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We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class ofcontinuous-depth graph neural networks (GNNs) that employs the Kuramoto modelto mitigate the over-smoothing phenomenon, in which node features in GNNsbecome indistinguishable as the number of layers increases. The Kuramoto modelcaptures the synchronization behavior of non-linear coupled oscillators. Underthe view of coupled oscillators, we first show the connection between Kuramotomodel and basic GNN and then over-smoothing phenomenon in GNNs can beinterpreted as phase synchronization in Kuramoto model. The KuramotoGNNreplaces this phase synchronization with frequency synchronization to preventthe node features from converging into each other while allowing the system toreach a stable synchronized state. We experimentally verify the advantages ofthe KuramotoGNN over the baseline GNNs and existing methods in reducingover-smoothing on various graph deep learning benchmark tasks.

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