On the robustness of graph neural diffusion to topology perturbations

• Main Authors: Song, Yang, Kang, Qiyu, Wang, Sijie, Zhao, Kai, Tay, Wee Peng
• Other Authors: School of Electrical and Electronic Engineering
• Format: Conference or Workshop Item
• Language: English
• Published: 2023
• Subjects: Engineering::Computer science and engineering::Computing methodologies::Artificial intelligence; Graph Neural Networks; Deep Learning
• Online Access: https://hdl.handle.net/10356/166693; https://proceedings.neurips.cc/; https://nips.cc/Conferences/2022
• Institution: Nanyang Technological University

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.