Charting higher-order models of brain function beyond pairwise interactions.

Traditional models of brain connectivity primarily focus on pairwise interactions, overlooking collective dynamics among multiple regions. Although many higher-order interaction (HOI) metrics have been proposed, their comparative properties and utility remain unclear. Here, we systematically compare information-theoretic and topological HOI metrics using resting-state and task fMRI data from 100 unrelated Human Connectome Project subjects. We identify a taxonomy of redundant, synergistic, and topological metrics, with the latter bridging the redundancy-synergy continuum. Despite methodological differences, all HOI metrics align with the brain's sensorimotor-to-association hierarchy, yet reveal distinct molecular signatures linking redundancy to metabolic profiles and synergy/topological scaffolds to receptor architecture. HOI metrics outperform pairwise connectivity in brain fingerprinting, whereas pairwise models remain competitive for task decoding. Multivariate analyses further identify topological descriptors as key links between brain function and behavioral variability. Overall, our findings provide a conceptual map of HOI methods for studying multi-regional brain interactions across cognitive and clinical neuroscience.