  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.
