Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 31K / f / Solution

The Rademacher contraction lemma for ReLU (which is 1-Lipschitz and vanishes at zero), duality between ${\ell }_1$ and ${\ell }_{\infty }$, and part (d) give ${\mathcal{R}}_n(\mathcal{H})\le 2\lambda \sqrt{2\log (2p)/n}$. Combining with part (c) gives the claimed $4\lambda \sqrt{2\log (2p)}/\sqrt{n}$.