Certified Robustness for Top-k Predictions against Adversarial Perturbations via Randomized Smoothing
This work addresses a gap in certified robustness for real-world applications where top-k predictions are more relevant than top-1, though it is incremental as it extends existing randomized smoothing methods from top-1 to top-k.
The paper tackles the problem of deriving certified robustness for top-k predictions against adversarial perturbations, using randomized smoothing with Gaussian noise to achieve a tight robustness bound in the ℓ₂ norm, resulting in a certified top-5 accuracy of 62.8% on ImageNet for perturbations with norms less than 0.5.
It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to top-1 predictions. In many real-world applications, top-$k$ predictions are more relevant. In this work, we aim to derive certified robustness for top-$k$ predictions. In particular, our certified robustness is based on randomized smoothing, which turns any classifier to a new classifier via adding noise to an input example. We adopt randomized smoothing because it is scalable to large-scale neural networks and applicable to any classifier. We derive a tight robustness in $\ell_2$ norm for top-$k$ predictions when using randomized smoothing with Gaussian noise. We find that generalizing the certified robustness from top-1 to top-$k$ predictions faces significant technical challenges. We also empirically evaluate our method on CIFAR10 and ImageNet. For example, our method can obtain an ImageNet classifier with a certified top-5 accuracy of 62.8\% when the $\ell_2$-norms of the adversarial perturbations are less than 0.5 (=127/255). Our code is publicly available at: \url{https://github.com/jjy1994/Certify_Topk}.