Reading Paths

Structured sequences through the material. Each path has a clear starting point, ordered topics, and estimated time. Pick the one that matches what you need to learn.

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 framework 2empirical risk minimization 3uniform convergence 4vc dimension 5rademacher complexity 6algorithmic 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 inequalities 2chernoff bounds 3subgaussian random variables 4subexponential random variables 5mcdiarmids inequality 6hanson wright inequality 7matrix concentration

Applied~12 hours8 topics

Build an LLM from Scratch

Transformer architecture, attention mechanism, positional encoding, KV cache, scaling laws, optimizers, RLHF. The math behind modern language models.

1transformer architecture 2attention mechanism theory 3positional encoding 4kv cache 5scaling laws 6optimizer theory sgd adam muon 7rlhf and alignment 8post training 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 probability 2radon nikodym and conditional expectation 3convex duality 4martingale theory 5information theory foundations 6maximum likelihood estimation 7fisher 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 generalization 2double descent 3neural tangent kernel 4mean field theory 5benign overfitting 6random matrix theory overview 7scaling 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 overview 2test time compute and search 3dpo vs grpo vs rl reasoning 4reward models and verifiers 5agentic rl and tool use 6context engineering 7diffusion models 8mixture of experts 9mamba and state space models 10speculative decoding and quantization