Papers › Stronger and Faster Wasserstein Adversarial Attacks

Stronger and Faster Wasserstein Adversarial Attacks

6 Aug 2020ICML 2020 1arXiv:2008.02883archive 2025-07-28

Kaiwen Wu, Allen Houze Wang, Yao-Liang Yu

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to "small, imperceptible" perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the ℓₚ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the ℓₚ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to 3.4% within a Wasserstein perturbation ball of radius $0.005$, in contrast to 65.6% using the previous Wasserstein attack based on an \emph{approximate} projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.

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