(De)Randomized Smoothing for Certifiable Defense against Patch Attacks

Abstract

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. Additionally, the algorithm we propose is de-randomized, providing deterministic certificates. To the best of our knowledge, there exists only one prior method for certifiable defense against patch attacks, which relies on interval bound propagation. While this sole existing method performs well on MNIST, it has several limitations: it requires computationally expensive training, does not scale to ImageNet, and performs poorly on CIFAR-10. In contrast, our proposed method effectively addresses all of these issues: our classifier can be trained quickly, achieves high clean and certified robust accuracy on CIFAR-10, and provides certificates at the ImageNet scale. For example, for a 5*5 patch attack on CIFAR-10, our method achieves up to around 57.8% certified accuracy (with a classifier around 83.9% clean accuracy), compared to at most 30.3% certified accuracy for the existing method (with a classifier with around 47.8% clean accuracy), effectively establishing a new state-of-the-art. Code is available at https://github.com/alevine0/patchSmoothing.