HP-GMN: Graph Memory Networks for Heterophilous Graphs

Graph neural networks (GNNs) have achieved great success in various graph problems. However, most GNNs are Message Passing Neural Networks (MPNNs) based on the homophily assumption, where nodes with the same label are connected in graphs. Real-world problems bring us heterophily problems, where nodes with different labels are connected in graphs. MPNNs fail to address the heterophily problem because they mix information from different distributions and are not good at capturing global patterns. Therefore, we investigate a novel Graph Memory Networks model on Heterophilous Graphs (HP-GMN) to the heterophily problem in this paper. In HP-GMN, local information and global patterns are learned by local statistics and the memory to facilitate the prediction. We further propose regularization terms to help the memory learn global information. We conduct extensive experiments to show that our method achieves state-of-the-art performance on both homophilous and heterophilous graphs.