Adversarial Training and Robustness for Multiple Perturbations

Florian Tramèr and Dan Boneh

Conference on Neural Information Processing Systems (NeurIPS) 2019 (Spotlight Presentation)


Defenses against adversarial examples, such as adversarial training, are typically tailored to a single perturbation type (e.g., small Linf-noise). For other perturbations, these defenses offer no guarantees and, at times, even increase the model’s vulnerability. Our aim is to understand the reasons underlying this robustness trade-off, and to train models that are simultaneously robust to multiple perturbation types. We prove that a trade-off in robustness to different types of Lp-bounded and spatial perturbations must exist in a natural and simple statistical setting. We corroborate our formal analysis by demonstrating similar robustness trade-offs on MNIST and CIFAR10. Building upon new multi-perturbation adversarial training schemes, and a novel efficient attack for finding L1-bounded adversarial examples, we show that no model trained against multiple attacks achieves robustness competitive with that of models trained on each attack individually. In particular, we uncover a pernicious gradient-masking phenomenon on MNIST, which causes adversarial training with first-order Linf, L1 and L2 adversaries to achieve merely 50% accuracy. Our results question the viability and computational scalability of extending adversarial robustness, and adversarial training, to multiple perturbation types.

  author   =   {Tram{\`e}r, Florian and Boneh, Dan},
  title   =   {Adversarial Training and Robustness for Multiple Perturbations},
  booktitle   =   {Conference on Neural Information Processing Systems (NeurIPS)},
  pages   =   {5866--5876},
  year   =   {2019},
  howpublished   =   {arXiv preprint arXiv:1904.13000},
  url   =   {}