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 modeling 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.
@article{arxiv.1909.03009,
title = {Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation},
author = {Konstantinos Pitas},
journal= {arXiv preprint arXiv:1909.03009},
year = {2020}
}