Provably Robust Node Classification via Low-Pass Message Passing

Abstract

Graph Convolutional Networks (GCNs) have achieved state-of-the-art performance on node classification. However, recent works have shown that GCNs are vulnerable to adversarial attacks, such as additions or deletions of adversarially-chosen edges in the graph, in order to mislead the node classification algorithms. How can we design robust GCNs that are resistant to such adversarial attacks? More challengingly, how can we do this in a way that is provably robust? We propose a robust node classification approach based on a low-pass `message passing' mechanism, that (a) reduces the effectiveness of adversarial attacks in experiments, and (b) provides theoretical guarantees against adversarial attacks. Our approach can be embedded into the existing GCN architectures to enhance their robustness. Empirical results show that our loss-pass method effectively improves the performance of multiple GCNs under miscellaneous perturbations and helps them to achieve superior performance on various graphs.