  One of the principal scientific challenges in deep learning is explaining
generalization, i.e., why the particular way the community now trains networks
to achieve small training error also leads to small error on held-out data from
the same population. It is widely appreciated that some worst-case theories --
such as those based on the VC dimension of the class of predictors induced by
modern neural network architectures -- are unable to explain empirical
performance. A large volume of work aims to close this gap, primarily by
developing bounds on generalization error, optimization error, and excess risk.
When evaluated empirically, however, most of these bounds are numerically
vacuous. Focusing on generalization bounds, this work addresses the question of
how to evaluate such bounds empirically. Jiang et al. (2020) recently described
a large-scale empirical study aimed at uncovering potential causal
relationships between bounds/measures and generalization. Building on their
study, we highlight where their proposed methods can obscure failures and
successes of generalization measures in explaining generalization. We argue
that generalization measures should instead be evaluated within the framework
of distributional robustness.
