  Graph neural networks (GNNs) have recently been shown to be vulnerable to
adversarial attacks, where slight perturbations in the graph structure can lead
to erroneous predictions. However, current robust models for defending against
such attacks inherit the transductive limitations of graph convolutional
networks (GCNs). As a result, they are constrained by fixed structures and do
not naturally generalize to unseen nodes. Here, we discover that transductive
GCNs inherently possess a distillable robustness, achieved through a
wave-induced resonance process. Based on this, we foster this resonance to
facilitate inductive and robust learning. Specifically, we first prove that the
signal formed by GCN-driven message passing (MP) is equivalent to the
edge-based Laplacian wave, where, within a wave system, resonance can naturally
emerge between the signal and its transmitting medium. This resonance provides
inherent resistance to malicious perturbations inflicted on the signal system.
We then prove that merely three MP iterations within GCNs can induce signal
resonance between nodes and edges, manifesting as a coupling between nodes and
their distillable surrounding local subgraph. Consequently, we present Graph
Resonance-fostering Network (GRN) to foster this resonance via learning node
representations from their distilled resonating subgraphs. By capturing the
edge-transmitted signals within this subgraph and integrating them with the
node signal, GRN embeds these combined signals into the central node's
representation. This node-wise embedding approach allows for generalization to
unseen nodes. We validate our theoretical findings with experiments, and
demonstrate that GRN generalizes robustness to unseen nodes, whilst maintaining
state-of-the-art classification accuracy on perturbed graphs.
