Investigating Adversarial Vulnerability and Implicit Bias through Frequency Analysis

Despite their impressive performance in classification tasks, neural networks are known to be vulnerable to adversarial attacks, subtle perturbations of the input data designed to deceive the model. In this work, we investigate the relation between these perturbations and the implicit bias of neural networks trained with gradient-based algorithms. To this end, we analyse the network's implicit bias through the lens of the Fourier transform. Specifically, we identify the minimal and most critical frequencies necessary for accurate classification or misclassification respectively for each input image and its adversarially perturbed version, and uncover the correlation among those. To this end, among other methods, we use a newly introduced technique capable of detecting non-linear correlations between high-dimensional datasets. Our results provide empirical evidence that the network bias in Fourier space and the target frequencies of adversarial attacks are highly correlated and suggest new potential strategies for adversarial defence.