Learning Brain Hypergraphs from Pairwise-Irreducible Interactions

Brain hypergraph and other higher-order models aim to capture information beyond pairwise functional connectivity. Current methods, however, assign higher-order status by construction, from group size, statistical order, or architecture, so neither multiregional coactivation nor improved accuracy shows that a model uses information that pairwise statistics cannot explain. We propose HyPI (Hypergraph Learning from Pairwise-Irreducible Interactions), which replaces structure-defined with evidence-defined higher-order modeling. For each group of three or four regions, HyPI measures how far the observed joint activity departs from a pairwise maximum-entropy reference that matches all univariate and pairwise activation statistics. Departures are calibrated against temporal surrogates and screened for split-half reproducibility, yielding a hypergraph with a shared topology and subject-specific interaction vectors, which together form a subject's interaction profile. These vectors gate a residual branch over a frozen pairwise predictor, so a group contributes nothing when its calibrated interaction is zero. To certify higher-order use, we compare held-out risk against the pairwise predictor and against a capacity-matched model trained on reassigned profiles, and we replace the profiles at a fixed checkpoint to test whether predictions depend on the correct subject-specific profile. Synthetic experiments show recovery of planted interactions and identification of label-relevant ones. On ABIDE, REST-meta-MDD, ADNI, and ADHD-200, HyPI attains the highest mean accuracy across eight cohort–parcellation settings, and the controls show that models with similar accuracy differ markedly in certified higher-order use.