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# Wide stochastic networks: Gaussian limit and PAC-Bayesian training

*Proceedings of The 34th International Conference on Algorithmic Learning Theory*, PMLR 201:447-470, 2023.

#### 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.