Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 4 / b

Training minimizes the empirical categorical cross-entropy lossby stochastic gradient descent. The independent validation set monitors generalization, while the small fixed number of epochs limits how long the network can fit training noise; using validation loss for early stopping would make this safeguard explicit. A forward pass computes all layer activations, class probabilities, and the mini-batch loss. There are $10000/2=5000$ training mini-batches per epoch and hence $5\cdot 5000=25000$ training forward passes, in addition to validation evaluation after each epoch.