Hypergraph Pattern Machine: Compositional Tokenization for Higher-Order Interactions

Hypergraphs model higher-order relations that drive real-world decisions, from drug prescriptions to recommendations. A central structural signal in such data, beyond what pairwise relations can express, is interaction compositionality: whether a higher-order relation is compositional, emergent, or inhibitory with respect to its subsets, i.e., whether a set and its one-element-smaller subset are both observed, only the larger one is observed, or only the smaller one is observed. These patterns are read directly from the observed data. In adverse-event reports, for example, they distinguish drug sets whose reported association persists when a drug is added, appears only for the full set, or is absent after adding a drug; these are reporting patterns, not pharmacological mechanisms. However, existing hypergraph learning methods, which propagate messages over observed hyperedges, do not represent unobserved subsets explicitly and leave this signal implicit. To this end, we propose the Hypergraph Pattern Machine (HGPM), which makes the compositional pattern of subsets an explicit part of the input. It tokenizes observed and unobserved subsets around each target, organizes them in an inclusion DAG, and pretrains an inclusion-aware Transformer with masked reconstruction. On ten hypergraph benchmarks, HGPM matches or exceeds state-of-the-art methods. A qualitative case study on adverse-event reports further illustrates how HGPM separates candidate drugs that are close in feature space but have different recorded patterns.