Relating Implicit Bias and Adversarial Attacks through Intrinsic
  Dimension
Lorenzo Basile Nikos Karantzas Alberto D'Onofrio Luca Bortolussi Alex Rodriguez Fabio Anselmi
Despite their impressive performance in classification, neural networks are
known to be vulnerable to adversarial attacks. These attacks are small
perturbations of the input data designed to fool the model. Naturally, a
question arises regarding the potential connection between the architecture,
settings, or properties of the model and the nature of the attack. In this
work, we aim to shed light on this problem by focusing on the implicit bias of
the neural network, which refers to its inherent inclination to favor specific
patterns or outcomes. Specifically, we investigate one aspect of the implicit
bias, which involves the essential Fourier frequencies required for accurate
image classification. We conduct tests to assess the statistical relationship
between these frequencies and those necessary for a successful attack. To delve
into this relationship, we propose a new method that can uncover non-linear
correlations between sets of coordinates, which, in our case, are the
aforementioned frequencies. By exploiting the entanglement between intrinsic
dimension and correlation, we provide empirical evidence that the network bias
in Fourier space and the target frequencies of adversarial attacks are closely
tied.