Beyond Pairwise Interactions: Charting Higher-Order Models of Brain Function

Traditional models of brain connectivity have primarily focused on pairwise interactions, over-looking the rich dynamics that emerge from simultaneous interactions among multiple brain regions. Although a plethora of higher-order interaction (HOI) metrics have been proposed, a systematic evaluation of their comparative properties and utility is missing. Here, we present the first large-scale analysis of information-theoretic and topological HOI metrics, applied to both resting-state and task fMRI data from 100 unrelated subjects of the Human Connectome Project. We identify a clear taxonomy of HOI metrics -- redundant, synergistic, and topological--, with the latter acting as bridges along the redundancy-synergy continuum. Despite methodological differences, all HOI metrics align with the brains overarching unimodal-to-transmodal functional hierarchy. However, certain metrics show specific associations with the neurotransmitter receptor architecture. HOI metrics outperform traditional pairwise models in brain fingerprinting and perform comparably in task decoding, underscoring their value for characterizing individual functional profiles. Finally, multivariate analysis reveals that -- among all HOI metrics -- topological descriptors are key to linking brain function with behavioral variability, positioning them as valuable tools for linking neural architecture and cognitive function. Overall, our findings establish HOIs as a powerful framework for capturing the brains multidimensional dynamics, providing a conceptual map to guide their application across cognitive and clinical neuroscience.