Provably Adversarially Robust Nearest Prototype Classifiers
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Nearest prototype classifiers (NPCs) assign to each input point the label of the nearest prototype with respect to a chosen distance metric. A direct advantage of NPCs is that the decisions are interpretable. Previous work could provide lower bounds on the minimal adversarial perturbation in the ℓ_p-threat model when using the same ℓ_p-distance for the NPCs. In this paper we provide a complete discussion on the complexity when using ℓ_p-distances for decision and ℓ_q-threat models for certification for p,q ∈{1,2,∞}. In particular we provide scalable algorithms for the exact computation of the minimal adversarial perturbation when using ℓ_2-distance and improved lower bounds in other cases. Using efficient improved lower bounds we train our Provably adversarially robust NPC (PNPC), for MNIST which have better ℓ_2-robustness guarantees than neural networks. Additionally, we show up to our knowledge the first certification results w.r.t. to the LPIPS perceptual metric which has been argued to be a more realistic threat model for image classification than ℓ_p-balls. Our PNPC has on CIFAR10 higher certified robust accuracy than the empirical robust accuracy reported in (Laidlaw et al., 2021). The code is available in our repository.
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