GREAD: Graph Neural Reaction-Diffusion Networks

Jeongwhan Choi, Seoyoung Hong, Noseong Park, Sung-Bae Cho
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5722-5747, 2023.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-choi23a, title = {{GREAD}: Graph Neural Reaction-Diffusion Networks}, author = {Choi, Jeongwhan and Hong, Seoyoung and Park, Noseong and Cho, Sung-Bae}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {5722--5747}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/choi23a/choi23a.pdf}, url = {https://proceedings.mlr.press/v202/choi23a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T GREAD: Graph Neural Reaction-Diffusion Networks %A Jeongwhan Choi %A Seoyoung Hong %A Noseong Park %A Sung-Bae Cho %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-choi23a %I PMLR %P 5722--5747 %U https://proceedings.mlr.press/v202/choi23a.html %V 202 %X 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.
APA
Choi, J., Hong, S., Park, N. & Cho, S.. (2023). GREAD: Graph Neural Reaction-Diffusion Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:5722-5747 Available from https://proceedings.mlr.press/v202/choi23a.html.

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