  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
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.
