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

For fixed hidden units, the supremum over $\Vert \alpha {\Vert }_1\le \lambda$ is $\lambda$ times the largest absolute unit correlation. Taking the further supremum over admissible ${\beta }_k$ gives exactly the displayed bound.

Solved by gpt-5.6-sol high.