HiBrain: Structure-Calibrated Higher-Order Hypergraph Learning for Brain Network Analysis

Pairwise connectivity does not fully characterize joint multi-region dependence, while higher-order network construction alone does not establish subject-specific structural support. We propose HiBrain, a structure-calibrated multi-order hypergraph framework for brain disorder classification. HiBrain assesses third- and fourth-order cumulant increments relative to fitted lower-order models and calibrates candidate hyperedge support using individual gray-matter evidence. It integrates these relations through joint-evidence sparse attention and adjacent-order propagation, while conditional innovation admission controls additional higher-order contributions to a multi-order base prediction. On ABIDE-II, REST-MDD, and SRPBS-SCZ for autism spectrum disorder (ASD), major depressive disorder (MDD), and schizophrenia (SCZ) classification, respectively, HiBrain achieved the highest mean accuracy among 12 evaluated methods, exceeding the strongest baseline by 4.54, 6.94, and 6.47 percentage points. Within the same framework, it exceeded the strongest attention alternative in accuracy by 3.04, 3.04, and 2.99 points, respectively. External evaluation on ABIDE-I showed a 4.01-point accuracy gain over the strongest evaluated baseline. Model-derived regional importance showed greater cerebellar emphasis at higher orders in ASD and MDD, and posterior cortical and cerebellar emphasis at higher orders in SCZ. Code is available at https://anonymous.4open.science/r/HiBrain-47DF.