Graph-Coupled Oscillator Networks

T. Konstantin Rusch*, Benjamin P. Chamberlain, James Rowbottom, Siddhartha Mishra, Michael M. Bronstein

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish
Pages (from-to)18888-18909
Number of pages22
JournalProceedings of Machine Learning Research
StatePublished - 2022
Externally publishedYes
Event39th International Conference on Machine Learning, ICML 2022 - Baltimore, United States
Duration: 17 Jul 202223 Jul 2022


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