On the Robustness of Neural Collapse and the Neural Collapse of Robustness

Jingtong Su, Ya Shi Zhang, Nikolaos Tsilivis, Julia Kempe

Keywords: Adversarial Robustness; Neural Collapse

TL;DR: Study robustness of NC under input perturbations and measure collapse/simplex formation on adversarially robust models. Simplices are fragile for standard nets, but reemerge in robust ones. Discover interesting properties of intermediate layers.

Abstract: Neural Collapse refers to the curious phenomenon in the end of training of a neural network, where feature vectors and classification weights converge to a very simple geometrical arrangement (a simplex). While it has been observed empirically in various cases and has been theoretically motivated, its connection with crucial properties of neural networks, like their generalization and robustness, remains unclear. In this work, we study the stability properties of these simplices. We find that the simplex structure disappears under small adversarial attacks, and that perturbed examples ``leap" between simplex vertices. We further analyze the geometry of networks that are optimized to be robust against adversarial perturbations of the input, and find that Neural Collapse is a pervasive phenomenon in these cases as well, with clean and perturbed representations forming aligned simplices, and giving rise to a robust simple nearest-neighbor classifier. By studying the propagation of the amount of collapse inside the network, we identify novel properties of both robust and non-robust machine learning models, and show that earlier, unlike later layers maintain reliable simplices on perturbed data.

Track: Extended Abstract Track

Submission Number: 30