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We perform accurate numerical experiments with fully-connected (FC)one-hidden layer neural networks trained with a discretized Langevin dynamicson the MNIST and CIFAR10 datasets. Our goal is to empirically determine theregimes of validity of a recently-derived Bayesian effective action for shallowarchitectures in the proportional limit. We explore the predictive power of thetheory as a function of the parameters (the temperature $T$, the magnitude ofthe Gaussian priors $\lambda_1$, $\lambda_0$, the size of the hidden layer$N_1$ and the size of the training set $P$) by comparing the experimental andpredicted generalization error. The very good agreement between the effectivetheory and the experiments represents an indication that global rescaling ofthe infinite-width kernel is a main physical mechanism for kernelrenormalization in FC Bayesian standard-scaled shallow networks.

Predictive power of a Bayesian effective action for fully-connected one hidden layer neural networks in the proportional limit