从耦合振子到图神经网络：通过基于Kuramoto模型的方法缓解过平滑
From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach
AI总结：
针对图神经网络层数增加引发的过平滑问题，提出基于Kuramoto模型的KuramotoGNN，以频率同步替代相位同步缓解过平滑，实验验证其在多基准任务上优于现有方法。
摘要：
我们提出Kuramoto图神经网络（KuramotoGNN），这是一类新型的连续深度图神经网络（GNN），采用Kuramoto模型来缓解过平滑现象——即随着层数增加，GNN中的节点特征会变得难以区分。Kuramoto模型用于刻画非线性耦合振子的同步行为。在耦合振子视角下，我们首先阐明了Kuramoto模型与基础GNN之间的联系，进而指出GNN中的过平滑现象可被解释为Kuramoto模型中的相位同步。KuramotoGNN用频率同步替代这种相位同步，在允许系统达到稳定同步状态的同时，防止节点特征相互趋同。我们在多种图深度学习基准任务上通过实验验证了KuramotoGNN在缓解过平滑方面优于基线GNN和现有方法的优势。
英文摘要：
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.
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