ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks
This addresses the common GNN problem of oversmoothing, allowing for deeper and more effective models in graph-based learning tasks.
The authors tackled the oversmoothing problem in graph neural networks (GNNs) by modeling message passing as an interacting particle system with attractive and repulsive forces, enabling deep networks of up to 100 layers with proven theoretical guarantees. Their ACMP method achieved state-of-the-art performance on node classification tasks across both homophilic and heterophilic datasets.
Neural message passing is a basic feature extraction unit for graph-structured data considering neighboring node features in network propagation from one layer to the next. We model such process by an interacting particle system with attractive and repulsive forces and the Allen-Cahn force arising in the modeling of phase transition. The dynamics of the system is a reaction-diffusion process which can separate particles without blowing up. This induces an Allen-Cahn message passing (ACMP) for graph neural networks where the numerical iteration for the particle system solution constitutes the message passing propagation. ACMP which has a simple implementation with a neural ODE solver can propel the network depth up to one hundred of layers with theoretically proven strictly positive lower bound of the Dirichlet energy. It thus provides a deep model of GNNs circumventing the common GNN problem of oversmoothing. GNNs with ACMP achieve state of the art performance for real-world node classification tasks on both homophilic and heterophilic datasets. Codes are available at https://github.com/ykiiiiii/ACMP.