Derivation: Backward Functions for Basic Modules and Vectorized Backpropagation

The previous lesson stated the backpropagation algorithm and its chain-rule justification at the level of a single hand-worked example. This optional derivation sub-note works out the backward function for the three building blocks used in this introductory topic — the affine (dense) layer, the ReLU activation, and the combined softmax-plus-cross-entropy output layer — and assembles them into a vectorised backward pass. Skip it on a first pass if you only need the conceptual algorithm; return when you want the algebra that frameworks automate.