Framelet Message Passing
This work addresses stability and oversmoothing issues in GNNs for applications like heterogeneous graph learning, though it appears incremental as it builds on existing message passing and neural ODE frameworks.
The authors tackled the problem of oversmoothing and instability in graph neural networks by proposing Framelet Message Passing, which integrates multiscale framelet transforms and neural ODE solvers, resulting in state-of-the-art performance on node classification tasks with low computational costs.
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.