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Paths

Theorem Trails

Start with theorem trails when you need statements, assumptions, source locators, Lean status, diagnostics, and checkpoints in one place. Use broader reading paths only after the theorem spine is clear.

Flagship theorem trails

Theorem trail index

12 claim-governed paths through the proof spine: theorem statement, assumptions, proof sketch, source locator, formal status, diagnostics, exercises, failure checks, and review queue.

Theorem statements

12/12

Every flagship row opens to a theorem-first trail page.

Source locators

29

Reviewed source-location records attached to trail claims.

Diagnostics

16

Canonical items tied to assumptions or proof steps.

Exercises

13

Topic exercises linked into the trail review surface.

Failure checks

24

Known misuse cases tied to evidence or diagnostics.

Lean exact

9/12

Trails with an exact Lean wrapper for the governed claim.

Broader reading paths

Longer topic sequences for foundation building, systems work, and research prep.

Start Here~8 hours6 topics

ML Theory Core

The classical spine: ERM, uniform convergence, VC dimension, Rademacher complexity. Start here if you want to understand why learning from data works.

1pac learning framework2empirical risk minimization3uniform convergence4vc dimension5rademacher complexity6algorithmic stability
Essential~10 hours7 topics

Concentration Inequalities

From Markov to Matrix Bernstein. The inequality toolkit that every generalization bound, random matrix argument, and stability proof depends on.

1concentration inequalities2chernoff bounds3subgaussian random variables4subexponential random variables5mcdiarmids inequality6hanson wright inequality7matrix concentration
Foundation~14 hours8 topics

Master Linear Algebra

Linear maps, matrix operations, norms, eigenspaces, SVD, PCA, Jacobians, and matrix calculus. The algebra spine behind ML theory and neural networks.

Open guided path →
1vectors matrices and linear maps2matrix operations and properties3matrix norms4eigenvalues and eigenvectors5singular value decomposition6principal component analysis7the jacobian matrix8matrix calculus
Foundation~10 hours10 topics

Basic Neural Network From Scratch

Build a tiny MLP before jumping to transformers: linear layers, activations, losses, gradient descent, backprop, softmax, cross-entropy, and generalization checks.

Open guided path →
1linear layer shapes memory2perceptron3activation functions4loss functions catalog5gradient descent variants6feedforward networks and backpropagation7softmax and numerical stability8cross entropy loss deep dive9train test split and data leakage10regularization in practice
Applied~12 hours7 topics

Build an LLM from Scratch

A two-stage decoder-only path: next-token prediction, causal masking, embeddings, transformer blocks, then KV cache, FlashAttention, and modern inference.

Open guided path →
1token prediction and language modeling2attention mechanism theory3transformer architecture4positional encoding5kv cache6flash attention7inference systems overview
Systems~18 hours6 topics

Deep Learning Systems From Scratch

A shape-and-memory rebuild track: linear layers, manual backprop, attention ledgers, transformer forward passes, KV cache, roofline reasoning, and accelerator constraints.

Open guided path →
1linear layer shapes memory2feedforward networks and backpropagation3attention mechanism theory4transformer architecture5kv cache6inference systems overview
Infrastructure~15 hours7 topics

Mathematical Maturity

Measure theory, Radon-Nikodym, convex duality, martingales, information theory. The serious math infrastructure that separates surface-level from real understanding.

1measure theoretic probability2radon nikodym and conditional expectation3convex duality4martingale theory5information theory foundations6maximum likelihood estimation7fisher information
Frontier~10 hours7 topics

Modern Generalization

Where classical theory fails and what replaces it. Implicit bias, double descent, NTK, benign overfitting, scaling laws. The frontier of understanding why deep learning works.

1implicit bias and modern generalization2double descent3neural tangent kernel4mean field theory5benign overfitting6random matrix theory overview7scaling laws
New~12 hours10 topics

Frontier ML (2025-2026)

Post-training, test-time compute, agents, MoE, Mamba, diffusion, context engineering. The topics that dominate current research and systems work.

1post training overview2test time compute and search3dpo vs grpo vs rl reasoning4reward models and verifiers5agentic rl and tool use6context engineering7diffusion models8mixture of experts9mamba and state space models10speculative decoding and quantization