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Graph neural networks (GNNs) have recently been shown to be vulnerable toadversarial attacks, where slight perturbations in the graph structure can leadto erroneous predictions. However, current robust models for defending againstsuch attacks inherit the transductive limitations of graph convolutionalnetworks (GCNs). As a result, they are constrained by fixed structures and donot naturally generalize to unseen nodes. Here, we discover that transductiveGCNs inherently possess a distillable robustness, achieved through awave-induced resonance process. Based on this, we foster this resonance tofacilitate inductive and robust learning. Specifically, we first prove that thesignal formed by GCN-driven message passing (MP) is equivalent to theedge-based Laplacian wave, where, within a wave system, resonance can naturallyemerge between the signal and its transmitting medium. This resonance providesinherent resistance to malicious perturbations inflicted on the signal system.We then prove that merely three MP iterations within GCNs can induce signalresonance between nodes and edges, manifesting as a coupling between nodes andtheir distillable surrounding local subgraph. Consequently, we present GraphResonance-fostering Network (GRN) to foster this resonance via learning noderepresentations from their distilled resonating subgraphs. By capturing theedge-transmitted signals within this subgraph and integrating them with thenode signal, GRN embeds these combined signals into the central node'srepresentation. This node-wise embedding approach allows for generalization tounseen nodes. We validate our theoretical findings with experiments, anddemonstrate that GRN generalizes robustness to unseen nodes, whilst maintainingstate-of-the-art classification accuracy on perturbed graphs.

Towards Inductive Robustness: Distilling and Fostering Wave-induced Resonance in Transductive GCNs Against Graph Adversarial Attacks