Towards the first adversarially robust neural network model on MNIST

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.

Wieland Brendel

Principal Investigator (PI)

Wieland Brendel received his Diploma in physics from the University of Regensburg (2010) and his Ph.D. in computational neuroscience from the École normale supérieure in Paris (2014). He joined the University of Tübingen as a postdoctoral researcher in the group of Matthias Bethge, became a Principal Investigator and Team Lead in the Tübingen AI Center (2018) and an Emmy Noether Group Leader for Robust Machine Learning (2020). In May 2022, Wieland joined the Max-Planck Institute for Intelligent Systems as an independent Group Leader and is now a Hector-endowed Fellow at the ELLIS Institute Tübingen (since September 2023). He received the 2023 German Pattern Recognition Award for his substantial contributions on robust, generalisable and interpretable machine vision. Aside of his research, Wieland co-founded a nationwide school competition (bw-ki.de) and a machine learning startup focused on visual quality control.