Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 4 / c / Solution

The usual Akaike information criterion correction assumes a regular maximum-likelihood fit with a meaningful fixed parameter dimension. Here stochastic optimization stopped after five epochs need not attain the maximum likelihood estimator, and neural-network symmetries, inactive units, and heavy overparameterization make the raw count $2502$ a poor effective dimension. Either failure invalidates a direct AIC comparison with an ordinary logistic regression.