  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.
