How Particle System Theory Enhances Hypergraph Message Passing

• URL: http://arxiv.org/abs/2505.18505v1
• Date: Sat, 24 May 2025 05:04:25 GMT
• Title: How Particle System Theory Enhances Hypergraph Message Passing
• Authors: Yixuan Ma, Kai Yi, Pietro Lio, Shi Jin, Yu Guang Wang,
• Abstract summary: Hypergraphs effectively model higher-order relationships in natural phenomena, capturing complex interactions beyond pairwise connections.<n>We introduce a novel hypergraph message passing framework inspired by interacting particle systems, where hyperedges act as fields inducing shared node dynamics.
• Score: 30.792540956996444
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hypergraphs effectively model higher-order relationships in natural phenomena, capturing complex interactions beyond pairwise connections. We introduce a novel hypergraph message passing framework inspired by interacting particle systems, where hyperedges act as fields inducing shared node dynamics. By incorporating attraction, repulsion, and Allen-Cahn forcing terms, particles of varying classes and features achieve class-dependent equilibrium, enabling separability through the particle-driven message passing. We investigate both first-order and second-order particle system equations for modeling these dynamics, which mitigate over-smoothing and heterophily thus can capture complete interactions. The more stable second-order system permits deeper message passing. Furthermore, we enhance deterministic message passing with stochastic element to account for interaction uncertainties. We prove theoretically that our approach mitigates over-smoothing by maintaining a positive lower bound on the hypergraph Dirichlet energy during propagation and thus to enable hypergraph message passing to go deep. Empirically, our models demonstrate competitive performance on diverse real-world hypergraph node classification tasks, excelling on both homophilic and heterophilic datasets.

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