From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach

Tuan Nguyen, Hirotada Honda, Takashi Sano, Vinh Nguyen, Shugo Nakamura, Tan Minh Nguyen
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2710-2718, 2024.

Abstract

We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become indistinguishable as the number of layers increases. The Kuramoto model captures the synchronization behavior of non-linear coupled oscillators. Under the view of coupled oscillators, we first show the connection between Kuramoto model and basic GNN and then over-smoothing phenomenon in GNNs can be interpreted as phase synchronization in Kuramoto model. The KuramotoGNN replaces this phase synchronization with frequency synchronization to prevent the node features from converging into each other while allowing the system to still reach a stable synchronized state. We experimentally verify the advantages of the KuramotoGNN over the baseline GNNs and existing methods in reducing over-smoothing on various graph deep learning benchmark tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-nguyen24c, title = {From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a {K}uramoto Model-based Approach}, author = {Nguyen, Tuan and Honda, Hirotada and Sano, Takashi and Nguyen, Vinh and Nakamura, Shugo and Minh Nguyen, Tan}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2710--2718}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/nguyen24c/nguyen24c.pdf}, url = {https://proceedings.mlr.press/v238/nguyen24c.html}, abstract = {We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become indistinguishable as the number of layers increases. The Kuramoto model captures the synchronization behavior of non-linear coupled oscillators. Under the view of coupled oscillators, we first show the connection between Kuramoto model and basic GNN and then over-smoothing phenomenon in GNNs can be interpreted as phase synchronization in Kuramoto model. The KuramotoGNN replaces this phase synchronization with frequency synchronization to prevent the node features from converging into each other while allowing the system to still reach a stable synchronized state. We experimentally verify the advantages of the KuramotoGNN over the baseline GNNs and existing methods in reducing over-smoothing on various graph deep learning benchmark tasks.} }
Endnote
%0 Conference Paper %T From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach %A Tuan Nguyen %A Hirotada Honda %A Takashi Sano %A Vinh Nguyen %A Shugo Nakamura %A Tan Minh Nguyen %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-nguyen24c %I PMLR %P 2710--2718 %U https://proceedings.mlr.press/v238/nguyen24c.html %V 238 %X We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become indistinguishable as the number of layers increases. The Kuramoto model captures the synchronization behavior of non-linear coupled oscillators. Under the view of coupled oscillators, we first show the connection between Kuramoto model and basic GNN and then over-smoothing phenomenon in GNNs can be interpreted as phase synchronization in Kuramoto model. The KuramotoGNN replaces this phase synchronization with frequency synchronization to prevent the node features from converging into each other while allowing the system to still reach a stable synchronized state. We experimentally verify the advantages of the KuramotoGNN over the baseline GNNs and existing methods in reducing over-smoothing on various graph deep learning benchmark tasks.
APA
Nguyen, T., Honda, H., Sano, T., Nguyen, V., Nakamura, S. & Minh Nguyen, T.. (2024). From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2710-2718 Available from https://proceedings.mlr.press/v238/nguyen24c.html.

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