Invariance is often cited as a desirable property of machine learning systems, claimed to improve model accuracy and reduce overfitting. Empirically, invariant models often generalize better than their non-invariant counterparts. But is it possible to show that invariant models provably do so? In this paper we explore the effect of invariance on model generalization. We find strong Bayesian and frequentist motivations for enforcing invariance which leverage recent results connecting PAC-Bayes generalization bounds and the marginal likelihood. We make use of these results to perform model selection on neural networks.
Clare Lyle, Marta Kwiatkowska, Mark van der Wilk, Yarin Gal
Understanding and Improving Generalization in Deep Learning workshop, ICML, 2019