Learning Track

Math to ML

You know calculus, linear algebra, and some probability. This path takes you from mathematical foundations through learning theory to understanding why ML models work, when they fail, and what the theorems actually say.

1/5

Phase 1: Core Foundations

Make sure your mathematical foundations are solid. If you can do these, you are ready for learning theory.

Probability Distributions

The language of randomness in ML

Expectation, Variance, Moments

What every bound depends on

Core Inequalities

Cauchy-Schwarz, Jensen, AM-GM

Multivariate Calculus

Gradients, Jacobians, Hessians

Eigenvalues

The spectral theorem, PCA, conditioning

2/5

Phase 2: Concentration and Estimation

The tools that make learning theory work. Every generalization bound uses these.

Concentration Inequalities

Markov, Chebyshev, Hoeffding, Bernstein

MLE

The default estimation method

Central Limit Theorem

Why everything is approximately Gaussian

Law of Large Numbers

Why averages converge

Bias-Variance Tradeoff

The most important concept in model selection

3/5

Phase 3: Learning Theory

Now you can understand why ML works. This is the core of the theoretical spine.

ERM

The framework behind all supervised learning

PAC Learning

When is a concept class learnable?

VC Dimension

Measuring hypothesis class complexity

Rademacher Complexity

Data-dependent complexity measure

Uniform Convergence

Why ERM generalizes

4/5

Phase 4: Optimization and Methods

How models are actually trained. The bridge between theory and practice.

Convex Optimization

GD convergence, strong convexity

SGD Convergence

The actual training algorithm

Regularization

Controlling complexity

Backpropagation

How neural networks learn

Adam

The default optimizer

5/5

Phase 5: Modern Deep Learning Theory

Why overparameterized networks generalize, and what classical theory gets wrong.

Double Descent

Classical bias-variance is incomplete

Implicit Bias

SGD selects solutions with specific properties

Scaling Laws

Power-law relationships in LLM training

Grokking

Delayed generalization after memorization

Transformers

The architecture behind every modern LLM

Not sure where to start?

If Phase 1 feels too basic, skip to Phase 2 or 3. If Phase 3 feels too hard, go back to Phase 2. The prerequisite sidebar on each page shows what you need.

Or search for a specific concept →