Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 5 / b / Solution

Stochastic gradient descent replaces the full empirical-loss gradient by the gradient on a randomly ordered observation or mini-batch, then updates $\theta \leftarrow \theta -\eta \hat{\nabla }L(\theta )$. The training half contains $768/2=384$ observations, so batches of 16 give $384/16=24$ updates per epoch. Over 100 epochs every parameter is updated $2400$ times.

Solved by gpt-5.6-sol high.