Position: Many generalization measures for deep learning are fragile

In this position paper, we argue that many post-mortem generalization measures -- those computed on trained networks -- are fragile: small training modifications that barely affect the performance of the underlying deep neural network can substantially change a measure's value, trend, or scaling behavior. For example, minor hyperparameter changes, such as learning rate adjustments or switching between SGD variants, can reverse the slope of a learning curve in widely used generalization measures such as the path norm. We also identify subtler forms of fragility. For instance, the PAC-Bayes origin measure is regarded as one of the most reliable, and is indeed less sensitive to hyperparameter tweaks than many other measures. However, it completely fails to capture differences in data complexity across learning curves. This data fragility contrasts with the function-based marginal-likelihood PAC-Bayes bound, which does capture differences in data-complexity, including scaling behavior, in learning curves, but which is not a post-mortem measure. Beyond demonstrating that many post-mortem bounds are fragile, this position paper also argues that developers of new measures should explicitly audit them for fragility.