Framelet message passing

• Published in: Applied and computational harmonic analysis Vol. 78; p. 101773
• Main Authors: Liu, Xinliang, Zhou, Bingxin, Zhang, Chutian, Wang, Yu Guang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.08.2025
• Subjects: Framelet transforms; Graph neural networks; Neural message passing; Oversmoothing; Spectral graph neural network; Stability; Graph neural networks; Neural message passing; Stability; Framelet transforms; Spectral graph neural network; Oversmoothing
• ISSN: 1063-5203
• DOI: 10.1016/j.acha.2025.101773

Graph neural networks have achieved champions in wide applications. Neural message passing is a typical key module for feature propagation by aggregating neighboring features. In this work, we propose a new message passing based on multiscale framelet transforms, called Framelet Message Passing. Different from traditional spatial methods, it integrates framelet representation of neighbor nodes from multiple hops away in node message update. We also propose a continuous message passing using neural ODE solvers. Both discrete and continuous cases can provably mitigate oversmoothing and achieve superior performance. Numerical experiments on real graph datasets show that the continuous version of the framelet message passing significantly outperforms existing methods when learning heterogeneous graphs and achieves state-of-the-art performance on classic node classification tasks with low computational costs.