Introduction
This site is the mathematical companion to Rust for Machine Learning. The book builds machine learning systems from first principles and deliberately keeps the mathematics to the minimum needed to keep building. This site is where the rest of that mathematics lives: formal definitions, theorems with full proofs, and complete derivations of every construction the book uses.
Nothing here is required to follow the book. Everything here is for the reader who, at some point in a chapter, asks "but why is that true?" — and wants a real answer.
How this site is organized
Each section covers the mathematics of one machine-learning subject, in the order the book develops them. Sections go live one at a time, as they are written; the full map of the book is below so you can see where each companion section will land.
| Book chapter | Companion section |
|---|---|
| Introduction — Programs that Learn | — |
| Chapter 1 — The First Neuron | The Perceptron |
| Chapter 2 — The Search for Structure | Maximum-Margin Separation (planned) |
| Chapter 3 — A Framework for Learning | The Statistical Learning Framework (planned) |
| Chapter 4 — Building the Toolkit | The Linear Algebra of Learning Systems (planned) |
| Chapter 5 — Representations by Hand | Kernels and Feature Spaces (planned) |
| Chapter 6 — From Hard Decisions to Probabilities | Probabilistic Classification (planned) |
| Chapter 7 — Optimization | Optimization for Learning (planned) |
| Chapter 8 — Neural Networks | (planned) |
| Chapter 9 — Deep Neural Networks | (planned) |
| Chapter 10 — Convolutional Neural Networks | (planned) |
| Chapter 11 — Recurrent and Sequential Networks | (planned) |
| Chapter 12 — Making Rust Fast | (planned) |
| Chapter 13 — Unsupervised Learning | (planned) |
| Chapter 14 — Reinforcement Learning | (planned) |
| Chapter 15 — A Glimpse into Transformers | (planned) |
| Chapter 16 — Rust for ML in Production | (planned) |
Every page opens with an In the book line pointing to the chapter and section it formalizes, and a Builds on line linking the earlier pages (or Background entries) it relies on. Preliminaries — dot-product identities, basic probability, differentiation rules — are collected once in the Background appendix and referenced, so each section stays focused on its subject.
How to read the proofs
Every mathematical claim on this site gets one of three treatments:
- A full proof — for named theorems and anything short enough to be self-contained (Novikoff's convergence theorem, convexity of the logistic loss).
- A complete derivation — for constructions: where the sigmoid comes from, how the SVM dual is obtained, why Adam's bias correction has the form it has.
- An explicit pointer — for results whose proofs are genuinely beyond the scope of a companion site, a reference to a textbook treatment in Further reading. There is no "it can be shown that" here without a link.
Proofs end with ∎. If a proof relies on a fact from the Background appendix, the fact is linked at the point of use.
Notation
Notation follows the book's conventions throughout — bold lowercase for vectors, plain italic for scalars — and is collected in the Notation appendix.