Wide stochastic networks: Gaussian limit and PAC-Bayesian training

Eugenio Clerico; George Deligiannidis; Arnaud Doucet

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arXiv · 2106.09798

Wide stochastic networks: Gaussian limit and PAC-Bayesian training

Eugenio Clerico·George Deligiannidis·Arnaud Doucet

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Abstract

The limit of infinite width allows for substantial simplifications in the analytical study of over-parameterised neural networks. With a suitable random initialisation, an extremely large network exhibits an approximately Gaussian behaviour. In the present work, we establish a similar result for a simple stochastic architecture whose parameters are random variables, holding both before and during training. The explicit evaluation of the output distribution allows for a PAC-Bayesian training procedure that directly optimises the generalisation bound. For a large but finite-width network, we show empirically on MNIST that this training approach can outperform standard PAC-Bayesian methods.

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Eugenio Clerico, George Deligiannidis, Arnaud Doucet. 2021-06-17. Wide stochastic networks: Gaussian limit and PAC-Bayesian training. https://arxiv.org/abs/2106.09798

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