English

First-order Adversarial Vulnerability of Neural Networks and Input Dimension

Machine Learning 2019-06-18 v4 Computer Vision and Pattern Recognition Machine Learning

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 1\ell_1-norm 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 dimension dependence persists after either usual or robust training, but gets attenuated with higher regularization.

Keywords

Cite

@article{arxiv.1802.01421,
  title  = {First-order Adversarial Vulnerability of Neural Networks and Input Dimension},
  author = {Carl-Johann Simon-Gabriel and Yann Ollivier and Léon Bottou and Bernhard Schölkopf and David Lopez-Paz},
  journal= {arXiv preprint arXiv:1802.01421},
  year   = {2019}
}

Comments

Paper previously called: "Adversarial Vulnerability of Neural Networks Increases with Input Dimension". 9 pages main text and references, 11 pages appendix, 14 figures