 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-2/31j/e/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

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} .

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