HC-Ref: Hierarchical Constrained Refinement for Robust Adversarial Training of GNNs

Recent studies have shown that attackers can catastrophically reduce the performance of GNNs by maliciously modifying the graph structure or node features on the graph. Adversarial training, which has been shown to be one of the most effective defense mechanisms against adversarial attacks in computer vision, holds great promise for enhancing the robustness of GNNs. There is limited research on defending against attacks by performing adversarial training on graphs, and it is crucial to delve deeper into this approach to optimize its effectiveness. Therefore, based on robust adversarial training on graphs, we propose a hierarchical constraint refinement framework (HC-Ref) that enhances the anti-perturbation capabilities of GNNs and downstream classifiers separately, ultimately leading to improved robustness. We propose corresponding adversarial regularization terms that are conducive to adaptively narrowing the domain gap between the normal part and the perturbation part according to the characteristics of different layers, promoting the smoothness of the predicted distribution of both parts. Moreover, existing research on graph robust adversarial training primarily concentrates on training from the standpoint of node feature perturbations and seldom takes into account alterations in the graph structure. This limitation makes it challenging to prevent attacks based on topological changes in the graph. This paper generates adversarial examples by utilizing graph structure perturbations, offering an effective approach to defend against attack methods that are based on topological changes. Extensive experiments on two real-world graph benchmarks show that HC-Ref successfully resists various attacks and has better node classification performance compared to several baseline methods.