GREAD: Graph Neural Reaction-Diffusion Equations

Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for designing the core processing layer of GNNs and therefore, they are inevitably vulnerable to the oversmoothing problem. Recently, a couple of papers paid attention to reaction equations in conjunctions with diffusion equations. However, they all consider limited forms of reaction equations. To this end, we present a reaction-diffusion equation-based GNN method that considers all popular types of reaction equations in addition to one special reaction equation designed by us. To our knowledge, our paper is one of the most comprehensive studies on reaction-diffusion equation-based GNNs. In our experiments with 9 datasets and 17 baselines, our method, called GREAD, outperforms them in almost all cases. Further synthetic data experiments show that GREAD mitigates the oversmoothing and performs well for various homophily rates.