Wide stochastic networks: Gaussian limit and PAC-Bayesian training

• URL: http://arxiv.org/abs/2106.09798v1
• Date: Thu, 17 Jun 2021 20:25:38 GMT
• Title: Wide stochastic networks: Gaussian limit and PAC-Bayesian training
• Authors: Eugenio Clerico, George Deligiannidis, Arnaud Doucet
• Abstract summary: We show that an extremely large network is approximated by a Gaussian process, both before and during training. The explicit evaluation of the output distribution allows for a PAC-Bayesian training procedure that directly optimize the bound. For a large but finite-width network, we show empirically on MNIST that this training approach can outperform standard PAC-Bayesian methods.
• Score: 21.979820411421827
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The limit of infinite width allows for substantial simplifications in the analytical study of overparameterized neural networks. With a suitable random initialization, an extremely large network is well approximated by a Gaussian process, both before and during training. In the present work, we establish a similar result for a simple stochastic architecture whose parameters are random variables. The explicit evaluation of the output distribution allows for a PAC-Bayesian training procedure that directly optimizes the generalization 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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