We introduce the concept of provably robust adversarial examples for deep neural networks – connected input regions constructed from standard adversarial examples which are guaranteed to be robust to a set of real-world perturbations (such as changes in pixel intensity and geometric transformations). We present a novel method called PARADE for generating these regions in a scalable manner which works by iteratively refining the region initially obtained via sampling until a refined region is certified to be adversarial with existing state-of-the-art verifiers. At each step, a novel optimization procedure is applied to maximize the region’s volume under the constraint that the convex relaxation of the network behavior with respect to the region implies a chosen bound on the certification objective. Our experimental evaluation shows the effectiveness of PARADE: it successfully finds large provably robust regions including ones containing approximately $10^{573}$ adversarial examples for pixel intensity and $10^{599}$ for geometric perturbations. The provability enables our robust examples to be significantly more effective against state-of-the-art defenses based on randomized smoothing than the individual attacks used to construct the regions.

@inproceedings{ dimitrov2022provably, title={Provably Robust Adversarial Examples}, author={Dimitar Iliev Dimitrov and Gagandeep Singh and Timon Gehr and Martin Vechev}, booktitle={International Conference on Learning Representations}, year={2022}, url={https://openreview.net/forum?id=UMfhoMtIaP5} }