The Perceptron
In the book: Chapter 1 — The First Neuron.
Chapter 1 builds the perceptron: a unit that computes a weighted sum and thresholds it, together with a learning rule that nudges the weights on every mistake. The chapter shows geometrically that it works. This section shows why — culminating in the perceptron convergence theorem, the guarantee the book invokes at the end of the chapter.
| Note | The claim it formalizes |
|---|---|
| The formal model | A perceptron's decision boundary is a hyperplane; predictions are half-space membership. |
| The learning rule | Each mistake-driven update provably moves the score of the offending example in the right direction. |
| Linear separability and XOR | AND and OR are linearly separable; XOR provably is not. |
| The convergence theorem | On separable data, the algorithm converges after finitely many updates — Novikoff's theorem, with proof. |
| Reading the bound | What the mistake bound actually says, and what it foreshadows. |