Perturbation Type Categorization for Multiple Adversarial Perturbation Robustness

Recent works in adversarial robustness have proposed defenses to improve the robustness of a single model against the union of multiple perturbation types. However, these methods still suffer significant trade-offs compared to the ones specifically trained to be robust against a single perturbation type. In this work, we introduce the problem of categorizing adversarial examples based on their perturbation types. We first theoretically show on a toy task that adversarial examples of different perturbation types constitute different distributions-making it possible to distinguish them. We support these arguments with experimental validation on multiple ℓ_p attacks and common corruptions. Instead of training a single classifier, we propose PROTECTOR, a two-stage pipeline that first categorizes the perturbation type of the input, and then makes the final prediction using the classifier specifically trained against the predicted perturbation type. We theoretically show that at test time the adversary faces a natural trade-off between fooling the perturbation classifier and the succeeding classifier optimized with perturbation-specific adversarial training. This makes it challenging for an adversary to plant strong attacks against the whole pipeline. Experiments on MNIST and CIFAR-10 show that PROTECTOR outperforms prior adversarial training-based defenses by over 5% when tested against the union of ℓ₁, ℓ₂, ℓ_∞ attacks. Additionally, our method extends to a more diverse attack suite, also showing large robustness gains against multiple ℓ_p, spatial and recolor attacks.