characteristic-functions","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:convex-duality","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:dimensionality-reduction-theory--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:dimensionality-reduction-theory","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:functional-analysis-core--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:functional-analysis-core","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gram-matrices-and-kernel-matrices--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:gram-matrices-and-kernel-matrices","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hanson-wright-inequality--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:hanson-wright-inequality","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:regularization-theory--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:regularization-theory","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:ridge-regression","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:spectral-clustering--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:spectral-clustering","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:support-vector-machines--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:support-vector-machines","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:svm-for-rf-classification--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:svm-for-rf-classification","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernel-trick--prerequisite-of--theorempath:kernels-and-rkhs","from":"theorempath:kernel-trick","to":"theorempath:kernels-and-rkhs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:kl-divergence","from":"theorempath:common-probability-distributions","to":"theorempath:kl-divergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:kl-divergence","from":"theorempath:information-theory-foundations","to":"theorempath:kl-divergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distance-metrics-compared--prerequisite-of--theorempath:kl-divergence","from":"theorempath:distance-metrics-compared","to":"theorempath:kl-divergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:total-variation-distance--prerequisite-of--theorempath:kl-divergence","from":"theorempath:total-variation-distance","to":"theorempath:kl-divergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:dynamic-programming--prerequisite-of--theorempath:knapsack-problem","from":"theorempath:dynamic-programming","to":"theorempath:knapsack-problem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:greedy-algorithms--prerequisite-of--theorempath:knapsack-problem","from":"theorempath:greedy-algorithms","to":"theorempath:knapsack-problem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:knn","from":"theorempath:common-probability-distributions","to":"theorempath:knn","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:order-statistics--prerequisite-of--theorempath:knn","from":"theorempath:order-statistics","to":"theorempath:knn","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:knowledge-distillation","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:knowledge-distillation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis--prerequisite-of--theorempath:knowledge-distillation","from":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","to":"theorempath:knowledge-distillation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:universal-approximation-theorem--prerequisite-of--theorempath:kolmogorov-arnold-networks","from":"theorempath:universal-approximation-theorem","to":"theorempath:kolmogorov-arnold-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:kolmogorov-arnold-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:kolmogorov-arnold-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:activation-functions--prerequisite-of--theorempath:kolmogorov-arnold-networks","from":"theorempath:activation-functions","to":"theorempath:kolmogorov-arnold-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:p-vs-np--prerequisite-of--theorempath:kolmogorov-complexity-and-mdl","from":"theorempath:p-vs-np","to":"theorempath:kolmogorov-complexity-and-mdl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:kolmogorov-probability-axioms","from":"theorempath:sets-functions-and-relations","to":"theorempath:kolmogorov-probability-axioms","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache--prerequisite-of--theorempath:kv-cache-optimization","from":"theorempath:kv-cache","to":"theorempath:kv-cache-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:kv-cache","from":"theorempath:attention-mechanism-theory","to":"theorempath:kv-cache","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-is-all-you-need-paper--prerequisite-of--theorempath:kv-cache","from":"theorempath:attention-is-all-you-need-paper","to":"theorempath:kv-cache","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-variants-and-efficiency--prerequisite-of--theorempath:kv-cache","from":"theorempath:attention-variants-and-efficiency","to":"theorempath:kv-cache","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:efficient-transformers-survey--prerequisite-of--theorempath:kv-cache","from":"theorempath:efficient-transformers-survey","to":"theorempath:kv-cache","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-layer-shapes-memory--prerequisite-of--theorempath:kv-cache","from":"theorempath:linear-layer-shapes-memory","to":"theorempath:kv-cache","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:label-smoothing-and-regularization","from":"theorempath:logistic-regression","to":"theorempath:label-smoothing-and-regularization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:stochastic-differential-equations","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fokker-planck-equation--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:fokker-planck-equation","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hamiltonian-monte-carlo--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:hamiltonian-monte-carlo","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:score-matching--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:score-matching","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sgd-as-sde--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:sgd-as-sde","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-processes-ml--prerequisite-of--theorempath:langevin-dynamics","from":"theorempath:stochastic-processes-ml","to":"theorempath:langevin-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:lasso-regression","from":"theorempath:linear-regression","to":"theorempath:lasso-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:lasso-regression","from":"theorempath:convex-optimization-basics","to":"theorempath:lasso-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:lasso-regression","from":"theorempath:ridge-regression","to":"theorempath:lasso-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgradients-and-subdifferentials--prerequisite-of--theorempath:lasso-regression","from":"theorempath:subgradients-and-subdifferentials","to":"theorempath:lasso-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-a-posteriori-estimation--prerequisite-of--theorempath:lasso-regression","from":"theorempath:maximum-a-posteriori-estimation","to":"theorempath:lasso-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:test-time-compute-and-search--prerequisite-of--theorempath:latent-reasoning","from":"theorempath:test-time-compute-and-search","to":"theorempath:latent-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:memory-systems-for-llms--prerequisite-of--theorempath:latent-reasoning","from":"theorempath:memory-systems-for-llms","to":"theorempath:latent-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-token-prediction--prerequisite-of--theorempath:latent-reasoning","from":"theorempath:multi-token-prediction","to":"theorempath:latent-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:law-of-large-numbers","from":"theorempath:random-variables","to":"theorempath:law-of-large-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:law-of-large-numbers","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:law-of-large-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:law-of-large-numbers","from":"theorempath:common-probability-distributions","to":"theorempath:law-of-large-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:borel-cantelli-lemmas--prerequisite-of--theorempath:law-of-large-numbers","from":"theorempath:borel-cantelli-lemmas","to":"theorempath:law-of-large-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modes-of-convergence-random-variables--prerequisite-of--theorempath:law-of-large-numbers","from":"theorempath:modes-of-convergence-random-variables","to":"theorempath:law-of-large-numbers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-tangent-kernel--prerequisite-of--theorempath:lazy-vs-feature-learning","from":"theorempath:neural-tangent-kernel","to":"theorempath:lazy-vs-feature-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mean-field-theory--prerequisite-of--theorempath:lazy-vs-feature-learning","from":"theorempath:mean-field-theory","to":"theorempath:lazy-vs-feature-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:learning-rate-scheduling","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:learning-rate-scheduling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adam-optimizer--prerequisite-of--theorempath:learning-rate-scheduling","from":"theorempath:adam-optimizer","to":"theorempath:learning-rate-scheduling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:batch-size-and-learning-dynamics--prerequisite-of--theorempath:learning-rate-scheduling","from":"theorempath:batch-size-and-learning-dynamics","to":"theorempath:learning-rate-scheduling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:learning-rate-scheduling","from":"theorempath:gradient-descent-variants","to":"theorempath:learning-rate-scheduling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-theory-foundations--prerequisite-of--theorempath:leverage-points-systems","from":"theorempath:decision-theory-foundations","to":"theorempath:leverage-points-systems","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:likelihood-ratio-wald-score-tests","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:likelihood-ratio-wald-score-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:likelihood-ratio-wald-score-tests","from":"theorempath:fisher-information","to":"theorempath:likelihood-ratio-wald-score-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neyman-pearson-and-hypothesis-testing-theory--prerequisite-of--theorempath:likelihood-ratio-wald-score-tests","from":"theorempath:neyman-pearson-and-hypothesis-testing-theory","to":"theorempath:likelihood-ratio-wald-score-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:asymptotic-statistics--prerequisite-of--theorempath:likelihood-ratio-wald-score-tests","from":"theorempath:asymptotic-statistics","to":"theorempath:likelihood-ratio-wald-score-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chi-squared-distribution-and-tests--prerequisite-of--theorempath:likelihood-ratio-wald-score-tests","from":"theorempath:chi-squared-distribution-and-tests","to":"theorempath:likelihood-ratio-wald-score-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:line-search-methods","from":"theorempath:convex-optimization-basics","to":"theorempath:line-search-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:line-search-methods","from":"theorempath:differentiation-in-rn","to":"theorempath:line-search-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:line-search-methods","from":"theorempath:newtons-method","to":"theorempath:line-search-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:linear-independence","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:linear-independence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:linear-layer-shapes-memory","from":"theorempath:matrix-operations-and-properties","to":"theorempath:linear-layer-shapes-memory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-calculus--prerequisite-of--theorempath:linear-layer-shapes-memory","from":"theorempath:matrix-calculus","to":"theorempath:linear-layer-shapes-memory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:linear-layer-shapes-memory","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:linear-layer-shapes-memory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:linear-regression","from":"theorempath:matrix-operations-and-properties","to":"theorempath:linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:linear-regression","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:elements-of-statistical-learning-book--prerequisite-of--theorempath:linear-regression","from":"theorempath:elements-of-statistical-learning-book","to":"theorempath:linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:naive-bayes--prerequisite-of--theorempath:linear-regression","from":"theorempath:naive-bayes","to":"theorempath:linear-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:transformer-architecture","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:token-prediction-and-language-modeling--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:token-prediction-and-language-modeling","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:scaling-laws","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mixture-of-experts--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:mixture-of-experts","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:post-training-overview--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:post-training-overview","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tokenization-and-information-theory--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:tokenization-and-information-theory","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fine-tuning-and-adaptation--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:fine-tuning-and-adaptation","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cohere-models--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:cohere-models","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gemini-and-google-models--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:gemini-and-google-models","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpt-series-evolution--prerequisite-of--theorempath:llama-and-open-weight-models","from":"theorempath:gpt-series-evolution","to":"theorempath:llama-and-open-weight-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adversarial-machine-learning--prerequisite-of--theorempath:llm-application-security","from":"theorempath:adversarial-machine-learning","to":"theorempath:llm-application-security","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:llm-application-security","from":"theorempath:rlhf-and-alignment","to":"theorempath:llm-application-security","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:lln-failures-heavy-tails","from":"theorempath:law-of-large-numbers","to":"theorempath:lln-failures-heavy-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:lln-failures-heavy-tails","from":"theorempath:central-limit-theorem","to":"theorempath:lln-failures-heavy-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:characteristic-functions--prerequisite-of--theorempath:lln-failures-heavy-tails","from":"theorempath:characteristic-functions","to":"theorempath:lln-failures-heavy-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fat-tails--prerequisite-of--theorempath:lln-failures-heavy-tails","from":"theorempath:fat-tails","to":"theorempath:lln-failures-heavy-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:lln-failures-heavy-tails","from":"theorempath:common-probability-distributions","to":"theorempath:lln-failures-heavy-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:modes-of-convergence-random-variables--prerequisite-of--theorempath:lln-failures-heavy-tails","from":"theorempath:modes-of-convergence-random-variables","to":"theorempath:lln-failures-heavy-tails","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:log-probability-computation","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:log-probability-computation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:logistic-regression","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:logistic-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:logistic-regression","from":"theorempath:convex-optimization-basics","to":"theorempath:logistic-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:data-preprocessing-and-feature-engineering--prerequisite-of--theorempath:logistic-regression","from":"theorempath:data-preprocessing-and-feature-engineering","to":"theorempath:logistic-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:logistic-regression","from":"theorempath:linear-regression","to":"theorempath:logistic-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:naive-bayes--prerequisite-of--theorempath:logistic-regression","from":"theorempath:naive-bayes","to":"theorempath:logistic-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:lognormal-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:lognormal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normal-distribution--prerequisite-of--theorempath:lognormal-distribution","from":"theorempath:normal-distribution","to":"theorempath:lognormal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:lognormal-distribution","from":"theorempath:central-limit-theorem","to":"theorempath:lognormal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:lognormal-distribution","from":"theorempath:distributions-atlas","to":"theorempath:lognormal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:logsplines","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:logsplines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:longitudinal-surveys-and-panel-data","from":"theorempath:linear-regression","to":"theorempath:longitudinal-surveys-and-panel-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-for-policy-evaluation--prerequisite-of--theorempath:longitudinal-surveys-and-panel-data","from":"theorempath:causal-inference-for-policy-evaluation","to":"theorempath:longitudinal-surveys-and-panel-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nonresponse-and-missing-data--prerequisite-of--theorempath:longitudinal-surveys-and-panel-data","from":"theorempath:nonresponse-and-missing-data","to":"theorempath:longitudinal-surveys-and-panel-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:small-area-estimation--prerequisite-of--theorempath:longitudinal-surveys-and-panel-data","from":"theorempath:small-area-estimation","to":"theorempath:longitudinal-surveys-and-panel-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:loss-functions-catalog","from":"theorempath:logistic-regression","to":"theorempath:loss-functions-catalog","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:loss-functions","from":"theorempath:random-variables","to":"theorempath:loss-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:loss-functions","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:loss-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-classes-and-function-spaces--prerequisite-of--theorempath:loss-functions","from":"theorempath:hypothesis-classes-and-function-spaces","to":"theorempath:loss-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nonlinear-dynamics-and-chaos-fundamentals--prerequisite-of--theorempath:lyapunov-based-machine-learning-for-chaos","from":"theorempath:nonlinear-dynamics-and-chaos-fundamentals","to":"theorempath:lyapunov-based-machine-learning-for-chaos","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:physics-informed-neural-networks--prerequisite-of--theorempath:lyapunov-based-machine-learning-for-chaos","from":"theorempath:physics-informed-neural-networks","to":"theorempath:lyapunov-based-machine-learning-for-chaos","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-series-forecasting-basics--prerequisite-of--theorempath:macroeconomic-time-series-forecasting","from":"theorempath:time-series-forecasting-basics","to":"theorempath:macroeconomic-time-series-forecasting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:recurrent-neural-networks","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:attention-mechanism-theory","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-learning-time-series--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:deep-learning-time-series","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:efficient-transformers-survey--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:efficient-transformers-survey","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mixture-of-experts--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:mixture-of-experts","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reservoir-computing-and-echo-state-networks--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:reservoir-computing-and-echo-state-networks","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:state-space-models--prerequisite-of--theorempath:mamba-and-state-space-models","from":"theorempath:state-space-models","to":"theorempath:mamba-and-state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chains-and-steady-state--prerequisite-of--theorempath:markov-chain-monte-carlo","from":"theorempath:markov-chains-and-steady-state","to":"theorempath:markov-chain-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:monte-carlo-methods--prerequisite-of--theorempath:markov-chain-monte-carlo","from":"theorempath:monte-carlo-methods","to":"theorempath:markov-chain-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-processes-ml--prerequisite-of--theorempath:markov-chain-monte-carlo","from":"theorempath:stochastic-processes-ml","to":"theorempath:markov-chain-monte-carlo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:markov-chains-and-steady-state","from":"theorempath:common-probability-distributions","to":"theorempath:markov-chains-and-steady-state","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:markov-chains-and-steady-state","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:markov-chains-and-steady-state","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pagerank-algorithm--prerequisite-of--theorempath:markov-chains-and-steady-state","from":"theorempath:pagerank-algorithm","to":"theorempath:markov-chains-and-steady-state","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:markov-decision-processes","from":"theorempath:convex-optimization-basics","to":"theorempath:markov-decision-processes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:markov-decision-processes","from":"theorempath:concentration-inequalities","to":"theorempath:markov-decision-processes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-state-estimation--prerequisite-of--theorempath:markov-decision-processes","from":"theorempath:bayesian-state-estimation","to":"theorempath:markov-decision-processes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chains-and-steady-state--prerequisite-of--theorempath:markov-decision-processes","from":"theorempath:markov-chains-and-steady-state","to":"theorempath:markov-decision-processes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-armed-bandits-theory--prerequisite-of--theorempath:markov-decision-processes","from":"theorempath:multi-armed-bandits-theory","to":"theorempath:markov-decision-processes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:online-learning-and-bandits--prerequisite-of--theorempath:markov-decision-processes","from":"theorempath:online-learning-and-bandits","to":"theorempath:markov-decision-processes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:markov-games-and-self-play","from":"theorempath:markov-decision-processes","to":"theorempath:markov-games-and-self-play","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-for-auction-design--prerequisite-of--theorempath:markov-games-and-self-play","from":"theorempath:reinforcement-learning-for-auction-design","to":"theorempath:markov-games-and-self-play","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:mars-multivariate-adaptive-regression-splines","from":"theorempath:linear-regression","to":"theorempath:mars-multivariate-adaptive-regression-splines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:martingale-theory","from":"theorempath:measure-theoretic-probability","to":"theorempath:martingale-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:matrix-calculus","from":"theorempath:the-jacobian-matrix","to":"theorempath:matrix-calculus","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:matrix-calculus","from":"theorempath:the-hessian-matrix","to":"theorempath:matrix-calculus","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:subgaussian-random-variables","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subexponential-random-variables--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:subexponential-random-variables","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:concentration-inequalities","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bernstein-inequality--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:bernstein-inequality","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-processes-and-chaining--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:empirical-processes-and-chaining","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-concentration-and-geometric-fa--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:measure-concentration-and-geometric-fa","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bennetts-inequality--prerequisite-of--theorempath:matrix-concentration","from":"theorempath:bennetts-inequality","to":"theorempath:matrix-concentration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:matrix-multiplication-algorithms","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:matrix-multiplication-algorithms","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:matrix-norms","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:matrix-norms","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:matrix-operations-and-properties","from":"theorempath:sets-functions-and-relations","to":"theorempath:matrix-operations-and-properties","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-independence--prerequisite-of--theorempath:matrix-operations-and-properties","from":"theorempath:linear-independence","to":"theorempath:matrix-operations-and-properties","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:maximum-a-posteriori-estimation","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:maximum-a-posteriori-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:maximum-a-posteriori-estimation","from":"theorempath:bayesian-estimation","to":"theorempath:maximum-a-posteriori-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:maximum-a-posteriori-estimation","from":"theorempath:common-probability-distributions","to":"theorempath:maximum-a-posteriori-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:maximum-a-posteriori-estimation","from":"theorempath:convex-optimization-basics","to":"theorempath:maximum-a-posteriori-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:common-probability-distributions","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:differentiation-in-rn","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:central-limit-theorem","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:kl-divergence","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:exponential-function-properties","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:information-theory-foundations","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:method-of-moments--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:method-of-moments","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:radon-nikodym-and-conditional-expectation--prerequisite-of--theorempath:maximum-likelihood-estimation","from":"theorempath:radon-nikodym-and-conditional-expectation","to":"theorempath:maximum-likelihood-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:mcdiarmids-inequality","from":"theorempath:concentration-inequalities","to":"theorempath:mcdiarmids-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:mcdiarmids-inequality","from":"theorempath:subgaussian-random-variables","to":"theorempath:mcdiarmids-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:mcdiarmids-inequality","from":"theorempath:martingale-theory","to":"theorempath:mcdiarmids-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hoeffdings-lemma--prerequisite-of--theorempath:mcdiarmids-inequality","from":"theorempath:hoeffdings-lemma","to":"theorempath:mcdiarmids-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gibbs-sampling--prerequisite-of--theorempath:mcmc-for-markov-random-fields","from":"theorempath:gibbs-sampling","to":"theorempath:mcmc-for-markov-random-fields","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:perfect-sampling--prerequisite-of--theorempath:mcmc-for-markov-random-fields","from":"theorempath:perfect-sampling","to":"theorempath:mcmc-for-markov-random-fields","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:mean-field-games","from":"theorempath:markov-decision-processes","to":"theorempath:mean-field-games","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mean-field-theory--prerequisite-of--theorempath:mean-field-games","from":"theorempath:mean-field-theory","to":"theorempath:mean-field-games","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agent-based-modeling-with-ml--prerequisite-of--theorempath:mean-field-games","from":"theorempath:agent-based-modeling-with-ml","to":"theorempath:mean-field-games","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-tangent-kernel--prerequisite-of--theorempath:mean-field-theory","from":"theorempath:neural-tangent-kernel","to":"theorempath:mean-field-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-geometry--prerequisite-of--theorempath:mean-field-theory","from":"theorempath:information-geometry","to":"theorempath:mean-field-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:measure-concentration-and-geometric-fa","from":"theorempath:subgaussian-random-variables","to":"theorempath:measure-concentration-and-geometric-fa","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:epsilon-nets-and-covering-numbers--prerequisite-of--theorempath:measure-concentration-and-geometric-fa","from":"theorempath:epsilon-nets-and-covering-numbers","to":"theorempath:measure-concentration-and-geometric-fa","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cardinality-and-countability--prerequisite-of--theorempath:measure-theoretic-probability","from":"theorempath:cardinality-and-countability","to":"theorempath:measure-theoretic-probability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:integration-and-change-of-variables--prerequisite-of--theorempath:measure-theoretic-probability","from":"theorempath:integration-and-change-of-variables","to":"theorempath:measure-theoretic-probability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-probability-axioms--prerequisite-of--theorempath:measure-theoretic-probability","from":"theorempath:kolmogorov-probability-axioms","to":"theorempath:measure-theoretic-probability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:measure-theoretic-probability","from":"theorempath:random-variables","to":"theorempath:measure-theoretic-probability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:measure-theoretic-probability","from":"theorempath:sets-functions-and-relations","to":"theorempath:measure-theoretic-probability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:zermelo-fraenkel-set-theory--prerequisite-of--theorempath:measure-theoretic-probability","from":"theorempath:zermelo-fraenkel-set-theory","to":"theorempath:measure-theoretic-probability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:game-theory--prerequisite-of--theorempath:mechanism-design","from":"theorempath:game-theory","to":"theorempath:mechanism-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nash-equilibrium--prerequisite-of--theorempath:mechanism-design","from":"theorempath:nash-equilibrium","to":"theorempath:mechanism-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:arrows-impossibility--prerequisite-of--theorempath:mechanism-design","from":"theorempath:arrows-impossibility","to":"theorempath:mechanism-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:auction-theory--prerequisite-of--theorempath:mechanism-design","from":"theorempath:auction-theory","to":"theorempath:mechanism-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:commons-governance-ostrom--prerequisite-of--theorempath:mechanism-design","from":"theorempath:commons-governance-ostrom","to":"theorempath:mechanism-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stable-matching-and-deferred-acceptance--prerequisite-of--theorempath:mechanism-design","from":"theorempath:stable-matching-and-deferred-acceptance","to":"theorempath:mechanism-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:mechanistic-interpretability","from":"theorempath:transformer-architecture","to":"theorempath:mechanistic-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:principal-component-analysis--prerequisite-of--theorempath:mechanistic-interpretability","from":"theorempath:principal-component-analysis","to":"theorempath:mechanistic-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-arnold-networks--prerequisite-of--theorempath:mechanistic-interpretability","from":"theorempath:kolmogorov-arnold-networks","to":"theorempath:mechanistic-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:residual-stream-and-transformer-internals--prerequisite-of--theorempath:mechanistic-interpretability","from":"theorempath:residual-stream-and-transformer-internals","to":"theorempath:mechanistic-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:mechanistic-interpretability","from":"theorempath:rlhf-and-alignment","to":"theorempath:mechanistic-interpretability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fused-kernels--prerequisite-of--theorempath:megakernels","from":"theorempath:fused-kernels","to":"theorempath:megakernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:megakernels","from":"theorempath:gpu-compute-model","to":"theorempath:megakernels","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:context-engineering--prerequisite-of--theorempath:memory-systems-for-llms","from":"theorempath:context-engineering","to":"theorempath:memory-systems-for-llms","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache--prerequisite-of--theorempath:memory-systems-for-llms","from":"theorempath:kv-cache","to":"theorempath:memory-systems-for-llms","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:meta-analysis","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:meta-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:meta-analysis","from":"theorempath:bayesian-estimation","to":"theorempath:meta-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reml-and-variance-component-estimation--prerequisite-of--theorempath:meta-analysis","from":"theorempath:reml-and-variance-component-estimation","to":"theorempath:meta-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:meta-learning","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:meta-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:test-time-training--prerequisite-of--theorempath:meta-learning","from":"theorempath:test-time-training","to":"theorempath:meta-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:method-of-moments","from":"theorempath:common-probability-distributions","to":"theorempath:method-of-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:metric-spaces-convergence-completeness","from":"theorempath:sets-functions-and-relations","to":"theorempath:metric-spaces-convergence-completeness","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:metropolis-hastings","from":"theorempath:common-probability-distributions","to":"theorempath:metropolis-hastings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chain-monte-carlo--prerequisite-of--theorempath:metropolis-hastings","from":"theorempath:markov-chain-monte-carlo","to":"theorempath:metropolis-hastings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chains-and-steady-state--prerequisite-of--theorempath:metropolis-hastings","from":"theorempath:markov-chains-and-steady-state","to":"theorempath:metropolis-hastings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:monte-carlo-methods--prerequisite-of--theorempath:metropolis-hastings","from":"theorempath:monte-carlo-methods","to":"theorempath:metropolis-hastings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:minimax-lower-bounds","from":"theorempath:concentration-inequalities","to":"theorempath:minimax-lower-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:minimax-lower-bounds","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:minimax-lower-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:minimax-lower-bounds","from":"theorempath:kl-divergence","to":"theorempath:minimax-lower-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cramer-rao-bound--prerequisite-of--theorempath:minimax-lower-bounds","from":"theorempath:cramer-rao-bound","to":"theorempath:minimax-lower-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:minimax-lower-bounds","from":"theorempath:fisher-information","to":"theorempath:minimax-lower-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-processes-and-chaining--prerequisite-of--theorempath:minimax-lower-bounds","from":"theorempath:empirical-processes-and-chaining","to":"theorempath:minimax-lower-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:minimax-saddle-points","from":"theorempath:convex-optimization-basics","to":"theorempath:minimax-saddle-points","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:minimax-saddle-points","from":"theorempath:convex-duality","to":"theorempath:minimax-saddle-points","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:game-theory--prerequisite-of--theorempath:minimax-theorem","from":"theorempath:game-theory","to":"theorempath:minimax-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:minimax-theorem","from":"theorempath:convex-duality","to":"theorempath:minimax-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nash-equilibrium--prerequisite-of--theorempath:minimax-theorem","from":"theorempath:nash-equilibrium","to":"theorempath:minimax-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:mirror-descent-and-frank-wolfe","from":"theorempath:convex-optimization-basics","to":"theorempath:mirror-descent-and-frank-wolfe","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:mirror-descent-and-frank-wolfe","from":"theorempath:convex-duality","to":"theorempath:mirror-descent-and-frank-wolfe","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:online-convex-optimization--prerequisite-of--theorempath:mirror-descent-and-frank-wolfe","from":"theorempath:online-convex-optimization","to":"theorempath:mirror-descent-and-frank-wolfe","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:projected-gradient-descent--prerequisite-of--theorempath:mirror-descent-and-frank-wolfe","from":"theorempath:projected-gradient-descent","to":"theorempath:mirror-descent-and-frank-wolfe","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:mistral-models","from":"theorempath:transformer-architecture","to":"theorempath:mistral-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mixture-of-experts--prerequisite-of--theorempath:mistral-models","from":"theorempath:mixture-of-experts","to":"theorempath:mistral-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:mistral-models","from":"theorempath:attention-mechanism-theory","to":"theorempath:mistral-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tokenization-and-information-theory--prerequisite-of--theorempath:mistral-models","from":"theorempath:tokenization-and-information-theory","to":"theorempath:mistral-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cohere-models--prerequisite-of--theorempath:mistral-models","from":"theorempath:cohere-models","to":"theorempath:mistral-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:floating-point-arithmetic--prerequisite-of--theorempath:mixed-precision-training","from":"theorempath:floating-point-arithmetic","to":"theorempath:mixed-precision-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adam-optimizer--prerequisite-of--theorempath:mixed-precision-training","from":"theorempath:adam-optimizer","to":"theorempath:mixed-precision-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributed-training-theory--prerequisite-of--theorempath:mixed-precision-training","from":"theorempath:distributed-training-theory","to":"theorempath:mixed-precision-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:learning-rate-scheduling--prerequisite-of--theorempath:mixed-precision-training","from":"theorempath:learning-rate-scheduling","to":"theorempath:mixed-precision-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:running-ml-workloads-on-gpus--prerequisite-of--theorempath:mixed-precision-training","from":"theorempath:running-ml-workloads-on-gpus","to":"theorempath:mixed-precision-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:webgpu-for-ml--prerequisite-of--theorempath:mixed-precision-training","from":"theorempath:webgpu-for-ml","to":"theorempath:mixed-precision-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-mixture-models-and-em--prerequisite-of--theorempath:mixture-density-networks","from":"theorempath:gaussian-mixture-models-and-em","to":"theorempath:mixture-density-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:mixture-density-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:mixture-density-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:mixture-of-experts","from":"theorempath:transformer-architecture","to":"theorempath:mixture-of-experts","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-compression-and-pruning--prerequisite-of--theorempath:mixture-of-experts","from":"theorempath:model-compression-and-pruning","to":"theorempath:mixture-of-experts","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:speculative-decoding-and-quantization--prerequisite-of--theorempath:mixture-of-experts","from":"theorempath:speculative-decoding-and-quantization","to":"theorempath:mixture-of-experts","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hardware-for-ml-practitioners--prerequisite-of--theorempath:ml-project-lifecycle","from":"theorempath:hardware-for-ml-practitioners","to":"theorempath:ml-project-lifecycle","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bellman-equations--prerequisite-of--theorempath:model-based-rl","from":"theorempath:bellman-equations","to":"theorempath:model-based-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:model-based-rl","from":"theorempath:markov-decision-processes","to":"theorempath:model-based-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-rl-for-control--prerequisite-of--theorempath:model-based-rl","from":"theorempath:deep-rl-for-control","to":"theorempath:model-based-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-systems-and-reinforcement-learning-neuroscience--prerequisite-of--theorempath:model-based-rl","from":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","to":"theorempath:model-based-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:synthetic-data-generation--prerequisite-of--theorempath:model-collapse-and-data-quality","from":"theorempath:synthetic-data-generation","to":"theorempath:model-collapse-and-data-quality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:model-comparison-table","from":"theorempath:transformer-architecture","to":"theorempath:model-comparison-table","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:claude-model-family--prerequisite-of--theorempath:model-comparison-table","from":"theorempath:claude-model-family","to":"theorempath:model-comparison-table","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deepseek-models--prerequisite-of--theorempath:model-comparison-table","from":"theorempath:deepseek-models","to":"theorempath:model-comparison-table","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gemini-and-google-models--prerequisite-of--theorempath:model-comparison-table","from":"theorempath:gemini-and-google-models","to":"theorempath:model-comparison-table","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mistral-models--prerequisite-of--theorempath:model-comparison-table","from":"theorempath:mistral-models","to":"theorempath:model-comparison-table","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:qwen-and-chinese-models--prerequisite-of--theorempath:model-comparison-table","from":"theorempath:qwen-and-chinese-models","to":"theorempath:model-comparison-table","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:model-compression-and-pruning","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:model-compression-and-pruning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrices-and-classification-metrics--prerequisite-of--theorempath:model-evaluation-best-practices","from":"theorempath:confusion-matrices-and-classification-metrics","to":"theorempath:model-evaluation-best-practices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-optimization-for-hyperparameters--prerequisite-of--theorempath:model-evaluation-best-practices","from":"theorempath:bayesian-optimization-for-hyperparameters","to":"theorempath:model-evaluation-best-practices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:model-merging-and-weight-averaging","from":"theorempath:transformer-architecture","to":"theorempath:model-merging-and-weight-averaging","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:model-theory-basics","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:model-theory-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:history-of-ai--prerequisite-of--theorempath:model-timeline","from":"theorempath:history-of-ai","to":"theorempath:model-timeline","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:key-researchers-and-ideas--prerequisite-of--theorempath:model-timeline","from":"theorempath:key-researchers-and-ideas","to":"theorempath:model-timeline","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:modes-of-convergence-random-variables","from":"theorempath:measure-theoretic-probability","to":"theorempath:modes-of-convergence-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:modes-of-convergence-random-variables","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:modes-of-convergence-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:moment-generating-functions","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:moment-generating-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:moment-generating-functions","from":"theorempath:common-probability-distributions","to":"theorempath:moment-generating-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:moment-generating-functions","from":"theorempath:exponential-function-properties","to":"theorempath:moment-generating-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:monte-carlo-methods","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:monte-carlo-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:monte-carlo-methods","from":"theorempath:law-of-large-numbers","to":"theorempath:monte-carlo-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:monte-carlo-methods","from":"theorempath:central-limit-theorem","to":"theorempath:monte-carlo-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:monty-hall-problem","from":"theorempath:common-probability-distributions","to":"theorempath:monty-hall-problem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:multi-agent-collaboration","from":"theorempath:markov-decision-processes","to":"theorempath:multi-agent-collaboration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:multi-agent-collaboration","from":"theorempath:policy-gradient-theorem","to":"theorempath:multi-agent-collaboration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:multi-armed-bandits-theory","from":"theorempath:common-probability-distributions","to":"theorempath:multi-armed-bandits-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-optimization-for-hyperparameters--prerequisite-of--theorempath:multi-armed-bandits-theory","from":"theorempath:bayesian-optimization-for-hyperparameters","to":"theorempath:multi-armed-bandits-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-regret-learning--prerequisite-of--theorempath:multi-armed-bandits-theory","from":"theorempath:no-regret-learning","to":"theorempath:multi-armed-bandits-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:online-convex-optimization--prerequisite-of--theorempath:multi-armed-bandits-theory","from":"theorempath:online-convex-optimization","to":"theorempath:multi-armed-bandits-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:multi-class-and-multi-label-classification","from":"theorempath:logistic-regression","to":"theorempath:multi-class-and-multi-label-classification","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:multi-token-prediction","from":"theorempath:transformer-architecture","to":"theorempath:multi-token-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:context-engineering--prerequisite-of--theorempath:multimodal-rag","from":"theorempath:context-engineering","to":"theorempath:multimodal-rag","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:audio-language-models--prerequisite-of--theorempath:multimodal-rag","from":"theorempath:audio-language-models","to":"theorempath:multimodal-rag","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:clip-and-openclip-in-practice--prerequisite-of--theorempath:multimodal-rag","from":"theorempath:clip-and-openclip-in-practice","to":"theorempath:multimodal-rag","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:semantic-search-and-embeddings--prerequisite-of--theorempath:multimodal-rag","from":"theorempath:semantic-search-and-embeddings","to":"theorempath:multimodal-rag","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multivariate-normal-distribution--prerequisite-of--theorempath:multivariate-distributions-atlas","from":"theorempath:multivariate-normal-distribution","to":"theorempath:multivariate-distributions-atlas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:multivariate-distributions-atlas","from":"theorempath:common-probability-distributions","to":"theorempath:multivariate-distributions-atlas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:multivariate-distributions-atlas","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:multivariate-distributions-atlas","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:joint-marginal-conditional-distributions--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:joint-marginal-conditional-distributions","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:positive-semidefinite-matrices--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:positive-semidefinite-matrices","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:the-jacobian-matrix","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:moment-generating-functions","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:characteristic-functions--prerequisite-of--theorempath:multivariate-normal-distribution","from":"theorempath:characteristic-functions","to":"theorempath:multivariate-normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:naive-bayes","from":"theorempath:common-probability-distributions","to":"theorempath:naive-bayes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:game-theory--prerequisite-of--theorempath:nash-equilibrium","from":"theorempath:game-theory","to":"theorempath:nash-equilibrium","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:nash-equilibrium","from":"theorempath:convex-optimization-basics","to":"theorempath:nash-equilibrium","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-regret-learning--prerequisite-of--theorempath:nash-equilibrium","from":"theorempath:no-regret-learning","to":"theorempath:nash-equilibrium","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:word-embeddings--prerequisite-of--theorempath:natural-language-processing-foundations","from":"theorempath:word-embeddings","to":"theorempath:natural-language-processing-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:neural-architecture-search","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:neural-architecture-search","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:training-dynamics-and-loss-landscapes--prerequisite-of--theorempath:neural-network-optimization-landscape","from":"theorempath:training-dynamics-and-loss-landscapes","to":"theorempath:neural-network-optimization-landscape","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:neural-network-optimization-landscape","from":"theorempath:the-hessian-matrix","to":"theorempath:neural-network-optimization-landscape","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:classical-odes--prerequisite-of--theorempath:neural-odes","from":"theorempath:classical-odes","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skip-connections-and-resnets--prerequisite-of--theorempath:neural-odes","from":"theorempath:skip-connections-and-resnets","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-flow-and-vanishing-gradients--prerequisite-of--theorempath:neural-odes","from":"theorempath:gradient-flow-and-vanishing-gradients","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:neural-odes","from":"theorempath:automatic-differentiation","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:equilibrium-and-implicit-models--prerequisite-of--theorempath:neural-odes","from":"theorempath:equilibrium-and-implicit-models","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lyapunov-based-machine-learning-for-chaos--prerequisite-of--theorempath:neural-odes","from":"theorempath:lyapunov-based-machine-learning-for-chaos","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nonlinear-dynamics-and-chaos-fundamentals--prerequisite-of--theorempath:neural-odes","from":"theorempath:nonlinear-dynamics-and-chaos-fundamentals","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pde-fundamentals-for-ml--prerequisite-of--theorempath:neural-odes","from":"theorempath:pde-fundamentals-for-ml","to":"theorempath:neural-odes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neural-odes--prerequisite-of--theorempath:neural-sdes","from":"theorempath:neural-odes","to":"theorempath:neural-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:neural-sdes","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:neural-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adjoint-sensitivity-method--prerequisite-of--theorempath:neural-sdes","from":"theorempath:adjoint-sensitivity-method","to":"theorempath:neural-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuous-normalizing-flows--prerequisite-of--theorempath:neural-sdes","from":"theorempath:continuous-normalizing-flows","to":"theorempath:neural-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:neural-sdes","from":"theorempath:stochastic-differential-equations","to":"theorempath:neural-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kernels-and-rkhs--prerequisite-of--theorempath:neural-tangent-kernel","from":"theorempath:kernels-and-rkhs","to":"theorempath:neural-tangent-kernel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ridge-regression--prerequisite-of--theorempath:neural-tangent-kernel","from":"theorempath:ridge-regression","to":"theorempath:neural-tangent-kernel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:implicit-bias-and-modern-generalization--prerequisite-of--theorempath:neural-tangent-kernel","from":"theorempath:implicit-bias-and-modern-generalization","to":"theorempath:neural-tangent-kernel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-for-ml--prerequisite-of--theorempath:neural-tangent-kernel","from":"theorempath:gaussian-processes-for-ml","to":"theorempath:neural-tangent-kernel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-processes-regression--prerequisite-of--theorempath:neural-tangent-kernel","from":"theorempath:gaussian-processes-regression","to":"theorempath:neural-tangent-kernel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-processes-ml--prerequisite-of--theorempath:neural-tangent-kernel","from":"theorempath:stochastic-processes-ml","to":"theorempath:neural-tangent-kernel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:newtons-method","from":"theorempath:convex-optimization-basics","to":"theorempath:newtons-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:taylor-expansion--prerequisite-of--theorempath:newtons-method","from":"theorempath:taylor-expansion","to":"theorempath:newtons-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:newtons-method","from":"theorempath:the-hessian-matrix","to":"theorempath:newtons-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:neyman-pearson-and-hypothesis-testing-theory","from":"theorempath:common-probability-distributions","to":"theorempath:neyman-pearson-and-hypothesis-testing-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:neyman-pearson-and-hypothesis-testing-theory","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:neyman-pearson-and-hypothesis-testing-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:natural-language-processing-foundations--prerequisite-of--theorempath:nlp-for-economic-text-analysis","from":"theorempath:natural-language-processing-foundations","to":"theorempath:nlp-for-economic-text-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:word-embeddings--prerequisite-of--theorempath:nlp-for-economic-text-analysis","from":"theorempath:word-embeddings","to":"theorempath:nlp-for-economic-text-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:nmf-nonnegative-matrix-factorization","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:nmf-nonnegative-matrix-factorization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-learning-framework--prerequisite-of--theorempath:no-free-lunch-theorem","from":"theorempath:pac-learning-framework","to":"theorempath:no-free-lunch-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:no-free-lunch-theorem","from":"theorempath:empirical-risk-minimization","to":"theorempath:no-free-lunch-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:loss-functions-catalog--prerequisite-of--theorempath:no-free-lunch-theorem","from":"theorempath:loss-functions-catalog","to":"theorempath:no-free-lunch-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:no-regret-learning","from":"theorempath:common-probability-distributions","to":"theorempath:no-regret-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:no-regret-learning","from":"theorempath:concentration-inequalities","to":"theorempath:no-regret-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hamiltonian-monte-carlo--prerequisite-of--theorempath:no-u-turn-sampler-and-neals-funnel","from":"theorempath:hamiltonian-monte-carlo","to":"theorempath:no-u-turn-sampler-and-neals-funnel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:no-u-turn-sampler-and-neals-funnel","from":"theorempath:bayesian-estimation","to":"theorempath:no-u-turn-sampler-and-neals-funnel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:burn-in-convergence-diagnostics--prerequisite-of--theorempath:no-u-turn-sampler-and-neals-funnel","from":"theorempath:burn-in-convergence-diagnostics","to":"theorempath:no-u-turn-sampler-and-neals-funnel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gibbs-sampling--prerequisite-of--theorempath:no-u-turn-sampler-and-neals-funnel","from":"theorempath:gibbs-sampling","to":"theorempath:no-u-turn-sampler-and-neals-funnel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:non-euclidean-and-hyperbolic-geometry","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:non-euclidean-and-hyperbolic-geometry","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:non-euclidean-and-hyperbolic-geometry","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:non-euclidean-and-hyperbolic-geometry","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:non-probability-sampling","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:non-probability-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:non-probability-sampling","from":"theorempath:law-of-large-numbers","to":"theorempath:non-probability-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:non-probability-sampling","from":"theorempath:central-limit-theorem","to":"theorempath:non-probability-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:double-debiased-machine-learning--prerequisite-of--theorempath:non-probability-sampling","from":"theorempath:double-debiased-machine-learning","to":"theorempath:non-probability-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:classical-odes--prerequisite-of--theorempath:nonlinear-dynamics-and-chaos-fundamentals","from":"theorempath:classical-odes","to":"theorempath:nonlinear-dynamics-and-chaos-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:nonlinear-dynamics-and-chaos-fundamentals","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:nonlinear-dynamics-and-chaos-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:coordinate-descent--prerequisite-of--theorempath:nonlinear-gauss-seidel","from":"theorempath:coordinate-descent","to":"theorempath:nonlinear-gauss-seidel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:nonlinear-gauss-seidel","from":"theorempath:newtons-method","to":"theorempath:nonlinear-gauss-seidel","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:nonresponse-and-missing-data","from":"theorempath:common-probability-distributions","to":"theorempath:nonresponse-and-missing-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:design-based-vs-model-based-inference--prerequisite-of--theorempath:nonresponse-and-missing-data","from":"theorempath:design-based-vs-model-based-inference","to":"theorempath:nonresponse-and-missing-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fuzzy-matching-and-record-linkage--prerequisite-of--theorempath:nonresponse-and-missing-data","from":"theorempath:fuzzy-matching-and-record-linkage","to":"theorempath:nonresponse-and-missing-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:official-statistics-and-national-surveys--prerequisite-of--theorempath:nonresponse-and-missing-data","from":"theorempath:official-statistics-and-national-surveys","to":"theorempath:nonresponse-and-missing-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survey-sampling-methods--prerequisite-of--theorempath:nonresponse-and-missing-data","from":"theorempath:survey-sampling-methods","to":"theorempath:nonresponse-and-missing-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:types-of-bias-in-statistics--prerequisite-of--theorempath:nonresponse-and-missing-data","from":"theorempath:types-of-bias-in-statistics","to":"theorempath:nonresponse-and-missing-data","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:normal-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:normal-distribution","from":"theorempath:distributions-atlas","to":"theorempath:normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-function-properties--prerequisite-of--theorempath:normal-distribution","from":"theorempath:exponential-function-properties","to":"theorempath:normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:normal-distribution","from":"theorempath:moment-generating-functions","to":"theorempath:normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:integration-and-change-of-variables--prerequisite-of--theorempath:normal-distribution","from":"theorempath:integration-and-change-of-variables","to":"theorempath:normal-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:normalization-flows","from":"theorempath:common-probability-distributions","to":"theorempath:normalization-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:normalization-flows","from":"theorempath:the-jacobian-matrix","to":"theorempath:normalization-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:normalization-flows","from":"theorempath:variational-autoencoders","to":"theorempath:normalization-flows","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:number-theory-and-ml","from":"theorempath:common-probability-distributions","to":"theorempath:number-theory-and-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:number-theory-and-ml","from":"theorempath:law-of-large-numbers","to":"theorempath:number-theory-and-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differential-privacy--prerequisite-of--theorempath:number-theory-and-ml","from":"theorempath:differential-privacy","to":"theorempath:number-theory-and-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:peano-axioms--prerequisite-of--theorempath:number-theory-and-ml","from":"theorempath:peano-axioms","to":"theorempath:number-theory-and-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:numerical-linear-algebra","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:numerical-linear-algebra","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:numerical-linear-algebra","from":"theorempath:matrix-operations-and-properties","to":"theorempath:numerical-linear-algebra","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:floating-point-arithmetic--prerequisite-of--theorempath:numerical-stability","from":"theorempath:floating-point-arithmetic","to":"theorempath:numerical-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:numerical-stability","from":"theorempath:matrix-operations-and-properties","to":"theorempath:numerical-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-norms--prerequisite-of--theorempath:numerical-stability","from":"theorempath:matrix-norms","to":"theorempath:numerical-stability","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:nvidia-gpu-architectures","from":"theorempath:gpu-compute-model","to":"theorempath:nvidia-gpu-architectures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cuda-programming-fundamentals--prerequisite-of--theorempath:nvidia-gpu-architectures","from":"theorempath:cuda-programming-fundamentals","to":"theorempath:nvidia-gpu-architectures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:parallel-processing-fundamentals--prerequisite-of--theorempath:nvidia-gpu-architectures","from":"theorempath:parallel-processing-fundamentals","to":"theorempath:nvidia-gpu-architectures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:running-ml-workloads-on-gpus--prerequisite-of--theorempath:nvidia-gpu-architectures","from":"theorempath:running-ml-workloads-on-gpus","to":"theorempath:nvidia-gpu-architectures","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:object-detection-and-segmentation","from":"theorempath:convolutional-neural-networks","to":"theorempath:object-detection-and-segmentation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hough-transform-and-circle-detection--prerequisite-of--theorempath:object-detection-and-segmentation","from":"theorempath:hough-transform-and-circle-detection","to":"theorempath:object-detection-and-segmentation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:occupancy-networks-and-neural-fields","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:occupancy-networks-and-neural-fields","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survey-sampling-methods--prerequisite-of--theorempath:official-statistics-and-national-surveys","from":"theorempath:survey-sampling-methods","to":"theorempath:official-statistics-and-national-surveys","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prasad-rao-mse-correction--prerequisite-of--theorempath:official-statistics-and-national-surveys","from":"theorempath:prasad-rao-mse-correction","to":"theorempath:official-statistics-and-national-surveys","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:small-area-estimation--prerequisite-of--theorempath:official-statistics-and-national-surveys","from":"theorempath:small-area-estimation","to":"theorempath:official-statistics-and-national-surveys","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:q-learning--prerequisite-of--theorempath:offline-reinforcement-learning","from":"theorempath:q-learning","to":"theorempath:offline-reinforcement-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:online-convex-optimization","from":"theorempath:convex-optimization-basics","to":"theorempath:online-convex-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-regret-learning--prerequisite-of--theorempath:online-convex-optimization","from":"theorempath:no-regret-learning","to":"theorempath:online-convex-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-regret-learning--prerequisite-of--theorempath:online-learning-and-bandits","from":"theorempath:no-regret-learning","to":"theorempath:online-learning-and-bandits","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adaptive-learning-is-not-iid--prerequisite-of--theorempath:online-learning-and-bandits","from":"theorempath:adaptive-learning-is-not-iid","to":"theorempath:online-learning-and-bandits","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:test-time-training--prerequisite-of--theorempath:online-learning-and-bandits","from":"theorempath:test-time-training","to":"theorempath:online-learning-and-bandits","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-multiplication-algorithms--prerequisite-of--theorempath:open-problems-in-matrix-computation","from":"theorempath:matrix-multiplication-algorithms","to":"theorempath:open-problems-in-matrix-computation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:open-problems-in-matrix-computation","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:open-problems-in-matrix-computation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:implicit-bias-and-modern-generalization--prerequisite-of--theorempath:open-problems-in-ml-theory","from":"theorempath:implicit-bias-and-modern-generalization","to":"theorempath:open-problems-in-ml-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:open-problems-in-ml-theory","from":"theorempath:scaling-laws","to":"theorempath:open-problems-in-ml-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuous-thought-machines--prerequisite-of--theorempath:open-problems-in-ml-theory","from":"theorempath:continuous-thought-machines","to":"theorempath:open-problems-in-ml-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:grokking--prerequisite-of--theorempath:open-problems-in-ml-theory","from":"theorempath:grokking","to":"theorempath:open-problems-in-ml-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:unsolved-problems-in-computer-science--prerequisite-of--theorempath:open-problems-in-ml-theory","from":"theorempath:unsolved-problems-in-computer-science","to":"theorempath:open-problems-in-ml-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:optimal-brain-surgery-and-pruning-theory","from":"theorempath:the-hessian-matrix","to":"theorempath:optimal-brain-surgery-and-pruning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:optimal-brain-surgery-and-pruning-theory","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:optimal-brain-surgery-and-pruning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis--prerequisite-of--theorempath:optimal-brain-surgery-and-pruning-theory","from":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","to":"theorempath:optimal-brain-surgery-and-pruning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:optimal-transport-and-earth-movers-distance","from":"theorempath:convex-duality","to":"theorempath:optimal-transport-and-earth-movers-distance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:wasserstein-distances--prerequisite-of--theorempath:optimal-transport-and-earth-movers-distance","from":"theorempath:wasserstein-distances","to":"theorempath:optimal-transport-and-earth-movers-distance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:convex-optimization-basics","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adam-optimizer--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:adam-optimizer","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:automatic-differentiation","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:gradient-descent-variants","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-geometry--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:information-geometry","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:preconditioned-optimizers--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:preconditioned-optimizers","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:riemannian-optimization--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:riemannian-optimization","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:training-dynamics-and-loss-landscapes--prerequisite-of--theorempath:optimizer-theory-sgd-adam-muon","from":"theorempath:training-dynamics-and-loss-landscapes","to":"theorempath:optimizer-theory-sgd-adam-muon","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:options-and-temporal-abstraction","from":"theorempath:markov-decision-processes","to":"theorempath:options-and-temporal-abstraction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:value-iteration-and-policy-iteration--prerequisite-of--theorempath:options-and-temporal-abstraction","from":"theorempath:value-iteration-and-policy-iteration","to":"theorempath:options-and-temporal-abstraction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-representations--prerequisite-of--theorempath:options-and-temporal-abstraction","from":"theorempath:policy-representations","to":"theorempath:options-and-temporal-abstraction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:order-statistics","from":"theorempath:common-probability-distributions","to":"theorempath:order-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:triangular-distribution--prerequisite-of--theorempath:order-statistics","from":"theorempath:triangular-distribution","to":"theorempath:order-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:calibration-and-uncertainty--prerequisite-of--theorempath:out-of-distribution-detection","from":"theorempath:calibration-and-uncertainty","to":"theorempath:out-of-distribution-detection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:anomaly-detection-gravitational-waves--prerequisite-of--theorempath:out-of-distribution-detection","from":"theorempath:anomaly-detection-gravitational-waves","to":"theorempath:out-of-distribution-detection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cnns-for-medical-imaging--prerequisite-of--theorempath:out-of-distribution-detection","from":"theorempath:cnns-for-medical-imaging","to":"theorempath:out-of-distribution-detection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:overfitting-and-underfitting","from":"theorempath:empirical-risk-minimization","to":"theorempath:overfitting-and-underfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-variance-tradeoff--prerequisite-of--theorempath:overfitting-and-underfitting","from":"theorempath:bias-variance-tradeoff","to":"theorempath:overfitting-and-underfitting","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:p-hacking-and-multiple-testing","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:p-hacking-and-multiple-testing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:meta-analysis--prerequisite-of--theorempath:p-hacking-and-multiple-testing","from":"theorempath:meta-analysis","to":"theorempath:p-hacking-and-multiple-testing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:pac-bayes-bounds","from":"theorempath:rademacher-complexity","to":"theorempath:pac-bayes-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:pac-bayes-bounds","from":"theorempath:bayesian-estimation","to":"theorempath:pac-bayes-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-learning-framework--prerequisite-of--theorempath:pac-bayes-bounds","from":"theorempath:pac-learning-framework","to":"theorempath:pac-bayes-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sample-complexity-bounds--prerequisite-of--theorempath:pac-bayes-bounds","from":"theorempath:sample-complexity-bounds","to":"theorempath:pac-bayes-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:concentration-inequalities","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:uniform-convergence--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:uniform-convergence","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:counting-and-combinatorics--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:counting-and-combinatorics","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-classes-and-function-spaces--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:hypothesis-classes-and-function-spaces","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:realizability-assumption--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:realizability-assumption","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:understanding-machine-learning-book--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:understanding-machine-learning-book","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:sets-functions-and-relations","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:loss-functions--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:loss-functions","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sluds-inequality--prerequisite-of--theorempath:pac-learning-framework","from":"theorempath:sluds-inequality","to":"theorempath:pac-learning-framework","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:document-intelligence--prerequisite-of--theorempath:paddleocr-and-practical-ocr","from":"theorempath:document-intelligence","to":"theorempath:paddleocr-and-practical-ocr","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hough-transform-and-circle-detection--prerequisite-of--theorempath:paddleocr-and-practical-ocr","from":"theorempath:hough-transform-and-circle-detection","to":"theorempath:paddleocr-and-practical-ocr","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:pagerank-algorithm","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:pagerank-algorithm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graph-algorithms-essentials--prerequisite-of--theorempath:pagerank-algorithm","from":"theorempath:graph-algorithms-essentials","to":"theorempath:pagerank-algorithm","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:parallel-processing-fundamentals","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:parallel-processing-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:broadcast-joins-distributed-compute--prerequisite-of--theorempath:parallel-processing-fundamentals","from":"theorempath:broadcast-joins-distributed-compute","to":"theorempath:parallel-processing-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:dask-parallel-python--prerequisite-of--theorempath:parallel-processing-fundamentals","from":"theorempath:dask-parallel-python","to":"theorempath:parallel-processing-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ray-distributed-python--prerequisite-of--theorempath:parallel-processing-fundamentals","from":"theorempath:ray-distributed-python","to":"theorempath:parallel-processing-fundamentals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:pareto-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:pareto-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:pareto-distribution","from":"theorempath:central-limit-theorem","to":"theorempath:pareto-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:law-of-large-numbers--prerequisite-of--theorempath:pareto-distribution","from":"theorempath:law-of-large-numbers","to":"theorempath:pareto-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:pareto-distribution","from":"theorempath:distributions-atlas","to":"theorempath:pareto-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:particle-filters","from":"theorempath:metropolis-hastings","to":"theorempath:particle-filters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:importance-sampling--prerequisite-of--theorempath:particle-filters","from":"theorempath:importance-sampling","to":"theorempath:particle-filters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graphslam-and-factor-graphs--prerequisite-of--theorempath:particle-filters","from":"theorempath:graphslam-and-factor-graphs","to":"theorempath:particle-filters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kalman-filter--prerequisite-of--theorempath:particle-filters","from":"theorempath:kalman-filter","to":"theorempath:particle-filters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:state-space-models--prerequisite-of--theorempath:particle-filters","from":"theorempath:state-space-models","to":"theorempath:particle-filters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fast-fourier-transform--prerequisite-of--theorempath:pde-fundamentals-for-ml","from":"theorempath:fast-fourier-transform","to":"theorempath:pde-fundamentals-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:pde-fundamentals-for-ml","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:pde-fundamentals-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:pde-fundamentals-for-ml","from":"theorempath:stochastic-differential-equations","to":"theorempath:pde-fundamentals-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:pde-fundamentals-for-ml","from":"theorempath:measure-theoretic-probability","to":"theorempath:pde-fundamentals-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:functional-analysis-core--prerequisite-of--theorempath:pde-fundamentals-for-ml","from":"theorempath:functional-analysis-core","to":"theorempath:pde-fundamentals-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:divergence-curl-and-line-integrals--prerequisite-of--theorempath:pde-fundamentals-for-ml","from":"theorempath:divergence-curl-and-line-integrals","to":"theorempath:pde-fundamentals-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:perfect-sampling","from":"theorempath:metropolis-hastings","to":"theorempath:perfect-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gibbs-sampling--prerequisite-of--theorempath:perfect-sampling","from":"theorempath:gibbs-sampling","to":"theorempath:perfect-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:permutation-tests","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:permutation-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bootstrap-methods--prerequisite-of--theorempath:permutation-tests","from":"theorempath:bootstrap-methods","to":"theorempath:permutation-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:neyman-pearson-and-hypothesis-testing-theory--prerequisite-of--theorempath:permutation-tests","from":"theorempath:neyman-pearson-and-hypothesis-testing-theory","to":"theorempath:permutation-tests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:perplexity-and-language-model-evaluation","from":"theorempath:information-theory-foundations","to":"theorempath:perplexity-and-language-model-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bits-nats-perplexity-bpb--prerequisite-of--theorempath:perplexity-and-language-model-evaluation","from":"theorempath:bits-nats-perplexity-bpb","to":"theorempath:perplexity-and-language-model-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:log-probability-computation--prerequisite-of--theorempath:perplexity-and-language-model-evaluation","from":"theorempath:log-probability-computation","to":"theorempath:perplexity-and-language-model-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:the-jacobian-matrix","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:automatic-differentiation","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:gradient-descent-variants","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:classical-odes--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:classical-odes","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:divergence-curl-and-line-integrals--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:divergence-curl-and-line-integrals","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-arnold-networks--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:kolmogorov-arnold-networks","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pde-fundamentals-for-ml--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:pde-fundamentals-for-ml","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:symbolic-regression-and-equation-discovery--prerequisite-of--theorempath:physics-informed-neural-networks","from":"theorempath:symbolic-regression-and-equation-discovery","to":"theorempath:physics-informed-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:plan-then-generate","from":"theorempath:transformer-architecture","to":"theorempath:plan-then-generate","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:poisson-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:poisson-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:poisson-distribution","from":"theorempath:distributions-atlas","to":"theorempath:poisson-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-distribution--prerequisite-of--theorempath:poisson-distribution","from":"theorempath:exponential-distribution","to":"theorempath:poisson-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:poisson-limit-theorem","from":"theorempath:common-probability-distributions","to":"theorempath:poisson-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:characteristic-functions--prerequisite-of--theorempath:poisson-limit-theorem","from":"theorempath:characteristic-functions","to":"theorempath:poisson-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:moment-generating-functions--prerequisite-of--theorempath:poisson-limit-theorem","from":"theorempath:moment-generating-functions","to":"theorempath:poisson-limit-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:markov-decision-processes","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:convex-optimization-basics","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-armed-bandits-theory--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:multi-armed-bandits-theory","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:online-learning-and-bandits--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:online-learning-and-bandits","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:q-learning--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:q-learning","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:td-learning--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:td-learning","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:value-iteration-and-policy-iteration--prerequisite-of--theorempath:policy-gradient-theorem","from":"theorempath:value-iteration-and-policy-iteration","to":"theorempath:policy-gradient-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:policy-optimization-ppo-trpo","from":"theorempath:policy-gradient-theorem","to":"theorempath:policy-optimization-ppo-trpo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:actor-critic-methods--prerequisite-of--theorempath:policy-optimization-ppo-trpo","from":"theorempath:actor-critic-methods","to":"theorempath:policy-optimization-ppo-trpo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ddpg--prerequisite-of--theorempath:policy-optimization-ppo-trpo","from":"theorempath:ddpg","to":"theorempath:policy-optimization-ppo-trpo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:offline-reinforcement-learning--prerequisite-of--theorempath:policy-optimization-ppo-trpo","from":"theorempath:offline-reinforcement-learning","to":"theorempath:policy-optimization-ppo-trpo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:td3--prerequisite-of--theorempath:policy-optimization-ppo-trpo","from":"theorempath:td3","to":"theorempath:policy-optimization-ppo-trpo","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:policy-representations","from":"theorempath:markov-decision-processes","to":"theorempath:policy-representations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:positional-encoding","from":"theorempath:attention-mechanism-theory","to":"theorempath:positional-encoding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-is-all-you-need-paper--prerequisite-of--theorempath:positional-encoding","from":"theorempath:attention-is-all-you-need-paper","to":"theorempath:positional-encoding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanisms-history--prerequisite-of--theorempath:positional-encoding","from":"theorempath:attention-mechanisms-history","to":"theorempath:positional-encoding","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:positive-semidefinite-matrices","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:positive-semidefinite-matrices","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:post-training-overview","from":"theorempath:rlhf-and-alignment","to":"theorempath:post-training-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:post-training-overview","from":"theorempath:transformer-architecture","to":"theorempath:post-training-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agentic-rl-and-tool-use--prerequisite-of--theorempath:post-training-overview","from":"theorempath:agentic-rl-and-tool-use","to":"theorempath:post-training-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bert-and-pretrain-finetune-paradigm--prerequisite-of--theorempath:post-training-overview","from":"theorempath:bert-and-pretrain-finetune-paradigm","to":"theorempath:post-training-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-optimization-ppo-trpo--prerequisite-of--theorempath:post-training-overview","from":"theorempath:policy-optimization-ppo-trpo","to":"theorempath:post-training-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:test-time-compute-and-search--prerequisite-of--theorempath:post-training-overview","from":"theorempath:test-time-compute-and-search","to":"theorempath:post-training-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:small-area-estimation--prerequisite-of--theorempath:prasad-rao-mse-correction","from":"theorempath:small-area-estimation","to":"theorempath:prasad-rao-mse-correction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:prasad-rao-mse-correction","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:prasad-rao-mse-correction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reml-and-variance-component-estimation--prerequisite-of--theorempath:prasad-rao-mse-correction","from":"theorempath:reml-and-variance-component-estimation","to":"theorempath:prasad-rao-mse-correction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:preconditioned-optimizers","from":"theorempath:convex-optimization-basics","to":"theorempath:preconditioned-optimizers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:preconditioned-optimizers","from":"theorempath:fisher-information","to":"theorempath:preconditioned-optimizers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:preconditioned-optimizers","from":"theorempath:the-hessian-matrix","to":"theorempath:preconditioned-optimizers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-gradient-methods--prerequisite-of--theorempath:preconditioned-optimizers","from":"theorempath:conjugate-gradient-methods","to":"theorempath:preconditioned-optimizers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders--prerequisite-of--theorempath:predictive-coding-and-autoencoders-in-the-brain","from":"theorempath:autoencoders","to":"theorempath:predictive-coding-and-autoencoders-in-the-brain","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:predictive-coding-and-autoencoders-in-the-brain","from":"theorempath:variational-autoencoders","to":"theorempath:predictive-coding-and-autoencoders-in-the-brain","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:predictive-coding-and-autoencoders-in-the-brain","from":"theorempath:kl-divergence","to":"theorempath:predictive-coding-and-autoencoders-in-the-brain","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-systems-and-reinforcement-learning-neuroscience--prerequisite-of--theorempath:predictive-coding-and-autoencoders-in-the-brain","from":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","to":"theorempath:predictive-coding-and-autoencoders-in-the-brain","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-coding-and-efficient-coding--prerequisite-of--theorempath:predictive-coding-and-autoencoders-in-the-brain","from":"theorempath:sparse-coding-and-efficient-coding","to":"theorempath:predictive-coding-and-autoencoders-in-the-brain","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:spiking-neural-networks--prerequisite-of--theorempath:predictive-coding-and-autoencoders-in-the-brain","from":"theorempath:spiking-neural-networks","to":"theorempath:predictive-coding-and-autoencoders-in-the-brain","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache--prerequisite-of--theorempath:prefix-caching","from":"theorempath:kv-cache","to":"theorempath:prefix-caching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache-optimization--prerequisite-of--theorempath:prefix-caching","from":"theorempath:kv-cache-optimization","to":"theorempath:prefix-caching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:singular-value-decomposition--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:singular-value-decomposition","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gram-matrices-and-kernel-matrices--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:gram-matrices-and-kernel-matrices","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:high-dimensional-covariance-estimation--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:high-dimensional-covariance-estimation","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nmf-nonnegative-matrix-factorization--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:nmf-nonnegative-matrix-factorization","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:positive-semidefinite-matrices--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:positive-semidefinite-matrices","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tensors-and-tensor-operations--prerequisite-of--theorempath:principal-component-analysis","from":"theorempath:tensors-and-tensor-operations","to":"theorempath:principal-component-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:probability-flow-ode","from":"theorempath:stochastic-differential-equations","to":"theorempath:probability-flow-ode","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fokker-planck-equation--prerequisite-of--theorempath:probability-flow-ode","from":"theorempath:fokker-planck-equation","to":"theorempath:probability-flow-ode","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:score-matching--prerequisite-of--theorempath:probability-flow-ode","from":"theorempath:score-matching","to":"theorempath:probability-flow-ode","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-reversal-of-sdes--prerequisite-of--theorempath:probability-flow-ode","from":"theorempath:time-reversal-of-sdes","to":"theorempath:probability-flow-ode","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:projected-gradient-descent","from":"theorempath:convex-optimization-basics","to":"theorempath:projected-gradient-descent","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:prompt-engineering-and-in-context-learning","from":"theorempath:transformer-architecture","to":"theorempath:prompt-engineering-and-in-context-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:proof-theory-and-cut-elimination","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:proof-theory-and-cut-elimination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tactics-vs-proof-terms--prerequisite-of--theorempath:proof-theory-and-cut-elimination","from":"theorempath:tactics-vs-proof-terms","to":"theorempath:proof-theory-and-cut-elimination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:theorem-proving-in-coq--prerequisite-of--theorempath:proof-theory-and-cut-elimination","from":"theorempath:theorem-proving-in-coq","to":"theorempath:proof-theory-and-cut-elimination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:theorem-proving-in-lean--prerequisite-of--theorempath:proof-theory-and-cut-elimination","from":"theorempath:theorem-proving-in-lean","to":"theorempath:proof-theory-and-cut-elimination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:type-theory--prerequisite-of--theorempath:proof-theory-and-cut-elimination","from":"theorempath:type-theory","to":"theorempath:proof-theory-and-cut-elimination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:evaluation-metrics-and-properties--prerequisite-of--theorempath:proper-scoring-rules","from":"theorempath:evaluation-metrics-and-properties","to":"theorempath:proper-scoring-rules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:roc-curve-and-auc--prerequisite-of--theorempath:proper-scoring-rules","from":"theorempath:roc-curve-and-auc","to":"theorempath:proper-scoring-rules","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expected-utility--prerequisite-of--theorempath:prospect-theory","from":"theorempath:expected-utility","to":"theorempath:prospect-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:prospect-theory","from":"theorempath:common-probability-distributions","to":"theorempath:prospect-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:proximal-gradient-methods","from":"theorempath:convex-optimization-basics","to":"theorempath:proximal-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:quasi-newton-methods--prerequisite-of--theorempath:proximal-gradient-methods","from":"theorempath:quasi-newton-methods","to":"theorempath:proximal-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgradients-and-subdifferentials--prerequisite-of--theorempath:proximal-gradient-methods","from":"theorempath:subgradients-and-subdifferentials","to":"theorempath:proximal-gradient-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:public-key-cryptography","from":"theorempath:sets-functions-and-relations","to":"theorempath:public-key-cryptography","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:public-key-cryptography","from":"theorempath:common-probability-distributions","to":"theorempath:public-key-cryptography","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hash-functions--prerequisite-of--theorempath:public-key-cryptography","from":"theorempath:hash-functions","to":"theorempath:public-key-cryptography","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:value-iteration-and-policy-iteration--prerequisite-of--theorempath:q-learning","from":"theorempath:value-iteration-and-policy-iteration","to":"theorempath:q-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bellman-equations--prerequisite-of--theorempath:q-learning","from":"theorempath:bellman-equations","to":"theorempath:q-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-approximation-theory--prerequisite-of--theorempath:q-learning","from":"theorempath:stochastic-approximation-theory","to":"theorempath:q-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:td-learning--prerequisite-of--theorempath:q-learning","from":"theorempath:td-learning","to":"theorempath:q-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:quantization-theory","from":"theorempath:matrix-operations-and-properties","to":"theorempath:quantization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:quantization-theory","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:quantization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-calculus--prerequisite-of--theorempath:quantization-theory","from":"theorempath:matrix-calculus","to":"theorempath:quantization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:quantization-theory","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:quantization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:quantization-theory","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:quantization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis--prerequisite-of--theorempath:quantization-theory","from":"theorempath:iterative-magnitude-pruning-and-lottery-ticket-hypothesis","to":"theorempath:quantization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:quasi-newton-methods","from":"theorempath:newtons-method","to":"theorempath:quasi-newton-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:line-search-methods--prerequisite-of--theorempath:quasi-newton-methods","from":"theorempath:line-search-methods","to":"theorempath:quasi-newton-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:secant-method--prerequisite-of--theorempath:quasi-newton-methods","from":"theorempath:secant-method","to":"theorempath:quasi-newton-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:qwen-and-chinese-models","from":"theorempath:transformer-architecture","to":"theorempath:qwen-and-chinese-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:empirical-risk-minimization","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vc-dimension--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:vc-dimension","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:concentration-inequalities","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:glivenko-cantelli-theorem--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:glivenko-cantelli-theorem","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-classes-and-function-spaces--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:hypothesis-classes-and-function-spaces","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mcdiarmids-inequality--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:mcdiarmids-inequality","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:subgaussian-random-variables","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:understanding-machine-learning-book--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:understanding-machine-learning-book","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:uniform-convergence--prerequisite-of--theorempath:rademacher-complexity","from":"theorempath:uniform-convergence","to":"theorempath:rademacher-complexity","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:radon-nikodym-and-conditional-expectation","from":"theorempath:measure-theoretic-probability","to":"theorempath:radon-nikodym-and-conditional-expectation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:decision-trees-and-ensembles--prerequisite-of--theorempath:random-forests","from":"theorempath:decision-trees-and-ensembles","to":"theorempath:random-forests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bootstrap-methods--prerequisite-of--theorempath:random-forests","from":"theorempath:bootstrap-methods","to":"theorempath:random-forests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bagging--prerequisite-of--theorempath:random-forests","from":"theorempath:bagging","to":"theorempath:random-forests","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-concentration--prerequisite-of--theorempath:random-matrix-theory-overview","from":"theorempath:matrix-concentration","to":"theorempath:random-matrix-theory-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:epsilon-nets-and-covering-numbers--prerequisite-of--theorempath:random-matrix-theory-overview","from":"theorempath:epsilon-nets-and-covering-numbers","to":"theorempath:random-matrix-theory-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:random-matrix-theory-overview","from":"theorempath:measure-theoretic-probability","to":"theorempath:random-matrix-theory-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inner-product-spaces-and-orthogonality--prerequisite-of--theorempath:random-matrix-theory-overview","from":"theorempath:inner-product-spaces-and-orthogonality","to":"theorempath:random-matrix-theory-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hanson-wright-inequality--prerequisite-of--theorempath:random-matrix-theory-overview","from":"theorempath:hanson-wright-inequality","to":"theorempath:random-matrix-theory-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:principal-component-analysis--prerequisite-of--theorempath:random-matrix-theory-overview","from":"theorempath:principal-component-analysis","to":"theorempath:random-matrix-theory-overview","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-probability-axioms--prerequisite-of--theorempath:random-variables","from":"theorempath:kolmogorov-probability-axioms","to":"theorempath:random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:random-variables","from":"theorempath:sets-functions-and-relations","to":"theorempath:random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:rao-blackwellization","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:rao-blackwellization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:importance-sampling--prerequisite-of--theorempath:rao-blackwellization","from":"theorempath:importance-sampling","to":"theorempath:rao-blackwellization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:realizability-assumption","from":"theorempath:empirical-risk-minimization","to":"theorempath:realizability-assumption","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-classes-and-function-spaces--prerequisite-of--theorempath:realizability-assumption","from":"theorempath:hypothesis-classes-and-function-spaces","to":"theorempath:realizability-assumption","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:post-training-overview--prerequisite-of--theorempath:reasoning-data-curation","from":"theorempath:post-training-overview","to":"theorempath:reasoning-data-curation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:alphaproof-and-ai-theorem-proving--prerequisite-of--theorempath:reasoning-data-curation","from":"theorempath:alphaproof-and-ai-theorem-proving","to":"theorempath:reasoning-data-curation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:synthetic-data-distillation--prerequisite-of--theorempath:reasoning-data-curation","from":"theorempath:synthetic-data-distillation","to":"theorempath:reasoning-data-curation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:recommender-systems","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:recommender-systems","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:recurrent-neural-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:recurrent-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:recurrent-neural-networks","from":"theorempath:convolutional-neural-networks","to":"theorempath:recurrent-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:macroeconomic-time-series-forecasting--prerequisite-of--theorempath:recurrent-neural-networks","from":"theorempath:macroeconomic-time-series-forecasting","to":"theorempath:recurrent-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:red-teaming-and-adversarial-eval","from":"theorempath:rlhf-and-alignment","to":"theorempath:red-teaming-and-adversarial-eval","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:calibration-and-uncertainty--prerequisite-of--theorempath:red-teaming-and-adversarial-eval","from":"theorempath:calibration-and-uncertainty","to":"theorempath:red-teaming-and-adversarial-eval","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:regularization-theory--prerequisite-of--theorempath:regularization-in-practice","from":"theorempath:regularization-theory","to":"theorempath:regularization-in-practice","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cross-entropy-loss-deep-dive--prerequisite-of--theorempath:regularization-in-practice","from":"theorempath:cross-entropy-loss-deep-dive","to":"theorempath:regularization-in-practice","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:regularization-theory","from":"theorempath:convex-optimization-basics","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-variance-tradeoff--prerequisite-of--theorempath:regularization-theory","from":"theorempath:bias-variance-tradeoff","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adaboost--prerequisite-of--theorempath:regularization-theory","from":"theorempath:adaboost","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:regularization-theory","from":"theorempath:convex-duality","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:elastic-net--prerequisite-of--theorempath:regularization-theory","from":"theorempath:elastic-net","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-boosting--prerequisite-of--theorempath:regularization-theory","from":"theorempath:gradient-boosting","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:overfitting-and-underfitting--prerequisite-of--theorempath:regularization-theory","from":"theorempath:overfitting-and-underfitting","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:xgboost--prerequisite-of--theorempath:regularization-theory","from":"theorempath:xgboost","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-complexity-tradeoff--prerequisite-of--theorempath:regularization-theory","from":"theorempath:bias-complexity-tradeoff","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-a-posteriori-estimation--prerequisite-of--theorempath:regularization-theory","from":"theorempath:maximum-a-posteriori-estimation","to":"theorempath:regularization-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:reinforcement-learning-environments-and-benchmarks","from":"theorempath:markov-decision-processes","to":"theorempath:reinforcement-learning-environments-and-benchmarks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-rl-for-control--prerequisite-of--theorempath:reinforcement-learning-environments-and-benchmarks","from":"theorempath:deep-rl-for-control","to":"theorempath:reinforcement-learning-environments-and-benchmarks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:auction-theory--prerequisite-of--theorempath:reinforcement-learning-for-auction-design","from":"theorempath:auction-theory","to":"theorempath:reinforcement-learning-for-auction-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mechanism-design--prerequisite-of--theorempath:reinforcement-learning-for-auction-design","from":"theorempath:mechanism-design","to":"theorempath:reinforcement-learning-for-auction-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:reinforcement-learning-for-drug-discovery","from":"theorempath:policy-gradient-theorem","to":"theorempath:reinforcement-learning-for-drug-discovery","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:reinforcement-learning-for-drug-discovery","from":"theorempath:markov-decision-processes","to":"theorempath:reinforcement-learning-for-drug-discovery","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:reinforcement-learning-for-synthesis-planning","from":"theorempath:markov-decision-processes","to":"theorempath:reinforcement-learning-for-synthesis-planning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:reinforcement-learning-for-synthesis-planning","from":"theorempath:policy-gradient-theorem","to":"theorempath:reinforcement-learning-for-synthesis-planning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:reinforcement-learning-from-human-feedback-deep-dive","from":"theorempath:policy-gradient-theorem","to":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:reinforcement-learning-from-human-feedback-deep-dive","from":"theorempath:rlhf-and-alignment","to":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-for-synthesis-planning--prerequisite-of--theorempath:reinforcement-learning-from-human-feedback-deep-dive","from":"theorempath:reinforcement-learning-for-synthesis-planning","to":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-design--prerequisite-of--theorempath:reinforcement-learning-from-human-feedback-deep-dive","from":"theorempath:reward-design","to":"theorempath:reinforcement-learning-from-human-feedback-deep-dive","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:monte-carlo-methods--prerequisite-of--theorempath:rejection-sampling","from":"theorempath:monte-carlo-methods","to":"theorempath:rejection-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:relational-algebra","from":"theorempath:sets-functions-and-relations","to":"theorempath:relational-algebra","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:relational-algebra","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:relational-algebra","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:reml-and-variance-component-estimation","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:reml-and-variance-component-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:reml-and-variance-component-estimation","from":"theorempath:linear-regression","to":"theorempath:reml-and-variance-component-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:reml-and-variance-component-estimation","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:reml-and-variance-component-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:contrastive-learning--prerequisite-of--theorempath:representation-learning-in-cosmology","from":"theorempath:contrastive-learning","to":"theorempath:representation-learning-in-cosmology","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:self-supervised-vision--prerequisite-of--theorempath:representation-learning-in-cosmology","from":"theorempath:self-supervised-vision","to":"theorempath:representation-learning-in-cosmology","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:representation-learning-theory","from":"theorempath:information-theory-foundations","to":"theorempath:representation-learning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:variational-autoencoders--prerequisite-of--theorempath:representation-learning-theory","from":"theorempath:variational-autoencoders","to":"theorempath:representation-learning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:equivariant-deep-learning--prerequisite-of--theorempath:representation-learning-theory","from":"theorempath:equivariant-deep-learning","to":"theorempath:representation-learning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hyperbolic-embeddings-for-graphs--prerequisite-of--theorempath:representation-learning-theory","from":"theorempath:hyperbolic-embeddings-for-graphs","to":"theorempath:representation-learning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:representation-learning-in-cosmology--prerequisite-of--theorempath:representation-learning-theory","from":"theorempath:representation-learning-in-cosmology","to":"theorempath:representation-learning-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:git-and-gitlab-for-ml-research--prerequisite-of--theorempath:reproducibility-and-experimental-rigor","from":"theorempath:git-and-gitlab-for-ml-research","to":"theorempath:reproducibility-and-experimental-rigor","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:python-for-ml-research--prerequisite-of--theorempath:reproducibility-and-experimental-rigor","from":"theorempath:python-for-ml-research","to":"theorempath:reproducibility-and-experimental-rigor","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:weights-and-biases-experiment-tracking--prerequisite-of--theorempath:reproducibility-and-experimental-rigor","from":"theorempath:weights-and-biases-experiment-tracking","to":"theorempath:reproducibility-and-experimental-rigor","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:reservoir-computing-and-echo-state-networks","from":"theorempath:recurrent-neural-networks","to":"theorempath:reservoir-computing-and-echo-state-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders-for-low-dimensional-dynamical-structures--prerequisite-of--theorempath:reservoir-computing-and-echo-state-networks","from":"theorempath:autoencoders-for-low-dimensional-dynamical-structures","to":"theorempath:reservoir-computing-and-echo-state-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lyapunov-based-machine-learning-for-chaos--prerequisite-of--theorempath:reservoir-computing-and-echo-state-networks","from":"theorempath:lyapunov-based-machine-learning-for-chaos","to":"theorempath:reservoir-computing-and-echo-state-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:nonlinear-dynamics-and-chaos-fundamentals--prerequisite-of--theorempath:reservoir-computing-and-echo-state-networks","from":"theorempath:nonlinear-dynamics-and-chaos-fundamentals","to":"theorempath:reservoir-computing-and-echo-state-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:symbolic-regression-and-equation-discovery--prerequisite-of--theorempath:reservoir-computing-and-echo-state-networks","from":"theorempath:symbolic-regression-and-equation-discovery","to":"theorempath:reservoir-computing-and-echo-state-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:residual-stream-and-transformer-internals","from":"theorempath:transformer-architecture","to":"theorempath:residual-stream-and-transformer-internals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fox-forget-gate--prerequisite-of--theorempath:residual-stream-and-transformer-internals","from":"theorempath:fox-forget-gate","to":"theorempath:residual-stream-and-transformer-internals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-flow-and-vanishing-gradients--prerequisite-of--theorempath:residual-stream-and-transformer-internals","from":"theorempath:gradient-flow-and-vanishing-gradients","to":"theorempath:residual-stream-and-transformer-internals","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:restricted-isometry-property","from":"theorempath:subgaussian-random-variables","to":"theorempath:restricted-isometry-property","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:reversible-jump-mcmc","from":"theorempath:metropolis-hastings","to":"theorempath:reversible-jump-mcmc","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:reward-design","from":"theorempath:markov-decision-processes","to":"theorempath:reward-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bellman-equations--prerequisite-of--theorempath:reward-design","from":"theorempath:bellman-equations","to":"theorempath:reward-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reinforcement-learning-for-drug-discovery--prerequisite-of--theorempath:reward-design","from":"theorempath:reinforcement-learning-for-drug-discovery","to":"theorempath:reward-design","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-models-and-verifiers--prerequisite-of--theorempath:reward-hacking","from":"theorempath:reward-models-and-verifiers","to":"theorempath:reward-hacking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:reward-hacking","from":"theorempath:rlhf-and-alignment","to":"theorempath:reward-hacking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hallucination-theory--prerequisite-of--theorempath:reward-hacking","from":"theorempath:hallucination-theory","to":"theorempath:reward-hacking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-design--prerequisite-of--theorempath:reward-hacking","from":"theorempath:reward-design","to":"theorempath:reward-hacking","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rlhf-and-alignment--prerequisite-of--theorempath:reward-models-and-verifiers","from":"theorempath:rlhf-and-alignment","to":"theorempath:reward-models-and-verifiers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:post-training-overview--prerequisite-of--theorempath:reward-models-and-verifiers","from":"theorempath:post-training-overview","to":"theorempath:reward-models-and-verifiers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reasoning-data-curation--prerequisite-of--theorempath:reward-models-and-verifiers","from":"theorempath:reasoning-data-curation","to":"theorempath:reward-models-and-verifiers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:test-time-compute-and-search--prerequisite-of--theorempath:reward-models-and-verifiers","from":"theorempath:test-time-compute-and-search","to":"theorempath:reward-models-and-verifiers","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:td-learning--prerequisite-of--theorempath:reward-systems-and-reinforcement-learning-neuroscience","from":"theorempath:td-learning","to":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:reward-systems-and-reinforcement-learning-neuroscience","from":"theorempath:markov-decision-processes","to":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:reward-systems-and-reinforcement-learning-neuroscience","from":"theorempath:policy-gradient-theorem","to":"theorempath:reward-systems-and-reinforcement-learning-neuroscience","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:ridge-regression","from":"theorempath:linear-regression","to":"theorempath:ridge-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:ridge-regression","from":"theorempath:convex-optimization-basics","to":"theorempath:ridge-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:shrinkage-estimation-james-stein--prerequisite-of--theorempath:ridge-regression","from":"theorempath:shrinkage-estimation-james-stein","to":"theorempath:ridge-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:elements-of-statistical-learning-book--prerequisite-of--theorempath:ridge-regression","from":"theorempath:elements-of-statistical-learning-book","to":"theorempath:ridge-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gauss-markov-theorem--prerequisite-of--theorempath:ridge-regression","from":"theorempath:gauss-markov-theorem","to":"theorempath:ridge-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-a-posteriori-estimation--prerequisite-of--theorempath:ridge-regression","from":"theorempath:maximum-a-posteriori-estimation","to":"theorempath:ridge-regression","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:convex-optimization-basics","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:the-hessian-matrix","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:equivariant-deep-learning--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:equivariant-deep-learning","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hyperbolic-embeddings-for-graphs--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:hyperbolic-embeddings-for-graphs","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:non-euclidean-and-hyperbolic-geometry--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:non-euclidean-and-hyperbolic-geometry","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:preconditioned-optimizers--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:preconditioned-optimizers","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tsne-and-umap--prerequisite-of--theorempath:riemannian-optimization","from":"theorempath:tsne-and-umap","to":"theorempath:riemannian-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:rlhf-and-alignment","from":"theorempath:policy-gradient-theorem","to":"theorempath:rlhf-and-alignment","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:rlhf-and-alignment","from":"theorempath:markov-decision-processes","to":"theorempath:rlhf-and-alignment","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:actor-critic-methods--prerequisite-of--theorempath:rlhf-and-alignment","from":"theorempath:actor-critic-methods","to":"theorempath:rlhf-and-alignment","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fine-tuning-and-adaptation--prerequisite-of--theorempath:rlhf-and-alignment","from":"theorempath:fine-tuning-and-adaptation","to":"theorempath:rlhf-and-alignment","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:rlhf-and-alignment","from":"theorempath:transformer-architecture","to":"theorempath:rlhf-and-alignment","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:rnns-for-signal-sequences","from":"theorempath:recurrent-neural-networks","to":"theorempath:rnns-for-signal-sequences","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signals-and-systems-for-ml--prerequisite-of--theorempath:rnns-for-signal-sequences","from":"theorempath:signals-and-systems-for-ml","to":"theorempath:rnns-for-signal-sequences","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:robust-adversarial-policies","from":"theorempath:markov-decision-processes","to":"theorempath:robust-adversarial-policies","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:minimax-lower-bounds--prerequisite-of--theorempath:robust-adversarial-policies","from":"theorempath:minimax-lower-bounds","to":"theorempath:robust-adversarial-policies","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:robust-statistics-and-m-estimators","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:robust-statistics-and-m-estimators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:minimax-saddle-points--prerequisite-of--theorempath:robust-statistics-and-m-estimators","from":"theorempath:minimax-saddle-points","to":"theorempath:robust-statistics-and-m-estimators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skewness-kurtosis-and-higher-moments--prerequisite-of--theorempath:robust-statistics-and-m-estimators","from":"theorempath:skewness-kurtosis-and-higher-moments","to":"theorempath:robust-statistics-and-m-estimators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:winsorization--prerequisite-of--theorempath:robust-statistics-and-m-estimators","from":"theorempath:winsorization","to":"theorempath:robust-statistics-and-m-estimators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:confusion-matrices-and-classification-metrics--prerequisite-of--theorempath:roc-curve-and-auc","from":"theorempath:confusion-matrices-and-classification-metrics","to":"theorempath:roc-curve-and-auc","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:roc-curve-and-auc","from":"theorempath:common-probability-distributions","to":"theorempath:roc-curve-and-auc","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gpu-compute-model--prerequisite-of--theorempath:running-ml-workloads-on-gpus","from":"theorempath:gpu-compute-model","to":"theorempath:running-ml-workloads-on-gpus","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vc-dimension--prerequisite-of--theorempath:sample-complexity-bounds","from":"theorempath:vc-dimension","to":"theorempath:sample-complexity-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:realizability-assumption--prerequisite-of--theorempath:sample-complexity-bounds","from":"theorempath:realizability-assumption","to":"theorempath:sample-complexity-bounds","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:sample-size-determination","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:sample-size-determination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:sample-size-determination","from":"theorempath:common-probability-distributions","to":"theorempath:sample-size-determination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survey-sampling-methods--prerequisite-of--theorempath:sample-size-determination","from":"theorempath:survey-sampling-methods","to":"theorempath:sample-size-determination","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:scale-location-shape-parameters","from":"theorempath:common-probability-distributions","to":"theorempath:scale-location-shape-parameters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:scale-location-shape-parameters","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:scale-location-shape-parameters","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:scaling-compute-optimal-training","from":"theorempath:scaling-laws","to":"theorempath:scaling-compute-optimal-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:scaling-laws","from":"theorempath:convex-optimization-basics","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:data-contamination-and-evaluation--prerequisite-of--theorempath:scaling-laws","from":"theorempath:data-contamination-and-evaluation","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributed-training-theory--prerequisite-of--theorempath:scaling-laws","from":"theorempath:distributed-training-theory","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:history-of-ai--prerequisite-of--theorempath:scaling-laws","from":"theorempath:history-of-ai","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ineffable-intelligence--prerequisite-of--theorempath:scaling-laws","from":"theorempath:ineffable-intelligence","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inference-systems-overview--prerequisite-of--theorempath:scaling-laws","from":"theorempath:inference-systems-overview","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lazy-vs-feature-learning--prerequisite-of--theorempath:scaling-laws","from":"theorempath:lazy-vs-feature-learning","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:optimizer-theory-sgd-adam-muon--prerequisite-of--theorempath:scaling-laws","from":"theorempath:optimizer-theory-sgd-adam-muon","to":"theorempath:scaling-laws","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:score-matching","from":"theorempath:stochastic-differential-equations","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fokker-planck-equation--prerequisite-of--theorempath:score-matching","from":"theorempath:fokker-planck-equation","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:score-matching","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fisher-information--prerequisite-of--theorempath:score-matching","from":"theorempath:fisher-information","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-generative-models-for-cosmic-structures--prerequisite-of--theorempath:score-matching","from":"theorempath:deep-generative-models-for-cosmic-structures","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:score-matching","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-reversal-of-sdes--prerequisite-of--theorempath:score-matching","from":"theorempath:time-reversal-of-sdes","to":"theorempath:score-matching","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:secant-method","from":"theorempath:newtons-method","to":"theorempath:secant-method","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:second-order-optimization-methods","from":"theorempath:newtons-method","to":"theorempath:second-order-optimization-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:second-order-optimization-methods","from":"theorempath:the-hessian-matrix","to":"theorempath:second-order-optimization-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-gradient-methods--prerequisite-of--theorempath:second-order-optimization-methods","from":"theorempath:conjugate-gradient-methods","to":"theorempath:second-order-optimization-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:equilibrium-and-implicit-models--prerequisite-of--theorempath:second-order-optimization-methods","from":"theorempath:equilibrium-and-implicit-models","to":"theorempath:second-order-optimization-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:riemannian-optimization--prerequisite-of--theorempath:second-order-optimization-methods","from":"theorempath:riemannian-optimization","to":"theorempath:second-order-optimization-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:trust-region-methods--prerequisite-of--theorempath:second-order-optimization-methods","from":"theorempath:trust-region-methods","to":"theorempath:second-order-optimization-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:self-play-and-multi-agent-rl","from":"theorempath:markov-decision-processes","to":"theorempath:self-play-and-multi-agent-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agent-based-modeling-with-ml--prerequisite-of--theorempath:self-play-and-multi-agent-rl","from":"theorempath:agent-based-modeling-with-ml","to":"theorempath:self-play-and-multi-agent-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-regret-learning--prerequisite-of--theorempath:self-play-and-multi-agent-rl","from":"theorempath:no-regret-learning","to":"theorempath:self-play-and-multi-agent-rl","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vision-transformer-lineage--prerequisite-of--theorempath:self-supervised-vision","from":"theorempath:vision-transformer-lineage","to":"theorempath:self-supervised-vision","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-for-protein-structure-alphafold--prerequisite-of--theorempath:self-supervised-vision","from":"theorempath:attention-for-protein-structure-alphafold","to":"theorempath:self-supervised-vision","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cnns-for-signal-feature-extraction--prerequisite-of--theorempath:self-supervised-vision","from":"theorempath:cnns-for-signal-feature-extraction","to":"theorempath:self-supervised-vision","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:word-embeddings--prerequisite-of--theorempath:semantic-search-and-embeddings","from":"theorempath:word-embeddings","to":"theorempath:semantic-search-and-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:inner-product-spaces-and-orthogonality--prerequisite-of--theorempath:semantic-search-and-embeddings","from":"theorempath:inner-product-spaces-and-orthogonality","to":"theorempath:semantic-search-and-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-retrieval--prerequisite-of--theorempath:semantic-search-and-embeddings","from":"theorempath:information-retrieval","to":"theorempath:semantic-search-and-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fuzzy-matching-and-record-linkage--prerequisite-of--theorempath:semantic-search-and-embeddings","from":"theorempath:fuzzy-matching-and-record-linkage","to":"theorempath:semantic-search-and-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:knn--prerequisite-of--theorempath:semantic-search-and-embeddings","from":"theorempath:knn","to":"theorempath:semantic-search-and-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metric-spaces-convergence-completeness--prerequisite-of--theorempath:sequences-and-series-of-functions","from":"theorempath:metric-spaces-convergence-completeness","to":"theorempath:sequences-and-series-of-functions","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:sets-functions-and-relations","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:sets-functions-and-relations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:sgd-as-sde","from":"theorempath:stochastic-differential-equations","to":"theorempath:sgd-as-sde","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:sgd-as-sde","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:sgd-as-sde","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fokker-planck-equation--prerequisite-of--theorempath:sgd-as-sde","from":"theorempath:fokker-planck-equation","to":"theorempath:sgd-as-sde","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:sgd-as-sde","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:sgd-as-sde","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:shrinkage-estimation-james-stein","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:shrinkage-estimation-james-stein","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cramer-rao-bound--prerequisite-of--theorempath:shrinkage-estimation-james-stein","from":"theorempath:cramer-rao-bound","to":"theorempath:shrinkage-estimation-james-stein","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:minimax-lower-bounds--prerequisite-of--theorempath:shrinkage-estimation-james-stein","from":"theorempath:minimax-lower-bounds","to":"theorempath:shrinkage-estimation-james-stein","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:signal-detection-theory","from":"theorempath:common-probability-distributions","to":"theorempath:signal-detection-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:signal-detection-theory","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:signal-detection-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rnns-for-signal-sequences--prerequisite-of--theorempath:signal-detection-theory","from":"theorempath:rnns-for-signal-sequences","to":"theorempath:signal-detection-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-basics--prerequisite-of--theorempath:simpsons-paradox","from":"theorempath:causal-inference-basics","to":"theorempath:simpsons-paradox","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:singular-value-decomposition","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:singular-value-decomposition","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-independence--prerequisite-of--theorempath:singular-value-decomposition","from":"theorempath:linear-independence","to":"theorempath:singular-value-decomposition","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-norms--prerequisite-of--theorempath:singular-value-decomposition","from":"theorempath:matrix-norms","to":"theorempath:singular-value-decomposition","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:singular-value-decomposition","from":"theorempath:matrix-operations-and-properties","to":"theorempath:singular-value-decomposition","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:skewness-kurtosis-and-higher-moments","from":"theorempath:common-probability-distributions","to":"theorempath:skewness-kurtosis-and-higher-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:skewness-kurtosis-and-higher-moments","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:skewness-kurtosis-and-higher-moments","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:skip-connections-and-resnets","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:skip-connections-and-resnets","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:metropolis-hastings--prerequisite-of--theorempath:slice-sampling","from":"theorempath:metropolis-hastings","to":"theorempath:slice-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:sluds-inequality","from":"theorempath:common-probability-distributions","to":"theorempath:sluds-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:sluds-inequality","from":"theorempath:concentration-inequalities","to":"theorempath:sluds-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:small-area-estimation","from":"theorempath:bayesian-estimation","to":"theorempath:small-area-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:small-area-estimation","from":"theorempath:linear-regression","to":"theorempath:small-area-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reml-and-variance-component-estimation--prerequisite-of--theorempath:small-area-estimation","from":"theorempath:reml-and-variance-component-estimation","to":"theorempath:small-area-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:survey-weight-calibration-and-raking--prerequisite-of--theorempath:small-area-estimation","from":"theorempath:survey-weight-calibration-and-raking","to":"theorempath:small-area-estimation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:sparse-attention-and-long-context","from":"theorempath:attention-mechanism-theory","to":"theorempath:sparse-attention-and-long-context","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gemini-and-google-models--prerequisite-of--theorempath:sparse-attention-and-long-context","from":"theorempath:gemini-and-google-models","to":"theorempath:sparse-attention-and-long-context","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders--prerequisite-of--theorempath:sparse-autoencoders","from":"theorempath:autoencoders","to":"theorempath:sparse-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mechanistic-interpretability--prerequisite-of--theorempath:sparse-autoencoders","from":"theorempath:mechanistic-interpretability","to":"theorempath:sparse-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lasso-regression--prerequisite-of--theorempath:sparse-autoencoders","from":"theorempath:lasso-regression","to":"theorempath:sparse-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:residual-stream-and-transformer-internals--prerequisite-of--theorempath:sparse-autoencoders","from":"theorempath:residual-stream-and-transformer-internals","to":"theorempath:sparse-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-coding-and-efficient-coding--prerequisite-of--theorempath:sparse-autoencoders","from":"theorempath:sparse-coding-and-efficient-coding","to":"theorempath:sparse-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:truth-directions-and-linear-probes--prerequisite-of--theorempath:sparse-autoencoders","from":"theorempath:truth-directions-and-linear-probes","to":"theorempath:sparse-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lasso-regression--prerequisite-of--theorempath:sparse-recovery-and-compressed-sensing","from":"theorempath:lasso-regression","to":"theorempath:sparse-recovery-and-compressed-sensing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:sparse-recovery-and-compressed-sensing","from":"theorempath:subgaussian-random-variables","to":"theorempath:sparse-recovery-and-compressed-sensing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-coding-and-efficient-coding--prerequisite-of--theorempath:sparse-recovery-and-compressed-sensing","from":"theorempath:sparse-coding-and-efficient-coding","to":"theorempath:sparse-recovery-and-compressed-sensing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:spectral-clustering","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:spectral-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:k-means-clustering--prerequisite-of--theorempath:spectral-clustering","from":"theorempath:k-means-clustering","to":"theorempath:spectral-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pagerank-algorithm--prerequisite-of--theorempath:spectral-clustering","from":"theorempath:pagerank-algorithm","to":"theorempath:spectral-clustering","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:spectral-theory-of-operators","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:spectral-theory-of-operators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:complex-numbers-for-fourier--prerequisite-of--theorempath:spectral-theory-of-operators","from":"theorempath:complex-numbers-for-fourier","to":"theorempath:spectral-theory-of-operators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:functional-analysis-core--prerequisite-of--theorempath:spectral-theory-of-operators","from":"theorempath:functional-analysis-core","to":"theorempath:spectral-theory-of-operators","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:speculative-decoding-and-quantization","from":"theorempath:transformer-architecture","to":"theorempath:speculative-decoding-and-quantization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kv-cache--prerequisite-of--theorempath:speculative-decoding-and-quantization","from":"theorempath:kv-cache","to":"theorempath:speculative-decoding-and-quantization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:megakernels--prerequisite-of--theorempath:speculative-decoding-and-quantization","from":"theorempath:megakernels","to":"theorempath:speculative-decoding-and-quantization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:multi-token-prediction--prerequisite-of--theorempath:speculative-decoding-and-quantization","from":"theorempath:multi-token-prediction","to":"theorempath:speculative-decoding-and-quantization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signals-and-systems-for-ml--prerequisite-of--theorempath:speech-and-audio-ml","from":"theorempath:signals-and-systems-for-ml","to":"theorempath:speech-and-audio-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:speech-and-audio-ml","from":"theorempath:recurrent-neural-networks","to":"theorempath:speech-and-audio-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cnns-for-signal-feature-extraction--prerequisite-of--theorempath:speech-and-audio-ml","from":"theorempath:cnns-for-signal-feature-extraction","to":"theorempath:speech-and-audio-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:spiking-neural-networks","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:spiking-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:spiking-neural-networks","from":"theorempath:convolutional-neural-networks","to":"theorempath:spiking-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:order-statistics--prerequisite-of--theorempath:split-conformal-prediction","from":"theorempath:order-statistics","to":"theorempath:split-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:split-conformal-prediction","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:split-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cross-validation-theory--prerequisite-of--theorempath:split-conformal-prediction","from":"theorempath:cross-validation-theory","to":"theorempath:split-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tabular-foundation-models-bayesian-inference--prerequisite-of--theorempath:split-conformal-prediction","from":"theorempath:tabular-foundation-models-bayesian-inference","to":"theorempath:split-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rejection-sampling--prerequisite-of--theorempath:squeezed-rejection-sampling","from":"theorempath:rejection-sampling","to":"theorempath:squeezed-rejection-sampling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:stability-and-optimization-dynamics","from":"theorempath:convex-optimization-basics","to":"theorempath:stability-and-optimization-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:invariants-and-monovariants--prerequisite-of--theorempath:stability-and-optimization-dynamics","from":"theorempath:invariants-and-monovariants","to":"theorempath:stability-and-optimization-dynamics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-series-foundations--prerequisite-of--theorempath:state-space-models","from":"theorempath:time-series-foundations","to":"theorempath:state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-chains-and-steady-state--prerequisite-of--theorempath:state-space-models","from":"theorempath:markov-chains-and-steady-state","to":"theorempath:state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kalman-filter--prerequisite-of--theorempath:state-space-models","from":"theorempath:kalman-filter","to":"theorempath:state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:state-space-models","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:state-space-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:simpsons-paradox--prerequisite-of--theorempath:statistical-paradoxes-collection","from":"theorempath:simpsons-paradox","to":"theorempath:statistical-paradoxes-collection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:base-rate-fallacy--prerequisite-of--theorempath:statistical-paradoxes-collection","from":"theorempath:base-rate-fallacy","to":"theorempath:statistical-paradoxes-collection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:anthropic-bias-and-observation-selection--prerequisite-of--theorempath:statistical-paradoxes-collection","from":"theorempath:anthropic-bias-and-observation-selection","to":"theorempath:statistical-paradoxes-collection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:steins-paradox--prerequisite-of--theorempath:statistical-paradoxes-collection","from":"theorempath:steins-paradox","to":"theorempath:statistical-paradoxes-collection","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:statistical-significance-and-multiple-comparisons","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:statistical-significance-and-multiple-comparisons","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:steins-paradox","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:steins-paradox","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:shrinkage-estimation-james-stein--prerequisite-of--theorempath:steins-paradox","from":"theorempath:shrinkage-estimation-james-stein","to":"theorempath:steins-paradox","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:stochastic-approximation-theory","from":"theorempath:convex-optimization-basics","to":"theorempath:stochastic-approximation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:stochastic-approximation-theory","from":"theorempath:martingale-theory","to":"theorempath:stochastic-approximation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adaptive-learning-is-not-iid--prerequisite-of--theorempath:stochastic-approximation-theory","from":"theorempath:adaptive-learning-is-not-iid","to":"theorempath:stochastic-approximation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:borel-cantelli-lemmas--prerequisite-of--theorempath:stochastic-approximation-theory","from":"theorempath:borel-cantelli-lemmas","to":"theorempath:stochastic-approximation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:stochastic-approximation-theory","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:stochastic-approximation-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:martingale-theory--prerequisite-of--theorempath:stochastic-calculus-for-ml","from":"theorempath:martingale-theory","to":"theorempath:stochastic-calculus-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:stochastic-calculus-for-ml","from":"theorempath:measure-theoretic-probability","to":"theorempath:stochastic-calculus-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:classical-odes--prerequisite-of--theorempath:stochastic-calculus-for-ml","from":"theorempath:classical-odes","to":"theorempath:stochastic-calculus-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:brownian-motion--prerequisite-of--theorempath:stochastic-differential-equations","from":"theorempath:brownian-motion","to":"theorempath:stochastic-differential-equations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ito-lemma--prerequisite-of--theorempath:stochastic-differential-equations","from":"theorempath:ito-lemma","to":"theorempath:stochastic-differential-equations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-calculus-for-ml--prerequisite-of--theorempath:stochastic-differential-equations","from":"theorempath:stochastic-calculus-for-ml","to":"theorempath:stochastic-differential-equations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-descent-variants--prerequisite-of--theorempath:stochastic-gradient-descent-convergence","from":"theorempath:gradient-descent-variants","to":"theorempath:stochastic-gradient-descent-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:stochastic-gradient-descent-convergence","from":"theorempath:concentration-inequalities","to":"theorempath:stochastic-gradient-descent-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:coordinate-descent--prerequisite-of--theorempath:stochastic-gradient-descent-convergence","from":"theorempath:coordinate-descent","to":"theorempath:stochastic-gradient-descent-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:invariants-and-monovariants--prerequisite-of--theorempath:stochastic-gradient-descent-convergence","from":"theorempath:invariants-and-monovariants","to":"theorempath:stochastic-gradient-descent-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:online-convex-optimization--prerequisite-of--theorempath:stochastic-gradient-descent-convergence","from":"theorempath:online-convex-optimization","to":"theorempath:stochastic-gradient-descent-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:proximal-gradient-methods--prerequisite-of--theorempath:stochastic-gradient-descent-convergence","from":"theorempath:proximal-gradient-methods","to":"theorempath:stochastic-gradient-descent-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:stochastic-processes-ml","from":"theorempath:measure-theoretic-probability","to":"theorempath:stochastic-processes-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:stochastic-processes-ml","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:stochastic-processes-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:stochastic-processes-ml","from":"theorempath:concentration-inequalities","to":"theorempath:stochastic-processes-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:structured-output-and-constrained-generation","from":"theorempath:transformer-architecture","to":"theorempath:structured-output-and-constrained-generation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:tool-augmented-reasoning--prerequisite-of--theorempath:structured-output-and-constrained-generation","from":"theorempath:tool-augmented-reasoning","to":"theorempath:structured-output-and-constrained-generation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:student-t-distribution-and-t-test","from":"theorempath:distributions-atlas","to":"theorempath:student-t-distribution-and-t-test","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:normal-distribution--prerequisite-of--theorempath:student-t-distribution-and-t-test","from":"theorempath:normal-distribution","to":"theorempath:student-t-distribution-and-t-test","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chi-squared-distribution-and-tests--prerequisite-of--theorempath:student-t-distribution-and-t-test","from":"theorempath:chi-squared-distribution-and-tests","to":"theorempath:student-t-distribution-and-t-test","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:student-t-distribution-and-t-test","from":"theorempath:central-limit-theorem","to":"theorempath:student-t-distribution-and-t-test","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-testing-for-ml--prerequisite-of--theorempath:student-t-distribution-and-t-test","from":"theorempath:hypothesis-testing-for-ml","to":"theorempath:student-t-distribution-and-t-test","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:subgaussian-random-variables--prerequisite-of--theorempath:subexponential-random-variables","from":"theorempath:subgaussian-random-variables","to":"theorempath:subexponential-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:subexponential-random-variables","from":"theorempath:concentration-inequalities","to":"theorempath:subexponential-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bernstein-inequality--prerequisite-of--theorempath:subexponential-random-variables","from":"theorempath:bernstein-inequality","to":"theorempath:subexponential-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chernoff-bounds--prerequisite-of--theorempath:subexponential-random-variables","from":"theorempath:chernoff-bounds","to":"theorempath:subexponential-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bennetts-inequality--prerequisite-of--theorempath:subexponential-random-variables","from":"theorempath:bennetts-inequality","to":"theorempath:subexponential-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chi-squared-concentration--prerequisite-of--theorempath:subexponential-random-variables","from":"theorempath:chi-squared-concentration","to":"theorempath:subexponential-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:subgaussian-random-variables","from":"theorempath:concentration-inequalities","to":"theorempath:subgaussian-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chernoff-bounds--prerequisite-of--theorempath:subgaussian-random-variables","from":"theorempath:chernoff-bounds","to":"theorempath:subgaussian-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:skewness-kurtosis-and-higher-moments--prerequisite-of--theorempath:subgaussian-random-variables","from":"theorempath:skewness-kurtosis-and-higher-moments","to":"theorempath:subgaussian-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hoeffdings-lemma--prerequisite-of--theorempath:subgaussian-random-variables","from":"theorempath:hoeffdings-lemma","to":"theorempath:subgaussian-random-variables","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:subgradients-and-subdifferentials","from":"theorempath:convex-optimization-basics","to":"theorempath:subgradients-and-subdifferentials","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:greedy-algorithms--prerequisite-of--theorempath:submodular-optimization","from":"theorempath:greedy-algorithms","to":"theorempath:submodular-optimization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:sufficient-statistics-and-exponential-families","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:sufficient-statistics-and-exponential-families","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:support-vector-machines","from":"theorempath:convex-optimization-basics","to":"theorempath:support-vector-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:support-vector-machines","from":"theorempath:convex-duality","to":"theorempath:support-vector-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:support-vector-machines","from":"theorempath:logistic-regression","to":"theorempath:support-vector-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:perceptron--prerequisite-of--theorempath:support-vector-machines","from":"theorempath:perceptron","to":"theorempath:support-vector-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:loss-functions--prerequisite-of--theorempath:support-vector-machines","from":"theorempath:loss-functions","to":"theorempath:support-vector-machines","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:survey-sampling-methods","from":"theorempath:common-probability-distributions","to":"theorempath:survey-sampling-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:survey-sampling-methods","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:survey-sampling-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:types-of-bias-in-statistics--prerequisite-of--theorempath:survey-sampling-methods","from":"theorempath:types-of-bias-in-statistics","to":"theorempath:survey-sampling-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:survival-analysis","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:survival-analysis","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:support-vector-machines--prerequisite-of--theorempath:svm-for-rf-classification","from":"theorempath:support-vector-machines","to":"theorempath:svm-for-rf-classification","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signals-and-systems-for-ml--prerequisite-of--theorempath:svm-for-rf-classification","from":"theorempath:signals-and-systems-for-ml","to":"theorempath:svm-for-rf-classification","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lasso-regression--prerequisite-of--theorempath:symbolic-regression-and-equation-discovery","from":"theorempath:lasso-regression","to":"theorempath:symbolic-regression-and-equation-discovery","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sparse-recovery-and-compressed-sensing--prerequisite-of--theorempath:symbolic-regression-and-equation-discovery","from":"theorempath:sparse-recovery-and-compressed-sensing","to":"theorempath:symbolic-regression-and-equation-discovery","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rademacher-complexity--prerequisite-of--theorempath:symmetrization-inequality","from":"theorempath:rademacher-complexity","to":"theorempath:symmetrization-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:symmetrization-inequality","from":"theorempath:concentration-inequalities","to":"theorempath:symmetrization-inequality","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:knowledge-distillation--prerequisite-of--theorempath:synthetic-data-distillation","from":"theorempath:knowledge-distillation","to":"theorempath:synthetic-data-distillation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:synthetic-data-generation--prerequisite-of--theorempath:synthetic-data-distillation","from":"theorempath:synthetic-data-generation","to":"theorempath:synthetic-data-distillation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:synthetic-data-generation","from":"theorempath:common-probability-distributions","to":"theorempath:synthetic-data-generation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:document-intelligence--prerequisite-of--theorempath:table-extraction-and-structure-recognition","from":"theorempath:document-intelligence","to":"theorempath:table-extraction-and-structure-recognition","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:paddleocr-and-practical-ocr--prerequisite-of--theorempath:table-extraction-and-structure-recognition","from":"theorempath:paddleocr-and-practical-ocr","to":"theorempath:table-extraction-and-structure-recognition","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:greedy-algorithms--prerequisite-of--theorempath:tabu-search","from":"theorempath:greedy-algorithms","to":"theorempath:tabu-search","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ascent-algorithms--prerequisite-of--theorempath:tabu-search","from":"theorempath:ascent-algorithms","to":"theorempath:tabu-search","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:tabular-foundation-models-bayesian-inference","from":"theorempath:bayesian-estimation","to":"theorempath:tabular-foundation-models-bayesian-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:tabular-foundation-models-bayesian-inference","from":"theorempath:transformer-architecture","to":"theorempath:tabular-foundation-models-bayesian-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prompt-engineering-and-in-context-learning--prerequisite-of--theorempath:tabular-foundation-models-bayesian-inference","from":"theorempath:prompt-engineering-and-in-context-learning","to":"theorempath:tabular-foundation-models-bayesian-inference","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuity-in-rn--prerequisite-of--theorempath:taylor-expansion","from":"theorempath:continuity-in-rn","to":"theorempath:taylor-expansion","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:taylor-expansion","from":"theorempath:differentiation-in-rn","to":"theorempath:taylor-expansion","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:td-learning","from":"theorempath:markov-decision-processes","to":"theorempath:td-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:value-iteration-and-policy-iteration--prerequisite-of--theorempath:td-learning","from":"theorempath:value-iteration-and-policy-iteration","to":"theorempath:td-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bellman-equations--prerequisite-of--theorempath:td-learning","from":"theorempath:bellman-equations","to":"theorempath:td-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-approximation-theory--prerequisite-of--theorempath:td-learning","from":"theorempath:stochastic-approximation-theory","to":"theorempath:td-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ddpg--prerequisite-of--theorempath:td3","from":"theorempath:ddpg","to":"theorempath:td3","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:q-learning--prerequisite-of--theorempath:td3","from":"theorempath:q-learning","to":"theorempath:td3","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:policy-gradient-theorem--prerequisite-of--theorempath:td3","from":"theorempath:policy-gradient-theorem","to":"theorempath:td3","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:tensors-and-tensor-operations","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:tensors-and-tensor-operations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pandas-and-numpy-fundamentals--prerequisite-of--theorempath:tensors-and-tensor-operations","from":"theorempath:pandas-and-numpy-fundamentals","to":"theorempath:tensors-and-tensor-operations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:scaling-laws--prerequisite-of--theorempath:test-time-compute-and-search","from":"theorempath:scaling-laws","to":"theorempath:test-time-compute-and-search","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agentic-rl-and-tool-use--prerequisite-of--theorempath:test-time-compute-and-search","from":"theorempath:agentic-rl-and-tool-use","to":"theorempath:test-time-compute-and-search","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-gradient-descent-convergence--prerequisite-of--theorempath:test-time-training","from":"theorempath:stochastic-gradient-descent-convergence","to":"theorempath:test-time-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:test-time-training","from":"theorempath:recurrent-neural-networks","to":"theorempath:test-time-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:continuous-thought-machines--prerequisite-of--theorempath:test-time-training","from":"theorempath:continuous-thought-machines","to":"theorempath:test-time-training","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:matrix-operations-and-properties--prerequisite-of--theorempath:the-hessian-matrix","from":"theorempath:matrix-operations-and-properties","to":"theorempath:the-hessian-matrix","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:the-hessian-matrix","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:the-hessian-matrix","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:the-hessian-matrix","from":"theorempath:differentiation-in-rn","to":"theorempath:the-hessian-matrix","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:the-hessian-matrix","from":"theorempath:the-jacobian-matrix","to":"theorempath:the-hessian-matrix","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vector-calculus-chain-rule--prerequisite-of--theorempath:the-hessian-matrix","from":"theorempath:vector-calculus-chain-rule","to":"theorempath:the-hessian-matrix","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:the-jacobian-matrix","from":"theorempath:differentiation-in-rn","to":"theorempath:the-jacobian-matrix","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-differential-equations--prerequisite-of--theorempath:time-reversal-of-sdes","from":"theorempath:stochastic-differential-equations","to":"theorempath:time-reversal-of-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:fokker-planck-equation--prerequisite-of--theorempath:time-reversal-of-sdes","from":"theorempath:fokker-planck-equation","to":"theorempath:time-reversal-of-sdes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-regression--prerequisite-of--theorempath:time-series-forecasting-basics","from":"theorempath:linear-regression","to":"theorempath:time-series-forecasting-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:time-series-foundations--prerequisite-of--theorempath:time-series-forecasting-basics","from":"theorempath:time-series-foundations","to":"theorempath:time-series-forecasting-basics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kolmogorov-probability-axioms--prerequisite-of--theorempath:time-series-foundations","from":"theorempath:kolmogorov-probability-axioms","to":"theorempath:time-series-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:time-series-foundations","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:time-series-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stochastic-processes-ml--prerequisite-of--theorempath:time-series-foundations","from":"theorempath:stochastic-processes-ml","to":"theorempath:time-series-foundations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:token-prediction-and-language-modeling","from":"theorempath:information-theory-foundations","to":"theorempath:token-prediction-and-language-modeling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:token-prediction-and-language-modeling","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:token-prediction-and-language-modeling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:token-prediction-and-language-modeling","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:token-prediction-and-language-modeling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:token-prediction-and-language-modeling","from":"theorempath:common-probability-distributions","to":"theorempath:token-prediction-and-language-modeling","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:tokenization-and-information-theory","from":"theorempath:information-theory-foundations","to":"theorempath:tokenization-and-information-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:tokenization-and-information-theory","from":"theorempath:common-probability-distributions","to":"theorempath:tokenization-and-information-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:morphology-and-subword-modeling--prerequisite-of--theorempath:tokenization-and-information-theory","from":"theorempath:morphology-and-subword-modeling","to":"theorempath:tokenization-and-information-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:tool-augmented-reasoning","from":"theorempath:transformer-architecture","to":"theorempath:tool-augmented-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:chain-of-thought-and-reasoning--prerequisite-of--theorempath:tool-augmented-reasoning","from":"theorempath:chain-of-thought-and-reasoning","to":"theorempath:tool-augmented-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:prompt-engineering-and-in-context-learning--prerequisite-of--theorempath:tool-augmented-reasoning","from":"theorempath:prompt-engineering-and-in-context-learning","to":"theorempath:tool-augmented-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:agentic-rl-and-tool-use--prerequisite-of--theorempath:tool-augmented-reasoning","from":"theorempath:agentic-rl-and-tool-use","to":"theorempath:tool-augmented-reasoning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:total-variation-distance","from":"theorempath:common-probability-distributions","to":"theorempath:total-variation-distance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:total-variation-distance","from":"theorempath:measure-theoretic-probability","to":"theorempath:total-variation-distance","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:ml-project-lifecycle--prerequisite-of--theorempath:train-test-split-and-data-leakage","from":"theorempath:ml-project-lifecycle","to":"theorempath:train-test-split-and-data-leakage","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-optimization-basics--prerequisite-of--theorempath:training-dynamics-and-loss-landscapes","from":"theorempath:convex-optimization-basics","to":"theorempath:training-dynamics-and-loss-landscapes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:training-dynamics-and-loss-landscapes","from":"theorempath:the-hessian-matrix","to":"theorempath:training-dynamics-and-loss-landscapes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:stability-and-optimization-dynamics--prerequisite-of--theorempath:training-dynamics-and-loss-landscapes","from":"theorempath:stability-and-optimization-dynamics","to":"theorempath:training-dynamics-and-loss-landscapes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:transfer-learning","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:transfer-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:representation-learning-in-cosmology--prerequisite-of--theorempath:transfer-learning","from":"theorempath:representation-learning-in-cosmology","to":"theorempath:transfer-learning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanism-theory--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:attention-mechanism-theory","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:softmax-and-numerical-stability--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:softmax-and-numerical-stability","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adam-optimizer--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:adam-optimizer","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:attention-mechanisms-history--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:attention-mechanisms-history","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:byte-level-language-models--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:byte-level-language-models","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:convolutional-neural-networks","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:deep-learning-goodfellow-book--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:deep-learning-goodfellow-book","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributional-semantics--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:distributional-semantics","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:linear-layer-shapes-memory--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:linear-layer-shapes-memory","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:macroeconomic-time-series-forecasting--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:macroeconomic-time-series-forecasting","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:recurrent-neural-networks--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:recurrent-neural-networks","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:rnns-for-signal-sequences--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:rnns-for-signal-sequences","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:syntax-and-parsing--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:syntax-and-parsing","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:token-prediction-and-language-modeling--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:token-prediction-and-language-modeling","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:word-embeddings--prerequisite-of--theorempath:transformer-architecture","from":"theorempath:word-embeddings","to":"theorempath:transformer-architecture","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:triangular-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:triangular-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:random-variables--prerequisite-of--theorempath:triangular-distribution","from":"theorempath:random-variables","to":"theorempath:triangular-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:newtons-method--prerequisite-of--theorempath:trust-region-methods","from":"theorempath:newtons-method","to":"theorempath:trust-region-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-hessian-matrix--prerequisite-of--theorempath:trust-region-methods","from":"theorempath:the-hessian-matrix","to":"theorempath:trust-region-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:line-search-methods--prerequisite-of--theorempath:trust-region-methods","from":"theorempath:line-search-methods","to":"theorempath:trust-region-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:augmented-lagrangian-and-admm--prerequisite-of--theorempath:trust-region-methods","from":"theorempath:augmented-lagrangian-and-admm","to":"theorempath:trust-region-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:conjugate-gradient-methods--prerequisite-of--theorempath:trust-region-methods","from":"theorempath:conjugate-gradient-methods","to":"theorempath:trust-region-methods","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:mechanistic-interpretability--prerequisite-of--theorempath:truth-directions-and-linear-probes","from":"theorempath:mechanistic-interpretability","to":"theorempath:truth-directions-and-linear-probes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:residual-stream-and-transformer-internals--prerequisite-of--theorempath:truth-directions-and-linear-probes","from":"theorempath:residual-stream-and-transformer-internals","to":"theorempath:truth-directions-and-linear-probes","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:principal-component-analysis--prerequisite-of--theorempath:tsne-and-umap","from":"theorempath:principal-component-analysis","to":"theorempath:tsne-and-umap","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:self-organizing-maps--prerequisite-of--theorempath:tsne-and-umap","from":"theorempath:self-organizing-maps","to":"theorempath:tsne-and-umap","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:tweedie-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:tweedie-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sufficient-statistics-and-exponential-families--prerequisite-of--theorempath:tweedie-distribution","from":"theorempath:sufficient-statistics-and-exponential-families","to":"theorempath:tweedie-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:tweedie-distribution","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:tweedie-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:lambda-calculus--prerequisite-of--theorempath:type-theory","from":"theorempath:lambda-calculus","to":"theorempath:type-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:type-theory","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:type-theory","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:anthropic-bias-and-observation-selection--prerequisite-of--theorempath:types-of-bias-in-statistics","from":"theorempath:anthropic-bias-and-observation-selection","to":"theorempath:types-of-bias-in-statistics","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:empirical-risk-minimization","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:adaptive-learning-is-not-iid--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:adaptive-learning-is-not-iid","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bernstein-inequality--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:bernstein-inequality","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:realizability-assumption--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:realizability-assumption","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sequences-and-series-of-functions--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:sequences-and-series-of-functions","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:uniform-convergence","from":"theorempath:sets-functions-and-relations","to":"theorempath:uniform-convergence","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:universal-approximation-theorem","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:universal-approximation-theorem","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:p-vs-np--prerequisite-of--theorempath:unsolved-problems-in-computer-science","from":"theorempath:p-vs-np","to":"theorempath:unsolved-problems-in-computer-science","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:open-problems-in-matrix-computation--prerequisite-of--theorempath:unsolved-problems-in-computer-science","from":"theorempath:open-problems-in-matrix-computation","to":"theorempath:unsolved-problems-in-computer-science","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:value-iteration-and-policy-iteration","from":"theorempath:markov-decision-processes","to":"theorempath:value-iteration-and-policy-iteration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bellman-equations--prerequisite-of--theorempath:value-iteration-and-policy-iteration","from":"theorempath:bellman-equations","to":"theorempath:value-iteration-and-policy-iteration","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:importance-sampling--prerequisite-of--theorempath:variance-reduction-techniques","from":"theorempath:importance-sampling","to":"theorempath:variance-reduction-techniques","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:delta-method--prerequisite-of--theorempath:variance-stabilizing-transformations","from":"theorempath:delta-method","to":"theorempath:variance-stabilizing-transformations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:central-limit-theorem--prerequisite-of--theorempath:variance-stabilizing-transformations","from":"theorempath:central-limit-theorem","to":"theorempath:variance-stabilizing-transformations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:variance-stabilizing-transformations","from":"theorempath:common-probability-distributions","to":"theorempath:variance-stabilizing-transformations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:expectation-variance-covariance-moments--prerequisite-of--theorempath:variance-stabilizing-transformations","from":"theorempath:expectation-variance-covariance-moments","to":"theorempath:variance-stabilizing-transformations","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:autoencoders","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:autoencoders-for-low-dimensional-dynamical-structures--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:autoencoders-for-low-dimensional-dynamical-structures","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bayesian-estimation--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:bayesian-estimation","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gaussian-mixture-models-and-em--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:gaussian-mixture-models-and-em","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-theory-foundations--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:information-theory-foundations","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:kl-divergence--prerequisite-of--theorempath:variational-autoencoders","from":"theorempath:kl-divergence","to":"theorempath:variational-autoencoders","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:empirical-risk-minimization--prerequisite-of--theorempath:vc-dimension","from":"theorempath:empirical-risk-minimization","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:concentration-inequalities--prerequisite-of--theorempath:vc-dimension","from":"theorempath:concentration-inequalities","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:counting-and-combinatorics--prerequisite-of--theorempath:vc-dimension","from":"theorempath:counting-and-combinatorics","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:hypothesis-classes-and-function-spaces--prerequisite-of--theorempath:vc-dimension","from":"theorempath:hypothesis-classes-and-function-spaces","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:pac-learning-framework--prerequisite-of--theorempath:vc-dimension","from":"theorempath:pac-learning-framework","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:understanding-machine-learning-book--prerequisite-of--theorempath:vc-dimension","from":"theorempath:understanding-machine-learning-book","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:uniform-convergence--prerequisite-of--theorempath:vc-dimension","from":"theorempath:uniform-convergence","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:basic-logic-and-proof-techniques--prerequisite-of--theorempath:vc-dimension","from":"theorempath:basic-logic-and-proof-techniques","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:vc-dimension","from":"theorempath:sets-functions-and-relations","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:bias-complexity-tradeoff--prerequisite-of--theorempath:vc-dimension","from":"theorempath:bias-complexity-tradeoff","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:no-free-lunch-theorem--prerequisite-of--theorempath:vc-dimension","from":"theorempath:no-free-lunch-theorem","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sluds-inequality--prerequisite-of--theorempath:vc-dimension","from":"theorempath:sluds-inequality","to":"theorempath:vc-dimension","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:the-jacobian-matrix--prerequisite-of--theorempath:vector-calculus-chain-rule","from":"theorempath:the-jacobian-matrix","to":"theorempath:vector-calculus-chain-rule","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:vectors-matrices-and-linear-maps--prerequisite-of--theorempath:vector-calculus-chain-rule","from":"theorempath:vectors-matrices-and-linear-maps","to":"theorempath:vector-calculus-chain-rule","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:differentiation-in-rn--prerequisite-of--theorempath:vector-calculus-chain-rule","from":"theorempath:differentiation-in-rn","to":"theorempath:vector-calculus-chain-rule","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:sets-functions-and-relations--prerequisite-of--theorempath:vectors-matrices-and-linear-maps","from":"theorempath:sets-functions-and-relations","to":"theorempath:vectors-matrices-and-linear-maps","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:reward-models-and-verifiers--prerequisite-of--theorempath:verifier-design-and-process-reward","from":"theorempath:reward-models-and-verifiers","to":"theorempath:verifier-design-and-process-reward","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:world-models-and-planning--prerequisite-of--theorempath:video-world-models","from":"theorempath:world-models-and-planning","to":"theorempath:video-world-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:diffusion-models--prerequisite-of--theorempath:video-world-models","from":"theorempath:diffusion-models","to":"theorempath:video-world-models","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:transformer-architecture--prerequisite-of--theorempath:vision-transformer-lineage","from":"theorempath:transformer-architecture","to":"theorempath:vision-transformer-lineage","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convolutional-neural-networks--prerequisite-of--theorempath:vision-transformer-lineage","from":"theorempath:convolutional-neural-networks","to":"theorempath:vision-transformer-lineage","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:cnns-for-medical-imaging--prerequisite-of--theorempath:vision-transformer-lineage","from":"theorempath:cnns-for-medical-imaging","to":"theorempath:vision-transformer-lineage","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:graphslam-and-factor-graphs--prerequisite-of--theorempath:visual-semantic-slam","from":"theorempath:graphslam-and-factor-graphs","to":"theorempath:visual-semantic-slam","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:wasserstein-distances","from":"theorempath:common-probability-distributions","to":"theorempath:wasserstein-distances","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:measure-theoretic-probability--prerequisite-of--theorempath:wasserstein-distances","from":"theorempath:measure-theoretic-probability","to":"theorempath:wasserstein-distances","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:convex-duality--prerequisite-of--theorempath:wasserstein-distances","from":"theorempath:convex-duality","to":"theorempath:wasserstein-distances","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distance-metrics-compared--prerequisite-of--theorempath:wasserstein-distances","from":"theorempath:distance-metrics-compared","to":"theorempath:wasserstein-distances","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:total-variation-distance--prerequisite-of--theorempath:wasserstein-distances","from":"theorempath:total-variation-distance","to":"theorempath:wasserstein-distances","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:complex-numbers-for-fourier--prerequisite-of--theorempath:wave-based-neural-networks","from":"theorempath:complex-numbers-for-fourier","to":"theorempath:wave-based-neural-networks","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:signals-and-systems-for-ml--prerequisite-of--theorempath:wavelet-smoothing","from":"theorempath:signals-and-systems-for-ml","to":"theorempath:wavelet-smoothing","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:computer-architecture-for-ml--prerequisite-of--theorempath:webgpu-for-ml","from":"theorempath:computer-architecture-for-ml","to":"theorempath:webgpu-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:automatic-differentiation--prerequisite-of--theorempath:webgpu-for-ml","from":"theorempath:automatic-differentiation","to":"theorempath:webgpu-for-ml","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:weibull-distribution","from":"theorempath:common-probability-distributions","to":"theorempath:weibull-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:exponential-distribution--prerequisite-of--theorempath:weibull-distribution","from":"theorempath:exponential-distribution","to":"theorempath:weibull-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gamma-distribution--prerequisite-of--theorempath:weibull-distribution","from":"theorempath:gamma-distribution","to":"theorempath:weibull-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:distributions-atlas--prerequisite-of--theorempath:weibull-distribution","from":"theorempath:distributions-atlas","to":"theorempath:weibull-distribution","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:feedforward-networks-and-backpropagation--prerequisite-of--theorempath:weight-initialization","from":"theorempath:feedforward-networks-and-backpropagation","to":"theorempath:weight-initialization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:weight-initialization","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:weight-initialization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:activation-functions--prerequisite-of--theorempath:weight-initialization","from":"theorempath:activation-functions","to":"theorempath:weight-initialization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:split-conformal-prediction--prerequisite-of--theorempath:weighted-conformal-prediction","from":"theorempath:split-conformal-prediction","to":"theorempath:weighted-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:radon-nikodym-and-conditional-expectation--prerequisite-of--theorempath:weighted-conformal-prediction","from":"theorempath:radon-nikodym-and-conditional-expectation","to":"theorempath:weighted-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:importance-sampling--prerequisite-of--theorempath:weighted-conformal-prediction","from":"theorempath:importance-sampling","to":"theorempath:weighted-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:causal-inference-basics--prerequisite-of--theorempath:weighted-conformal-prediction","from":"theorempath:causal-inference-basics","to":"theorempath:weighted-conformal-prediction","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:eigenvalues-and-eigenvectors--prerequisite-of--theorempath:whitening-and-decorrelation","from":"theorempath:eigenvalues-and-eigenvectors","to":"theorempath:whitening-and-decorrelation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:principal-component-analysis--prerequisite-of--theorempath:whitening-and-decorrelation","from":"theorempath:principal-component-analysis","to":"theorempath:whitening-and-decorrelation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:floating-point-arithmetic--prerequisite-of--theorempath:whitening-and-decorrelation","from":"theorempath:floating-point-arithmetic","to":"theorempath:whitening-and-decorrelation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:order-statistics--prerequisite-of--theorempath:winsorization","from":"theorempath:order-statistics","to":"theorempath:winsorization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:common-probability-distributions--prerequisite-of--theorempath:winsorization","from":"theorempath:common-probability-distributions","to":"theorempath:winsorization","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:logistic-regression--prerequisite-of--theorempath:word-embeddings","from":"theorempath:logistic-regression","to":"theorempath:word-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:singular-value-decomposition--prerequisite-of--theorempath:word-embeddings","from":"theorempath:singular-value-decomposition","to":"theorempath:word-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:maximum-likelihood-estimation--prerequisite-of--theorempath:word-embeddings","from":"theorempath:maximum-likelihood-estimation","to":"theorempath:word-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:information-retrieval--prerequisite-of--theorempath:word-embeddings","from":"theorempath:information-retrieval","to":"theorempath:word-embeddings","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:world-models-and-planning--prerequisite-of--theorempath:world-model-evaluation","from":"theorempath:world-models-and-planning","to":"theorempath:world-model-evaluation","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:markov-decision-processes--prerequisite-of--theorempath:world-models-and-planning","from":"theorempath:markov-decision-processes","to":"theorempath:world-models-and-planning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:era-of-experience--prerequisite-of--theorempath:world-models-and-planning","from":"theorempath:era-of-experience","to":"theorempath:world-models-and-planning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:history-of-ai--prerequisite-of--theorempath:world-models-and-planning","from":"theorempath:history-of-ai","to":"theorempath:world-models-and-planning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:model-based-rl--prerequisite-of--theorempath:world-models-and-planning","from":"theorempath:model-based-rl","to":"theorempath:world-models-and-planning","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:gradient-boosting--prerequisite-of--theorempath:xgboost","from":"theorempath:gradient-boosting","to":"theorempath:xgboost","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:public-key-cryptography--prerequisite-of--theorempath:zero-knowledge-proofs","from":"theorempath:public-key-cryptography","to":"theorempath:zero-knowledge-proofs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true},{"id":"theorempath:p-vs-np--prerequisite-of--theorempath:zero-knowledge-proofs","from":"theorempath:p-vs-np","to":"theorempath:zero-knowledge-proofs","relation":"prerequisite","source":"topic-frontmatter","visibleEligible":true}]},"familyOverlay":{"sites":[{"id":"theorempath","name":"TheoremPath","canonicalHost":"theorempath.com","origin":"https://theorempath.com","tier":0,"ring":"canonical-spine","status":"live-monolith","canonicalFocus":"Formal definitions, theorem statements, proof obligations, assumptions, and mathematical generalizations.","linkGuidance":"Link out only when the application genuinely clarifies the formal object.","visibleLinkBudget":{"min":8,"max":14}},{"id":"dsapath","name":"DSAPath","canonicalHost":"dsapath.com","origin":"https://dsapath.com","tier":1,"ring":"technical-professional","status":"live-monolith","canonicalFocus":"Implementation-first data structures, algorithms, complexity, and common coding failure modes.","linkGuidance":"Link to TheoremPath for proof foundations and to IOIPath/SystemDesignPath/CUDAPath for genuine applications.","visibleLinkBudget":{"min":6,"max":12}},{"id":"probabilitypath","name":"ProbabilityPath","canonicalHost":"probabilitypath.com","origin":"https://probabilitypath.com","tier":1,"ring":"technical-professional","status":"planned","canonicalFocus":"Random variables, distributions, stochastic processes, expectation intuition, and applied probability models.","linkGuidance":"Bridge TheoremPath formalism to StatisticsPath, ActuaryPath, SystemDesignPath, and PhilosophyPath only where probability changes decisions.","visibleLinkBudget":{"min":6,"max":12}},{"id":"statisticspath","name":"StatisticsPath","canonicalHost":"statisticspath.com","origin":"https://statisticspath.com","tier":1,"ring":"technical-professional","status":"planned","canonicalFocus":"Inference, estimation, uncertainty quantification, regression, diagnostics, and model checking.","linkGuidance":"Link to TheoremPath for assumptions and proofs, ProbabilityPath for random structure, and ActuaryPath for professional use.","visibleLinkBudget":{"min":6,"max":12}},{"id":"calculuspath","name":"CalculusPath","canonicalHost":"calculuspath.com","origin":"https://calculuspath.com","tier":1,"ring":"technical-professional","status":"planned","canonicalFocus":"Learner-facing limits, derivatives, integrals, series, approximations, and computational calculus.","linkGuidance":"Keep pages computational and applied; link to TheoremPath when a rigorous analysis theorem is doing the work.","visibleLinkBudget":{"min":6,"max":12}},{"id":"actuarypath","name":"ActuaryPath","canonicalHost":"actuarypath.com","origin":"https://actuarypath.com","tier":1,"ring":"technical-professional","status":"external-project","canonicalFocus":"Actuarial exams, risk, life contingencies, loss models, credibility, reserving, pricing, and professional judgment.","linkGuidance":"Use ProbabilityPath, StatisticsPath, CalculusPath, and TheoremPath as foundations; avoid thin exam-note clones.","visibleLinkBudget":{"min":6,"max":10}},{"id":"systemdesignpath","name":"SystemDesignPath","canonicalHost":"systemdesignpath.com","origin":"https://systemdesignpath.com","tier":1,"ring":"technical-professional","status":"planned","canonicalFocus":"Production architecture, constraints, trade-offs, reliability, observability, security, cost, and operations.","linkGuidance":"Link to math only where it improves a design decision; do not write interview-template fluff.","visibleLinkBudget":{"min":5,"max":9}},{"id":"cudapath","name":"CUDAPath","canonicalHost":"cudapath.com","origin":"https://cudapath.com","tier":1,"ring":"technical-professional","status":"planned","canonicalFocus":"Profiler-driven CUDA and GPU programming from C++/systems foundations to high-performance kernels.","linkGuidance":"Tie performance claims to official docs or measured benchmarks; never claim an optimization is universally faster.","visibleLinkBudget":{"min":6,"max":10}},{"id":"ioipath","name":"IOIPath","canonicalHost":"ioipath.com","origin":"https://ioipath.com","tier":1,"ring":"contest-excellence","status":"planned","canonicalFocus":"IOI-style algorithmic modeling, constraints, correctness proofs, C++ implementation, subtasks, testing, and contest execution.","linkGuidance":"Depend on DSAPath for implementation primitives and TheoremPath for proof structure; keep broader CP topics labeled as out-of-scope when needed.","visibleLinkBudget":{"min":6,"max":10}},{"id":"putnampath","name":"PutnamPath","canonicalHost":"putnampath.com","origin":"https://putnampath.com","tier":1,"ring":"contest-excellence","status":"planned","canonicalFocus":"Undergraduate proof-contest synthesis across analysis, algebra, combinatorics, number theory, linear algebra, and probability.","linkGuidance":"Link to TheoremPath for theorem depth and IMOPath for elementary proof moves; avoid copying official problem statements.","visibleLinkBudget":{"min":6,"max":10}},{"id":"imopath","name":"IMOPath","canonicalHost":"imopath.com","origin":"https://imopath.com","tier":1,"ring":"contest-excellence","status":"planned","canonicalFocus":"Proof-first olympiad technique graph from fundamentals to shortlist-level synthesis.","linkGuidance":"Teach recognition, false starts, clean proof writing, and original exposition; avoid trick lists.","visibleLinkBudget":{"min":6,"max":10}},{"id":"philosophypath","name":"PhilosophyPath","canonicalHost":"philosophypath.com","origin":"https://philosophypath.com","tier":2,"ring":"conceptual-bridge","status":"live-monolith","canonicalFocus":"Logic, epistemology, decision theory, philosophy of language, ethics, and philosophy of science/math.","linkGuidance":"Use serious bridges through logic, probability interpretation, causality, semantics, and argumentation.","visibleLinkBudget":{"min":5,"max":9}},{"id":"linguisticspath","name":"LinguisticsPath","canonicalHost":"linguisticspath.com","origin":"https://linguisticspath.com","tier":2,"ring":"conceptual-bridge","status":"live-monolith","canonicalFocus":"Syntax, semantics, phonology, pragmatics, formal grammars, and NLP-adjacent language theory.","linkGuidance":"Bridge to technical pages through formal language, parsing, semantics, probability, and information theory.","visibleLinkBudget":{"min":5,"max":9}},{"id":"classicspath","name":"ClassicsPath","canonicalHost":"classicspath.com","origin":"https://classicspath.com","tier":3,"ring":"humanities-edge","status":"live-monolith","canonicalFocus":"Ancient texts, ancient languages, rhetoric, ancient philosophy/science, and Greco-Roman intellectual history.","linkGuidance":"Connect lightly through Euclid, Aristotle, rhetoric, philology, and history of science; do not force technical links.","visibleLinkBudget":{"min":3,"max":7}},{"id":"literaturepath","name":"LiteraturePath","canonicalHost":"literaturepath.com","origin":"https://literaturepath.com","tier":3,"ring":"humanities-edge","status":"live-monolith","canonicalFocus":"Literary works, narrative, genres, rhetoric, interpretation, criticism, and cultural literacy.","linkGuidance":"Connect through rhetoric, semantics, pragmatics, interpretation, and philosophy of language; keep technical links rare.","visibleLinkBudget":{"min":3,"max":7}},{"id":"computationpath","name":"ComputationPath","canonicalHost":"computationpath.com","origin":"https://computationpath.com","tier":2,"ring":"technical-professional","status":"live-monolith","canonicalFocus":"Computing foundations, machines, logic, systems primitives, and CS theory outside the main ML curriculum.","linkGuidance":"Use as the CS-foundations bridge where DSAPath would be too implementation-heavy.","visibleLinkBudget":{"min":5,"max":9}},{"id":"pedagogypath","name":"PedagogyPath","canonicalHost":"pedagogypath.com","origin":"https://pedagogypath.com","tier":2,"ring":"internal-support","status":"live-monolith","canonicalFocus":"Adaptive learning, psychometrics, tutoring systems, FSRS, IRT, BKT, and curriculum engineering.","linkGuidance":"Use for learning-system design and diagnostics, not as generic education commentary.","visibleLinkBudget":{"min":4,"max":8}},{"id":"proofspath","name":"ProofsPath","canonicalHost":"proofspath.com","origin":"https://proofspath.com","tier":2,"ring":"contest-excellence","status":"legacy-bridge","canonicalFocus":"Current proof-technique bridge for induction, inequalities, and olympiad-style moves until IMOPath becomes the dedicated domain.","linkGuidance":"Keep useful pages, but assign future olympiad contest ownership to IMOPath and formal proof ownership to TheoremPath.","visibleLinkBudget":{"min":4,"max":8}}],"concepts":[{"id":"proof.induction","name":"Induction","canonicalSite":"theorempath","canonicalSlug":"basic-logic-and-proof-techniques","canonicalUrl":"https://theorempath.com/topics/basic-logic-and-proof-techniques","domains":["theorempath","dsapath","ioipath","imopath","putnampath"],"conceptType":"proof-technique","importance":5,"theoremPathCentrality":5},{"id":"proof.invariants","name":"Invariants","canonicalSite":"theorempath","canonicalSlug":"basic-logic-and-proof-techniques","canonicalUrl":"https://theorempath.com/topics/basic-logic-and-proof-techniques","domains":["theorempath","dsapath","ioipath","imopath","putnampath"],"conceptType":"proof-technique","importance":5,"theoremPathCentrality":4},{"id":"probability.bayes_theorem","name":"Bayes' theorem","canonicalSite":"theorempath","canonicalSlug":"bayes-theorem","canonicalUrl":"https://theorempath.com/topics/bayes-theorem","domains":["theorempath","probabilitypath","statisticspath","actuarypath","philosophypath","linguisticspath"],"conceptType":"theorem","importance":5,"theoremPathCentrality":5},{"id":"probability.conditional_expectation","name":"Conditional expectation","canonicalSite":"theorempath","canonicalSlug":"conditional-expectation","canonicalUrl":"https://theorempath.com/topics/conditional-expectation","domains":["theorempath","probabilitypath","statisticspath","actuarypath"],"conceptType":"definition","importance":5,"theoremPathCentrality":5},{"id":"stochastic.markov_chains","name":"Markov chains","canonicalSite":"theorempath","canonicalSlug":"markov-chains","canonicalUrl":"https://theorempath.com/topics/markov-chains","domains":["theorempath","probabilitypath","statisticspath","actuarypath","systemdesignpath","linguisticspath"],"conceptType":"model","importance":5,"theoremPathCentrality":5},{"id":"information.entropy","name":"Entropy","canonicalSite":"theorempath","canonicalSlug":"entropy-cross-entropy-and-kl-divergence","canonicalUrl":"https://theorempath.com/topics/entropy-cross-entropy-and-kl-divergence","domains":["theorempath","probabilitypath","statisticspath","linguisticspath","systemdesignpath"],"conceptType":"definition","importance":5,"theoremPathCentrality":5},{"id":"calculus.taylor_expansion","name":"Taylor expansion","canonicalSite":"theorempath","canonicalSlug":"calculus-foundations","canonicalUrl":"https://theorempath.com/topics/calculus-foundations","domains":["theorempath","calculuspath","putnampath","cudapath"],"conceptType":"theorem","importance":5,"theoremPathCentrality":5},{"id":"analysis.compactness","name":"Compactness","canonicalSite":"theorempath","canonicalSlug":"compactness-and-heine-borel","canonicalUrl":"https://theorempath.com/topics/compactness-and-heine-borel","domains":["theorempath","putnampath","philosophypath"],"conceptType":"theorem","importance":4,"theoremPathCentrality":5},{"id":"linear_algebra.eigenvalues","name":"Eigenvalues","canonicalSite":"theorempath","canonicalSlug":"spectral-theory-foundations","canonicalUrl":"https://theorempath.com/topics/spectral-theory-foundations","domains":["theorempath","putnampath","statisticspath","cudapath"],"conceptType":"definition","importance":5,"theoremPathCentrality":5},{"id":"graph.shortest_paths.dijkstra","name":"Dijkstra's algorithm","canonicalSite":"dsapath","canonicalSlug":"dijkstra","canonicalUrl":"https://dsapath.com/topics/dijkstra","domains":["dsapath","ioipath","theorempath"],"conceptType":"algorithm","importance":5,"theoremPathCentrality":2},{"id":"data_structure.segment_tree","name":"Segment tree","canonicalSite":"dsapath","canonicalSlug":"segment-tree","canonicalUrl":"https://dsapath.com/topics/segment-tree","domains":["dsapath","ioipath"],"conceptType":"data-structure","importance":4,"theoremPathCentrality":1},{"id":"parallel.prefix_scan","name":"Prefix scan","canonicalSite":"dsapath","canonicalSlug":"prefix-sums","canonicalUrl":"https://dsapath.com/topics/prefix-sums","domains":["dsapath","ioipath","cudapath","theorempath"],"conceptType":"algorithm","importance":5,"theoremPathCentrality":3},{"id":"systems.littles_law","name":"Little's Law","canonicalSite":"systemdesignpath","canonicalSlug":"littles-law","canonicalUrl":"https://systemdesignpath.com/topics/littles-law","domains":["systemdesignpath","probabilitypath","theorempath"],"conceptType":"theorem","importance":5,"theoremPathCentrality":3},{"id":"systems.idempotency","name":"Idempotency","canonicalSite":"systemdesignpath","canonicalSlug":"idempotency","canonicalUrl":"https://systemdesignpath.com/topics/idempotency","domains":["systemdesignpath","dsapath","theorempath"],"conceptType":"design-pattern","importance":5,"theoremPathCentrality":2},{"id":"gpu.memory_coalescing","name":"CUDA memory coalescing","canonicalSite":"cudapath","canonicalSlug":"memory-coalescing","canonicalUrl":"https://cudapath.com/topics/memory-coalescing","domains":["cudapath","dsapath","theorempath"],"conceptType":"method","importance":5,"theoremPathCentrality":1},{"id":"olympiad.extremal_principle","name":"Extremal principle","canonicalSite":"imopath","canonicalSlug":"extremal-principle","canonicalUrl":"https://imopath.com/topics/extremal-principle","domains":["imopath","putnampath","theorempath"],"conceptType":"proof-technique","importance":5,"theoremPathCentrality":3},{"id":"olympiad.double_counting","name":"Double counting","canonicalSite":"imopath","canonicalSlug":"double-counting","canonicalUrl":"https://imopath.com/topics/double-counting","domains":["imopath","putnampath","theorempath"],"conceptType":"proof-technique","importance":5,"theoremPathCentrality":3},{"id":"language.context_free_grammar","name":"Context-free grammar","canonicalSite":"linguisticspath","canonicalSlug":"context-free-grammars","canonicalUrl":"https://linguisticspath.com/topics/context-free-grammars","domains":["linguisticspath","theorempath","dsapath","computationpath"],"conceptType":"linguistic-concept","importance":4,"theoremPathCentrality":3},{"id":"philosophy.bayesian_epistemology","name":"Bayesian epistemology","canonicalSite":"philosophypath","canonicalSlug":"bayesian-epistemology","canonicalUrl":"https://philosophypath.com/topics/bayesian-epistemology","domains":["philosophypath","probabilitypath","statisticspath"],"conceptType":"philosophical-concept","importance":4,"theoremPathCentrality":2},{"id":"classics.euclid_elements","name":"Euclid's Elements","canonicalSite":"classicspath","canonicalSlug":"euclids-elements","canonicalUrl":"https://classicspath.com/topics/euclids-elements","domains":["classicspath","theorempath","philosophypath"],"conceptType":"text","importance":3,"theoremPathCentrality":2}],"edges":[{"id":"theorempath--basic-logic-and-proof-techniques--implementation-version--dsapath--dynamic-programming","fromSite":"theorempath","fromSlug":"basic-logic-and-proof-techniques","toSite":"dsapath","toSlug":"dynamic-programming","relation":"implementation-version","anchorText":"dynamic programming correctness","reason":"Dynamic programming uses induction and invariants as implementation-level proof obligations.","strength":5,"requiredForUnderstanding":false,"renderLocation":"related-paths","source":"curriculum-spec","confidence":0.95,"visibleEligible":true},{"id":"dsapath--dynamic-programming--proof-foundation--theorempath--basic-logic-and-proof-techniques","fromSite":"dsapath","fromSlug":"dynamic-programming","toSite":"theorempath","toSlug":"basic-logic-and-proof-techniques","relation":"proof-foundation","anchorText":"inductive proof structure","reason":"The correctness argument for DP recurrences relies on induction over states or subproblem size.","strength":5,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.95,"visibleEligible":true},{"id":"ioipath--dijkstra-shortest-paths--implementation-version--dsapath--priority-queues","fromSite":"ioipath","fromSlug":"dijkstra-shortest-paths","toSite":"dsapath","toSlug":"priority-queues","relation":"implementation-version","anchorText":"priority queue implementation details","reason":"The IOI solution depends on heap-based extract-min behavior and stale-entry handling.","strength":5,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.95,"visibleEligible":true},{"id":"ioipath--dijkstra-shortest-paths--proof-foundation--theorempath--basic-logic-and-proof-techniques","fromSite":"ioipath","fromSlug":"dijkstra-shortest-paths","toSite":"theorempath","toSlug":"basic-logic-and-proof-techniques","relation":"proof-foundation","anchorText":"settled-node invariant","reason":"The correctness proof uses an invariant over settled nodes and nonnegative edge weights.","strength":4,"requiredForUnderstanding":false,"renderLocation":"body","source":"curriculum-spec","confidence":0.9,"visibleEligible":true},{"id":"cudapath--parallel-prefix-scan--implementation-version--dsapath--prefix-sums","fromSite":"cudapath","fromSlug":"parallel-prefix-scan","toSite":"dsapath","toSlug":"prefix-sums","relation":"implementation-version","anchorText":"sequential prefix sums","reason":"CUDA scan pages should contrast the parallel algorithm with the sequential DSA primitive.","strength":4,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.9,"visibleEligible":false},{"id":"cudapath--parallel-prefix-scan--formal-foundation--theorempath--associativity-and-monoids","fromSite":"cudapath","fromSlug":"parallel-prefix-scan","toSite":"theorempath","toSlug":"associativity-and-monoids","relation":"formal-foundation","anchorText":"associativity requirement","reason":"Parallel scan correctness depends on the operation being associative.","strength":4,"requiredForUnderstanding":true,"renderLocation":"body","source":"curriculum-spec","confidence":0.9,"visibleEligible":true},{"id":"systemdesignpath--littles-law--probabilistic-application--probabilitypath--queueing-intuition","fromSite":"systemdesignpath","fromSlug":"littles-law","toSite":"probabilitypath","toSlug":"queueing-intuition","relation":"probabilistic-application","anchorText":"queueing intuition","reason":"Little's Law is easier to use when arrival rate, waiting time, and in-flight work are separated.","strength":4,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.9,"visibleEligible":false},{"id":"systemdesignpath--availability--probabilistic-application--probabilitypath--independent-events","fromSite":"systemdesignpath","fromSlug":"availability","toSite":"probabilitypath","toSlug":"independent-events","relation":"probabilistic-application","anchorText":"independent event assumptions","reason":"Availability calculations are often wrong when independence assumptions are unstated.","strength":5,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.92,"visibleEligible":true},{"id":"actuarypath--credibility-theory--formal-foundation--theorempath--conditional-expectation","fromSite":"actuarypath","fromSlug":"credibility-theory","toSite":"theorempath","toSlug":"conditional-expectation","relation":"formal-foundation","anchorText":"conditional expectation","reason":"Credibility theory relies on conditional expectation and variance decomposition.","strength":5,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.95,"visibleEligible":true},{"id":"putnampath--compactness-putnam--formal-foundation--theorempath--compactness-and-heine-borel","fromSite":"putnampath","fromSlug":"compactness-putnam","toSite":"theorempath","toSlug":"compactness-and-heine-borel","relation":"formal-foundation","anchorText":"Heine-Borel and extreme-value theorem","reason":"The Putnam page should teach recognition while TheoremPath owns the exact theorem and assumptions.","strength":5,"requiredForUnderstanding":true,"renderLocation":"prerequisites","source":"curriculum-spec","confidence":0.95,"visibleEligible":true},{"id":"putnampath--extremal-principle--contest-application--imopath--extremal-principle","fromSite":"putnampath","fromSlug":"extremal-principle","toSite":"imopath","toSlug":"extremal-principle","relation":"contest-application","anchorText":"elementary extremal principle","reason":"Putnam versions often reuse the same minimal-counterexample move introduced in olympiad training.","strength":4,"requiredForUnderstanding":false,"renderLocation":"related-paths","source":"curriculum-spec","confidence":0.9,"visibleEligible":true},{"id":"linguisticspath--context-free-grammars--implementation-version--dsapath--parsing-algorithms","fromSite":"linguisticspath","fromSlug":"context-free-grammars","toSite":"dsapath","toSlug":"parsing-algorithms","relation":"implementation-version","anchorText":"parsing algorithms","reason":"Formal grammar pages should point to implementation-level parsing when the learner needs algorithms.","strength":4,"requiredForUnderstanding":false,"renderLocation":"related-paths","source":"curriculum-spec","confidence":0.88,"visibleEligible":true},{"id":"classicspath--euclids-elements--historical-context--theorempath--axiomatic-geometry","fromSite":"classicspath","fromSlug":"euclids-elements","toSite":"theorempath","toSlug":"axiomatic-geometry","relation":"historical-context","anchorText":"axiomatic geometry","reason":"Euclid is a historically explicit bridge into axiomatic mathematical method.","strength":4,"requiredForUnderstanding":false,"renderLocation":"body","source":"curriculum-spec","confidence":0.88,"visibleEligible":true},{"id":"literaturepath--metaphor--linguistic-context--linguisticspath--semantics-and-pragmatics","fromSite":"literaturepath","fromSlug":"metaphor","toSite":"linguisticspath","toSlug":"semantics-and-pragmatics","relation":"linguistic-context","anchorText":"semantics and pragmatics","reason":"Metaphor has a genuine language-theory treatment through meaning and use.","strength":4,"requiredForUnderstanding":false,"renderLocation":"related-paths","source":"curriculum-spec","confidence":0.86,"visibleEligible":false},{"id":"systemdesignpath--microservices--sibling-treatment--literaturepath--narrative-structure","fromSite":"systemdesignpath","fromSlug":"microservices","toSite":"literaturepath","toSlug":"narrative-structure","relation":"sibling-treatment","anchorText":"narrative structure","reason":"Keyword-only example retained as a hidden negative control; it should never render visibly.","strength":1,"requiredForUnderstanding":false,"renderLocation":"hidden-graph-only","source":"agent-suggested","confidence":0.4,"visibleEligible":false}]}}