  Improving the accuracy of deep neural networks (DNNs) on out-of-distribution
(OOD) data is critical to an acceptance of deep learning (DL) in real world
applications. It has been observed that accuracies on in-distribution (ID)
versus OOD data follow a linear trend and models that outperform this baseline
are exceptionally rare (and referred to as "effectively robust"). Recently,
some promising approaches have been developed to improve OOD robustness: model
pruning, data augmentation, and ensembling or zero-shot evaluating large
pretrained models. However, there still is no clear understanding of the
conditions on OOD data and model properties that are required to observe
effective robustness. We approach this issue by conducting a comprehensive
empirical study of diverse approaches that are known to impact OOD robustness
on a broad range of natural and synthetic distribution shifts of CIFAR-10 and
ImageNet. In particular, we view the "effective robustness puzzle" through a
Fourier lens and ask how spectral properties of both models and OOD data
influence the corresponding effective robustness. We find this Fourier lens
offers some insight into why certain robust models, particularly those from the
CLIP family, achieve OOD robustness. However, our analysis also makes clear
that no known metric is consistently the best explanation (or even a strong
explanation) of OOD robustness. Thus, to aid future research into the OOD
puzzle, we address the gap in publicly-available models with effective
robustness by introducing a set of pretrained models--RobustNets--with varying
levels of OOD robustness.
