In the last couple of years, several adversarial attack methods based on different threat models have been proposed for the image classification problem. Most existing defenses consider additive threat models in which sample perturbations have bounded L_p norms. These defenses, however, can be vulnerable against adversarial attacks under non-additive threat models. An example of an attack method based on a non-additive threat model is the Wasserstein adversarial attack proposed by Wong et al. (2019), where the distance between an image and its adversarial example is determined by the Wasserstein metric ("earth-mover distance") between their normalized pixel intensities. Until now, there has been no certifiable defense against this type of attack. In this work, we propose the first defense with certified robustness against Wasserstein Adversarial attacks using randomized smoothing. We develop this certificate by considering the space of possible flows between images, and representing this space such that Wasserstein distance between images is upper-bounded by L_1 distance in this flow-space. We can then apply existing randomized smoothing certificates for the L_1 metric. In MNIST and CIFAR-10 datasets, we find that our proposed defense is also practically effective, demonstrating significantly improved accuracy under Wasserstein adversarial attack compared to unprotected models.
(De)Randomized Smoothing for Certifiable Defense against Patch Attacks
Patch adversarial attacks on images, in which the attacker can distort pixels within a region of bounded size, are an important threat model since they provide a quantitative model for physical adversarial attacks. In this paper, we introduce a certifiable defense against patch attacks that guarantees for a given image and patch attack size, no patch adversarial examples exist. Our method is related to the broad class of randomized smoothing robustness schemes which provide high-confidence probabilistic robustness certificates. By exploiting the fact that patch attacks are more constrained than general sparse attacks, we derive meaningfully large robustness certificates against them. Additionally, in contrast to smoothing-based defenses against L_p and sparse attacks, our defense method against patch attacks is de-randomized, yielding improved, deterministic certificates. Compared to the existing patch certification method proposed by Chiang et al. (2020), which relies on interval bound propagation, our method can be trained significantly faster, achieves high clean and certified robust accuracy on CIFAR-10, and provides certificates at ImageNet scale. For example, for a 5-by-5 patch attack on CIFAR-10, our method achieves up to around 57.6% certified accuracy (with a classifier with around 83.8% clean accuracy), compared to at most 30.3% certified accuracy for the existing more »
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- Advances in Neural Information Processing Systems Foundation (NeurIPS)
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- National Science Foundation
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