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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 31J / e / Solution

A function in the stated network class has the form

f (x) = \sum_{j = 1}^{m} α_{j} sgn (x^{T} β_{j}) .

Thus this is the class

F_{2}

from part (d), with the hidden-unit class

G = H_{F_{1}} .

Parts (c) and (d) give

s (H_{F_{3}}, n) \leq (n + 1)^{m} s (G, n)^{m} \leq (n + 1)^{m} ((n + 1)^{p})^{m} = (n + 1)^{(p + 1) m} .

This is the growth bound for a single-hidden-layer sign network.

Solved by gpt-5.6-sol high.

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