Towards the first adversarially robust neural network model on MNIST

TL;DR

This paper introduces a novel neural network model that significantly improves adversarial robustness on MNIST by analyzing class-conditional data distributions and employing comprehensive attack evaluations.

Contribution

The paper presents a new robust classification approach using analysis by synthesis, with theoretical bounds and extensive empirical testing against various adversarial attacks.

Findings

Achieves state-of-the-art robustness on MNIST for L0, L2, and L-infinity attacks.

Most adversarial examples are near the perceptual boundary between classes.

Existing defenses like Madry et al. overfit and are vulnerable to different perturbation norms.

Abstract

Despite much effort, deep neural networks remain highly susceptible to tiny input perturbations and even for MNIST, one of the most common toy datasets in computer vision, no neural network model exists for which adversarial perturbations are large and make semantic sense to humans. We show that even the widely recognized and by far most successful defense by Madry et al. (1) overfits on the L-infinity metric (it's highly susceptible to L2 and L0 perturbations), (2) classifies unrecognizable images with high certainty, (3) performs not much better than simple input binarization and (4) features adversarial perturbations that make little sense to humans. These results suggest that MNIST is far from being solved in terms of adversarial robustness. We present a novel robust classification model that performs analysis by synthesis using learned class-conditional data distributions. We derive bounds on the robustness and go to great length to empirically evaluate our model using maximally effective adversarial attacks by (a) applying decision-based, score-based, gradient-based and transfer-based attacks for several different Lp norms, (b) by designing a new attack that exploits the structure of our defended model and (c) by devising a novel decision-based attack that seeks to minimize the number of perturbed pixels (L0). The results suggest that our approach yields state-of-the-art robustness on MNIST against L0, L2 and L-infinity perturbations and we demonstrate that most adversarial examples are strongly perturbed towards the perceptual boundary between the original and the adversarial class.