How Particle System Theory Enhances Hypergraph Message Passing

2025-05-24

AI Summary

To address oversmoothing and heterogeneity in hypergraph message passing—which impair higher-order relational modeling—this paper proposes a novel particle-system-inspired hypergraph neural network. Hyperedges are modeled as interaction fields, and nodes as particles governed by attractive, repulsive, and Allen–Cahn phase-field forces to achieve dynamic equilibrium. We are the first to incorporate first- and second-order Lagrangian particle dynamics into hypergraph learning; theoretically, this preserves a lower bound on the Dirichlet energy to suppress oversmoothing. Moreover, our framework unifies deterministic and stochastic message passing to capture interaction uncertainty. Extensive experiments demonstrate state-of-the-art performance on multiple real-world hypergraph node classification benchmarks. Notably, our method significantly improves generalization on heterophilic graphs and enables deeper network stacking without degradation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• Modeling higher-order interactions in hypergraphs using particle systems
• Mitigating over-smoothing and heterophily in hypergraph message passing
• Enhancing deterministic message passing with stochastic elements for uncertainties

Innovation

• Hypergraph message passing with particle system dynamics
• Class-dependent equilibrium via attraction and repulsion forces
• Second-order equations mitigate over-smoothing and heterophily