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Despite much effort, deep neural networks remain highly susceptible to tinyinput perturbations and even for MNIST, one of the most common toy datasets incomputer vision, no neural network model exists for which adversarialperturbations are large and make semantic sense to humans. We show that eventhe 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 L0perturbations), (2) classifies unrecognizable images with high certainty, (3)performs not much better than simple input binarization and (4) featuresadversarial perturbations that make little sense to humans. These resultssuggest that MNIST is far from being solved in terms of adversarial robustness.We present a novel robust classification model that performs analysis bysynthesis using learned class-conditional data distributions. We derive boundson the robustness and go to great length to empirically evaluate our modelusing maximally effective adversarial attacks by (a) applying decision-based,score-based, gradient-based and transfer-based attacks for several different Lpnorms, (b) by designing a new attack that exploits the structure of ourdefended model and (c) by devising a novel decision-based attack that seeks tominimize the number of perturbed pixels (L0). The results suggest that ourapproach yields state-of-the-art robustness on MNIST against L0, L2 andL-infinity perturbations and we demonstrate that most adversarial examples arestrongly perturbed towards the perceptual boundary between the original and theadversarial class.

Towards the first adversarially robust neural network model on MNIST