FirstOrder Adversarial Vulnerability of Neural Networks and Input Dimension
[edit]
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:58095817, 2019.
Abstract
Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisingly, vulnerability does not depend on network topology: for many standard network architectures, we prove that at initialization, the L1norm of these gradients grows as the square root of the input dimension, leaving the networks increasingly vulnerable with growing image size. We empirically show that this dimensiondependence persists after either usual or robust training, but gets attenuated with higher regularization.
Related Material


