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 ∞ metric (it's highly susceptible to L 2 and L 0 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 decisionbased, score-based, gradient-based and transfer-based attacks for several different L p 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 (L 0 ). The results suggest that our approach yields state-of-the-art robustness on MNIST against L 0 , L 2 and L ∞ perturbations and we demonstrate that most adversarial examples are strongly perturbed towards the perceptual boundary between the original and the adversarial class.
In REF a generative model was used not just for adversarial detection but also robust classification on MNIST, leading to state-of-the-art robust classification accuracy.
Towards the first adversarially robust neural network model on MNIST
ICLR 2019
arXiv: Computer Vision and Pattern Recognition
Computer Science