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.
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Adversarial Training and Robustness for Multiple Perturbations
Defenses against adversarial examples, such as adversarial training, are typically tailored
to a single perturbation type (e.g., small ℓ∞-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. We propose new multi-perturbation adversarial training schemes, as well as an efficient attack for the
ℓ1-norm, and use these to show that models trained against multiple attacks fail to achieve
robustness competitive with that of models trained on each attack individually. In particular,
we find that adversarial training with first-order ℓ∞, ℓ1 and ℓ2 attacks on MNIST achieves
merely 50% robust accuracy, partly because of gradient-masking. Finally, we propose affine
attacks that linearly interpolate between perturbation types and further degrade the accuracy
of adversarially trained models.
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- Award ID(s):
- 2343611
- NSF-PAR ID:
- 10472239
- Publisher / Repository:
- arXiv:1904.13000 Accepted at NeurIPS 2019
- Date Published:
- Subject(s) / Keyword(s):
- ["Machine Learning (cs.LG)","Cryptography and Security (cs.CR)","Machine Learning (stat.ML)"]
- Format(s):
- Medium: X
- Location:
- arXiv:1904.13000 Accepted at NeurIPS 2019
- Sponsoring Org:
- National Science Foundation
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