Neural message passing is a basic feature extraction unit for graph-structured data that takes account of the impact of 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 system is a reaction-diffusion process which can separate particles to different clusters. This induces an Allen-Cahn message passing (ACMP) for graph neural networks where the numerical iteration for the solution constitutes the message passing propagation. The mechanism behind ACMP is phase transition of particles which enables the formation of multi-clusters and thus GNNs prediction for node classification. ACMP can propel the network depth to hundreds of layers with theoretically proven strictly positive lower bound of the Dirichlet energy. It thus provides a deep model of GNNs which circumvents the common GNN problem of oversmoothing. Experiments for various real node classification datasets, with possible high homophily difficulty, show the GNNs with ACMP can achieve state of the art performance with no decay of Dirichlet energy.

本论文提出基于相互作用粒子系统的Allen-Cahn消息传递机制，通过多个聚类形成的方式解决节点预测的问题，从而可以在图神经网络中实现数百层的深度，并解决常见问题中的过度平滑。经过实验验证，在各种实际节点分类数据集上，此机制性能达到了最先进的水平，而且没有能量耗散的问题。

ACMP：具有粒子相变的图神经网络的Allen-Cahn信息传递