Graph Neural Aggregation-diffusion with Metastability
This addresses over-smoothing issues in graph neural networks for researchers and practitioners, representing an incremental improvement by generalizing existing diffusion-based models.
The paper tackles the problem of over-smoothing in graph neural networks by proposing GRADE, a model based on graph aggregation-diffusion equations that induces metastability in node representations, allowing features to cluster and persist over time, which alleviates over-smoothing as evidenced by enhanced Dirichlet energy.
Continuous graph neural models based on differential equations have expanded the architecture of graph neural networks (GNNs). Due to the connection between graph diffusion and message passing, diffusion-based models have been widely studied. However, diffusion naturally drives the system towards an equilibrium state, leading to issues like over-smoothing. To this end, we propose GRADE inspired by graph aggregation-diffusion equations, which includes the delicate balance between nonlinear diffusion and aggregation induced by interaction potentials. The node representations obtained through aggregation-diffusion equations exhibit metastability, indicating that features can aggregate into multiple clusters. In addition, the dynamics within these clusters can persist for long time periods, offering the potential to alleviate over-smoothing effects. This nonlinear diffusion in our model generalizes existing diffusion-based models and establishes a connection with classical GNNs. We prove that GRADE achieves competitive performance across various benchmarks and alleviates the over-smoothing issue in GNNs evidenced by the enhanced Dirichlet energy.