We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear forced and damped oscillators, coupled via the adjacency structure of the underlying graph. The flexibility of our framework permits any basic GNN layer (e.g. convolutional or attentional) as the coupling function, from which a multi-layer deep neural network is built up via the dynamics of the proposed ODEs. We relate the oversmoothing problem, commonly encountered in GNNs, to the stability of steady states of the underlying ODE and show that zero-Dirichlet energy steady states are not stable for our proposed ODEs. This demonstrates that the proposed framework mitigates the oversmoothing problem. Finally, we show that our approach offers competitive performance with respect to the state-of-the-art on a variety of graph-based learning tasks.

提出了一种名为Graph-Coupled Oscillator Networks（GraphCON）的新型用于图上深度学习的框架，该框架基于二阶常微分方程（ODEs）的离散化模型，模拟了通过底层图的邻接结构耦合的非线性控制和阻尼振荡器网络，并且解决了过度平滑问题和梯度消失问题。

图耦合振荡器网络