GREAD: Graph Neural Reaction-Diffusion Networks

25 Nov 2022  ·  Jeongwhan Choi, Seoyoung Hong, Noseong Park, Sung-Bae Cho ·

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 notorious 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 28 baselines, our method, called GREAD, outperforms them in a majority of cases. Further synthetic data experiments show that it mitigates the oversmoothing problem and works well for various homophily rates.

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification Chameleon (48%/32%/20% fixed splits) GREAD-BS Accuracy 67.98 # 1
Node Classification Citeseer (48%/32%/20% fixed splits) GREAD-BS Accuracy 77.53 # 1
Node Classification Cora (48%/32%/20% fixed splits) GREAD-BS Accuracy 88.39 # 1
Node Classification Cornell (48%/32%/20% fixed splits) GREAD-BS Accuracy 86.22 # 2
Node Classification Cornell (48%/32%/20% fixed splits) GREAD-AC Accuracy 87.03 # 1
Node Classification Cornell (48%/32%/20% fixed splits) GREAD-F Accuracy 85.41 # 3
Node Classification Film(48%/32%/20% fixed splits) GREAD-BS Accuracy 37.49 # 1
Node Classification PubMed (48%/32%/20% fixed splits) GREAD-BS Accuracy 90.21 # 1
Node Classification Squirrel (48%/32%/20% fixed splits) GREAD-BS Accuracy 51.01 # 1
Node Classification Texas (48%/32%/20% fixed splits) GREAD-BS Accuracy 87.57 # 2
Node Classification Texas (48%/32%/20% fixed splits) GREAD-F Accuracy 88.11 # 1
Node Classification Wisconsin (48%/32%/20% fixed splits) GREAD-BS Accuracy 88.04 # 1
Node Classification Wisconsin (48%/32%/20% fixed splits) GREAD-F Accuracy 86.47 # 2

Methods