EP4: Machine Learning on Structures

Chaired by Prof. Shi JIN, this 4th webinar invites Prof. Yu Guang WANG and Prof. Zheng MA to present their latest research about Machine Learning on Structures. Allen-Cahn Messsage Passing on Graphs and Hypergraphs via Particle System Theory We introduce a novel message passing framework for graphs and hypergraphs inspired by interacting particle system theory. This approach models neural message passing as a system of particles subject to attractive, repulsive, and Allen-Cahn forces, which arise in phase transition models. The resulting reaction-diffusion dynamics enable the separation of particles into class-dependent equilibria, forming the basis for Allen-Cahn Message Passing (ACMP). A key contribution of ACMP is its proven ability to mitigate the oversmoothing problem in Graph Neural Networks (GNNs) by maintaining a strictly positive lower bound on the Dirichlet energy. This allows for the construction of very deep GNNs, with hundreds of layers, implemented easily with neural ODE solvers. We extend this model to hypergraphs, where hyperedges create fields that induce shared dynamics among nodes, capturing complex higher-order interactions. Investigating both first and second-order particle system equations, we find the latter offers more stability for deeper message passing. The framework is further enhanced with stochastic elements to handle interaction uncertainties. Our models demonstrate state-of-the-art performance on a variety of real-world node classification tasks, showing strong results on both homophilic and heterophilic datasets for graphs and hypergraphs alike.