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Neural diffusion on graphs is a novel class of graph neural networks that hasattracted increasing attention recently. The capability of graph neural partialdifferential equations (PDEs) in addressing common hurdles of graph neuralnetworks (GNNs), such as the problems of over-smoothing and bottlenecks, hasbeen investigated but not their robustness to adversarial attacks. In thiswork, we explore the robustness properties of graph neural PDEs. We empiricallydemonstrate that graph neural PDEs are intrinsically more robust againsttopology perturbation as compared to other GNNs. We provide insights into thisphenomenon by exploiting the stability of the heat semigroup under graphtopology perturbations. We discuss various graph diffusion operators and relatethem to existing graph neural PDEs. Furthermore, we propose a general graphneural PDE framework based on which a new class of robust GNNs can be defined.We verify that the new model achieves comparable state-of-the-art performanceon several benchmark datasets.

On the Robustness of Graph Neural Diffusion to Topology Perturbations