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arXiv · 2006.08888

PAC-Bayesian Generalization Bounds for MultiLayer Perceptrons

Xinjie Lan·Xin Guo·Kenneth E. Barner
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Abstract

We study PAC-Bayesian generalization bounds for Multilayer Perceptrons (MLPs) with the cross entropy loss. Above all, we introduce probabilistic explanations for MLPs in two aspects: (i) MLPs formulate a family of Gibbs distributions, and (ii) minimizing the cross-entropy loss for MLPs is equivalent to Bayesian variational inference, which establish a solid probabilistic foundation for studying PAC-Bayesian bounds on MLPs. Furthermore, based on the Evidence Lower Bound (ELBO), we prove that MLPs with the cross entropy loss inherently guarantee PAC- Bayesian generalization bounds, and minimizing PAC-Bayesian generalization bounds for MLPs is equivalent to maximizing the ELBO. Finally, we validate the proposed PAC-Bayesian generalization bound on benchmark datasets.

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BibTeXRIS

Xinjie Lan, Xin Guo, Kenneth E. Barner. 2020-06-16. PAC-Bayesian Generalization Bounds for MultiLayer Perceptrons. https://arxiv.org/abs/2006.08888

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