Graph-Coupled Oscillator Networks
This addresses the problem of training deep GNNs for researchers and practitioners by mitigating oversmoothing and gradient issues, though it is incremental as it builds on existing GNN layers.
The authors tackled the oversmoothing and gradient problems in deep graph neural networks (GNNs) by proposing Graph-Coupled Oscillator Networks (GraphCON), a framework based on ODEs, which mitigates these issues and offers competitive performance on various graph-based learning tasks.
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 controlled 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. Moreover, we prove that GraphCON mitigates the exploding and vanishing gradients problem to facilitate training of deep multi-layer GNNs. 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.