Temporal Hypergraph Coarsening with Local Repair and Static-Recomputation Guarantees

Large hypergraphs are increasingly used to model higher-order machine learning data, including group recommendation sessions, temporal hyperlink events, biological co-activation sets, and evolving tag or topic groups. Existing hypergraph coarsening methods reduce hypergraph size, but they are usually applied to a fixed snapshot; when events arrive over time, the standard alternative is to recompute the coarsening from scratch. We study temporal hypergraph coarsening as an incremental maintenance problem. We propose THGC, a framework that maintains a coarsened hypergraph under timestamped event streams through a Temporal Update Engine and a Coarsening Strategy Interface. The repair step is driven by TAPS, a Temporally-Aware Proximity Score that combines recency-weighted Personalized PageRank with a local conductance signal so that repair decisions account for both temporal interaction history and cut structure. The maintained object remains a hypergraph, with coarse hyperedges and incidence structure; graph projections are used only as local scoring surrogates. We give stability bounds relating temporal score drift, coarsening error, and the deviation from full static recomputation. Experimental results on temporal hypergraph benchmarks demonstrate significant speedups in update time while preserving the quality of the coarsened representation.