  Sharpness of minima is a promising quantity that can correlate with
generalization in deep networks and, when optimized during training, can
improve generalization. However, standard sharpness is not invariant under
reparametrizations of neural networks, and, to fix this,
reparametrization-invariant sharpness definitions have been proposed, most
prominently adaptive sharpness (Kwon et al., 2021). But does it really capture
generalization in modern practical settings? We comprehensively explore this
question in a detailed study of various definitions of adaptive sharpness in
settings ranging from training from scratch on ImageNet and CIFAR-10 to
fine-tuning CLIP on ImageNet and BERT on MNLI. We focus mostly on transformers
for which little is known in terms of sharpness despite their widespread usage.
Overall, we observe that sharpness does not correlate well with generalization
but rather with some training parameters like the learning rate that can be
positively or negatively correlated with generalization depending on the setup.
Interestingly, in multiple cases, we observe a consistent negative correlation
of sharpness with out-of-distribution error implying that sharper minima can
generalize better. Finally, we illustrate on a simple model that the right
sharpness measure is highly data-dependent, and that we do not understand well
this aspect for realistic data distributions. The code of our experiments is
available at https://github.com/tml-epfl/sharpness-vs-generalization.
