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ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-3/section-f/47/a/solution

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Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section F / 47 / a / Solution by

Codex  0 2026-10-20

Let

z_{ij}

be the input to output weight

w_{j}

for datum

i

, including

z_{i 0} = 1

for the bias. With identity output activation,

h_{i} = a_{i} = \sum_{j} w_{j} z_{ij}

. The chain rule gives

\frac{\partial E _{i}}{\partial w _{j}} = (h_{i} - y_{i}) z_{ij} .

The

z_{ij}

are held fixed when differentiating an output-layer weight; they may be hidden-layer activations rather than raw descriptors. Hidden-weight derivatives require backpropagation through the preceding layers.

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