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# Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation

*Proceedings of the 37th International Conference on Machine Learning*, PMLR 119:7739-7749, 2020.

#### Abstract

Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a promising direction in obtaining non-vacuous bounds. We show empirically that this approach gives negligible gains when modelling the posterior as a Gaussian with diagonal covariance—known as the mean-field approximation. We investigate common explanations, such as the failure of VI due to problems in optimization or choosing a suboptimal prior. Our results suggest that investigating richer posteriors is the most promising direction forward.