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

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.

Graph Agent Network: Empowering Nodes with Decentralized Communications Capabilities for Adversarial Resilience

End-to-end training with global optimization have popularized graph neural networks (GNNs) for node classification, yet inadvertently introduced vulnerabilities to adversarial edge-perturbing attacks. Adversaries can exploit the inherent opened interfaces of GNNs' input and output, perturbing critical edges and thus manipulating the classification results. Current defenses, due to their persistent utilization of global-optimization-based end-to-end training schemes, inherently encapsulate the vulnerabilities of GNNs. This is specifically evidenced in their inability to defend against targeted secondary attacks. In this paper, we propose the Graph Agent Network (GAgN) to address the aforementioned vulnerabilities of GNNs. GAgN is a graph-structured agent network in which each node is designed as an 1-hop-view agent. Through the decentralized interactions between agents, they can learn to infer global perceptions to perform tasks including inferring embeddings, degrees and neighbor relationships for given nodes. This empowers nodes to filtering adversarial edges while carrying out classification tasks. Furthermore, agents' limited view prevents malicious messages from propagating globally in GAgN, thereby resisting global-optimization-based secondary attacks. We prove that single-hidden-layer multilayer perceptrons (MLPs) are theoretically sufficient to achieve these functionalities. Experimental results show that GAgN effectively implements all its intended capabilities and, compared to state-of-the-art defenses, achieves optimal classification accuracy on the perturbed datasets.