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.

我们提出了Kuramoto Graph Neural Network(KuramotoGNN)，一种新颖的连续深度图神经网络(GNN)，它采用Kuramoto模型来减轻过度平滑现象，在GNN中，随着层数的增加，节点特征变得无法区分。Kuramoto模型捕捉了非线性耦合振荡器的同步行为。通过耦合振荡器的视角，我们首先展示了Kuramoto模型与基本GNN之间的联系，然后证明了GNN中的过度平滑现象可以解释为Kuramoto模型中的相位同步。KuramotoGNN通过频率同步来替代相位同步，防止节点特征收敛到彼此，同时允许系统达到稳定的同步状态。我们在各种图深度学习基准任务上实验证明了KuramotoGNN相对于基准GNN和现有方法在减少过度平滑方面的优势。

从耦合振子到图神经网络: 通过库拉莫托模型方法减少过度平滑