<ul><li>Hypergraphs model higher-order relationships in natural phenomena by capturing complex interactions beyond pairwise connections.</li><li>A novel hypergraph message passing framework inspired by interacting particle systems is introduced, where hyperedges induce shared node dynamics.</li><li>Incorporating attraction, repulsion, and Allen-Cahn forcing terms enables particles of varying classes to achieve class-dependent equilibrium for separability through particle-driven message passing.</li><li>The approach includes first-order and second-order particle system equations to capture complete interactions, with the more stable second-order system allowing deeper message passing.</li></ul>

How Particle System Theory Enhances Hypergraph Message Passing

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