Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural 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 performance on several benchmark datasets.

翻译：图上的神经扩散是一类新型图神经网络，近年来日益受到关注。图神经偏微分方程（PDEs）在解决图神经网络（GNNs）的常见难题（如过平滑和瓶颈问题）方面的能力已得到研究，但其对对抗攻击的鲁棒性尚未被探索。本文研究了图神经PDEs的鲁棒性特性。我们通过实验证明，与其他GNNs相比，图神经PDEs对拓扑扰动具有内在更强的鲁棒性。我们利用热半群在图拓扑扰动下的稳定性来阐释这一现象。我们讨论了各种图扩散算子，并将其与现有图神经PDEs建立关联。此外，我们提出一个通用图神经PDE框架，可据此定义一类新的鲁棒GNNs。我们验证了新模型在多个基准数据集上取得了与现有最优方法相媲美的性能。