Graph neural networks (GNNs) have achieved champion 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. It turns both discrete and continuous cases can provably achieve network stability and limit oversmoothing due to the multiscale property of framelets. 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.

本研究提出了一种基于多尺度小波变换的新型消息传递方法，即Framelet Message Passing，并结合神经ODE求解器进行连续消息传递，证明了离散和连续情况均可实现网络稳定性和限制过度平滑，并在学习异构图时显著优于现有方法，在低计算成本下达到了经典节点分类任务的最新水平。

Framelet消息传递