The formal model

In the book: Chapter 1, §"Intuition: AND and OR" and §"Why the Perceptron Works". Builds on: Background: the dot product.

Planned. Defines the perceptron as $h(\mathbf{x})=\mathrm{sign}({\mathbf{w}}^{\top }\mathbf{x}+b)$, makes precise what the book shows in pictures: the set $\{\mathbf{x}:{\mathbf{w}}^{\top }\mathbf{x}+b=0\}$ is a hyperplane, the two prediction regions are half-spaces, $\mathbf{w}$ is normal to the boundary, and $b$ controls its offset from the origin.