  Despite the enormous success of artificial neural networks (ANNs) in many
disciplines, the characterization of their computations and the origin of key
properties such as generalization and robustness remain open questions. Recent
literature suggests that robust networks with good generalization properties
tend to be biased towards processing low frequencies in images. To explore the
frequency bias hypothesis further, we develop an algorithm that allows us to
learn modulatory masks highlighting the essential input frequencies needed for
preserving a trained network's performance. We achieve this by imposing
invariance in the loss with respect to such modulations in the input
frequencies. We first use our method to test the low-frequency preference
hypothesis of adversarially trained or data-augmented networks. Our results
suggest that adversarially robust networks indeed exhibit a low-frequency bias
but we find this bias is also dependent on directions in frequency space.
However, this is not necessarily true for other types of data augmentation. Our
results also indicate that the essential frequencies in question are
effectively the ones used to achieve generalization in the first place.
Surprisingly, images seen through these modulatory masks are not recognizable
and resemble texture-like patterns.

Computer Vision and Pattern Recognition;Machine Learning;Image and Video Processing