Fast and Accurate Temporal Hypergraph Representation for Hyperedge Prediction

Temporal hypergraph representation learning is a concept that integrates high-order structure learning with temporal dynamics, enabling more accurate analysis of temporal and high-order interactions. To enhance model expressiveness, the latest work samples multi-hop hyperedge-centric neighbors directly from temporal hypergraphs and encodes them for high-order structure learning, achieving promising performance. Such modeling, however, incurs prohibitive computational complexity, which increases exponentially with model depth and quadratically with average hyperedge cardinality, thereby limiting model scalability. In this paper, we propose FastHeP, a fast and accurate approach for temporal hyperedge prediction, which can handle large temporal hypergraphs. The key idea is to minimize computational complexity while maintaining model expressiveness. Concretely, we design an online hyperedge-centric neighbor store, which can store time-aware and redundancy-aware neighbors for nodes with rational theoretical guarantees. Upon the neighbor store, we propose a novel hybrid message passing to model temporal high-order structures, theoretically preserving strong expressive power. This explicitly learns local high-order structures for nodes of each hyperedge via graph attention, generating the node-wise structure features. These structure features are then fused into global correlations modeling among hyperedges, with a theoretical guarantee of permutation invariance. Last, FastHeP leverages local and global high-order semantics to generate temporal hyperedge embeddings, which is efficient in a linear complexity w.r.t. model depth and average hyperedge cardinality. Extensive experiments show that FastHeP achieves up to two orders of magnitude speed-up against baselines, with an average accuracy improvement of 5.1%.