Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach
This work addresses adversarial robustness in GNNs, a critical issue for applications like social networks and recommendation systems, though it is incremental as it builds on existing neural flow methods.
The paper tackles the vulnerability of graph neural networks (GNNs) to adversarial perturbations by proposing the use of conservative Hamiltonian neural flows to enhance robustness, with experiments showing substantial improvements against various attacks on benchmark datasets.
Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at https://github.com/zknus/NeurIPS-2023-HANG-Robustness.