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Explaining how overparametrized neural networks simultaneously achieve lowrisk and zero empirical risk on benchmark datasets is an open problem.PAC-Bayes bounds optimized using variational inference (VI) have been recentlyproposed as a promising direction in obtaining non-vacuous bounds. We showempirically that this approach gives negligible gains when modeling theposterior as a Gaussian with diagonal covariance--known as the mean-fieldapproximation. We investigate common explanations, such as the failure of VIdue to problems in optimization or choosing a suboptimal prior. Our resultssuggest that investigating richer posteriors is the most promising directionforward.

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