Adversarial Attacks on Hyperbolic Networks

Abstract: As hyperbolic deep learning grows in popularity, so does the need for adversarial robustness in the context of such a non-Euclidean geometry. To this end, this paper proposes hyperbolic alternatives to the commonly used FGM and PGD adversarial attacks. Through interpretable synthetic benchmarks and experiments on existing datasets, we show how the existing and newly proposed attacks differ. Moreover, we investigate the differences in adversarial robustness between Euclidean and fully hyperbolic networks. We find that these networks suffer from different types of vulnerabilities and that the newly proposed hyperbolic attacks cannot address these differences. Therefore, we conclude that the shifts in adversarial robustness are due to the models learning distinct patterns resulting from their different geometries.