Understanding robustness and generalization of artificial neural networks through Fourier masks

TL;DR

This paper investigates the frequency biases of neural networks, developing a method to identify essential input frequencies and revealing that robustness and generalization are linked to processing low-frequency information, with surprising texture-like patterns emerging.

Contribution

The authors introduce a novel algorithm to learn input frequency masks that preserve network performance, providing new insights into frequency biases related to robustness and generalization in neural networks.

Findings

Adversarially robust networks show a low-frequency bias.

Essential frequencies are crucial for generalization.

Textures emerge when images are processed through frequency masks.

Abstract

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.