Expected Perturbation Scores for Adversarial Detection

Shuhai Zhang, Feng Liu, Jiahao Yang, Yifan Yang, Bo Han, Mingkui Tan

Abstract: Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in the high-dimension space. Recently, the gradients of log probability density (a.k.a., score) w.r.t. samples is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we can perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two distributions under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we propose an EPS-based adversarial detection (EPS-AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. To verify the validity of our proposed method, we also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Empirical studies on CIFAR-10 and ImageNet across different network architectures including ResNet, WideResNet, and ViT show the superior adversarial detection performance of EPS-AD compared to existing methods.

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