Adversarial Attacks on Hyperbolic Networks

TL;DR

This paper introduces hyperbolic-specific adversarial attacks and compares their effectiveness to Euclidean models, revealing that hyperbolic networks have unique vulnerabilities and robustness characteristics.

Contribution

It proposes new hyperbolic adversarial attack methods and analyzes the robustness differences between hyperbolic and Euclidean networks.

Findings

Hyperbolic networks exhibit distinct vulnerabilities from Euclidean networks.

Existing attacks are less effective on hyperbolic models due to geometric differences.

Hyperbolic attacks reveal unique robustness patterns in 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.