Almost Tight L0-norm Certified Robustness of Top-k Predictions against Adversarial Perturbations

Jinyuan Jia, Binghui Wang, Xiaoyu Cao, Hongbin Liu, Neil Zhenqiang Gong

Keywords: Certified robustness, adversarial perturbation

Abstract: Top-k predictions are used in many real-world applications such as machine learning as a service, recommender systems, and web searches. $\ell_0$-norm adversarial perturbation characterizes an attack that arbitrarily modifies some features of an input such that a classifier makes an incorrect prediction for the perturbed input. $\ell_0$-norm adversarial perturbation is easy to interpret and can be implemented in the physical world. Therefore, certifying robustness of top-k predictions against $\ell_0$-norm adversarial perturbation is important. However, existing studies either focused on certifying $\ell_0$-norm robustness of top-1 predictions or $\ell_2$-norm robustness of top-k predictions. In this work, we aim to bridge the gap. Our approach is based on randomized smoothing, which builds a provably robust classifier from an arbitrary classifier via randomizing an input. Our major theoretical contribution is an almost tight $\ell_0$-norm certified robustness guarantee for top-k predictions. We empirically evaluate our method on CIFAR10 and ImageNet. For instance, our method can build a classifier that achieves a certified top-3 accuracy of 69.2\% on ImageNet when an attacker can arbitrarily perturb 5 pixels of a testing image. We will publish our code upon paper acceptance.

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