HPSO: Particle Swarm Optimization with Hypergraph-Based Topology

What the math gives to ML

The paper's transferable asset is not PSO itself, but the replacement of pairwise communication with explicit multi-way interaction groups represented by a vertex–hyperedge incidence matrix. This can be transplanted into Transformer or MoE layers as a sparse, dynamic routing mechanism: tokens first communicate within hyperedges, then hyperedge summaries are redistributed to member tokens. The adaptive topology idea suggests rebuilding groups from cumulative token displacement, so communication patterns follow changing representation geometry rather than remaining fixed. The extracted mathematics is limited to the incidence representation, so the strongest practical proposal is a controlled hypergraph communication module with empirical topology updates rather than a claimed convergence guarantee.