GCNH: A Simple Method For Representation Learning On Heterophilous Graphs

Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open research problem. Recent works have proposed extensions to standard GNN architectures to improve performance on heterophilous graphs, trading off model simplicity for prediction accuracy. However, these models fail to capture basic graph properties, such as neighborhood label distribution, which are fundamental for learning. In this work, we propose GCN for Heterophily (GCNH), a simple yet effective GNN architecture applicable to both heterophilous and homophilous scenarios. GCNH learns and combines separate representations for a node and its neighbors, using one learned importance coefficient per layer to balance the contributions of center nodes and neighborhoods. We conduct extensive experiments on eight real-world graphs and a set of synthetic graphs with varying degrees of heterophily to demonstrate how the design choices for GCNH lead to a sizable improvement over a vanilla GCN. Moreover, GCNH outperforms state-of-the-art models of much higher complexity on four out of eight benchmarks, while producing comparable results on the remaining datasets. Finally, we discuss and analyze the lower complexity of GCNH, which results in fewer trainable parameters and faster training times than other methods, and show how GCNH mitigates the oversmoothing problem.