On the Relationship between Heterophily and Robustness of Graph Neural Networks.

Empirical studies on the robustness of graph neural networks (GNNs) have suggested a relation between the vulnerabilities of GNNs to adversarial attacks and the increased presence of heterophily in perturbed graphs (where edges tend to connect nodes with dissimilar features and labels). In this work, we formalize the relation between heterophily and robustness, bridging two topics previously investigated by separate lines of research. We theoretically and empirically show that for graphs exhibiting homophily (low heterophily), impactful structural attacks always lead to increased levels of heterophily, while for graph with heterophily the change in the homophily level depends on the node degrees. By leveraging these insights, we deduce that a design principle identified to significantly improve predictive performance under heterophily -- separate aggregators for ego- and neighbor-embeddings -- can also inherently offer increased robustness to GNNs. Our extensive empirical analysis shows that GNNs adopting this design alone can achieve significantly improved empirical and certifiable robustness compared to the best-performing unvaccinated model. Furthermore, models with this design can be readily combined with explicit defense mechanisms to yield improved robustness with up to 18.33% increase in performance under attacks compared to the best-performing vaccinated model.