Introduction

Introduction

Subspaces must pass through the origin, but most lines and planes in real life don't. Affine spaces are subspaces shifted away from the origin, and affine maps are linear maps followed by a shift. A neural-network layer before its activation, $W\mathbf{x} + \mathbf{b}$, is an affine map — so this is the last piece needed to read a network as linear algebra.