🤖 AI Summary
To address over-smoothing in deep graph neural networks (GNNs), this paper proposes Attraction-Repulsion Phase-Transition Message Passing (ACMP), the first framework to incorporate the Allen–Cahn phase-field equation into GNN message passing. ACMP establishes a novel propagation paradigm grounded in reaction-diffusion partial differential equations (PDEs) and particle dynamics. Theoretically, we prove that the Dirichlet energy of ACMP admits a strict positive lower bound, fundamentally suppressing feature homogenization and enabling stable training beyond 100 layers. Implementation employs a neural ODE solver for robust discretization, unifying attraction/repulsion forces and phase-transition driving forces within a single differentiable architecture. Empirically, ACMP achieves state-of-the-art performance on node classification across both homophilic and heterophilic graph benchmarks. Critically, its 100-layer variant exhibits no performance degradation, significantly enhancing the expressive power and generalization capability of deep GNNs.
📝 Abstract
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.
