Higher-order interactions control the self-sustained activity in neural systems

Higher-order interactions (HOI) exist widely in various complex networks. In neural systems, the mechanisms by which HOI and their structures modulate function remain unclear. Starting from a Hodgkin–Huxley excitatory–inhibitory network on Watts–Strogatz topologies, we first show that triadic motifs in purely pairwise-coupled circuits induce an effective multi-neuron influence that correlates with the persistence of delay-period activity. Motivated by this phenomenology, we introduce an additional HOI term as an effective interaction to explicitly probe higher-order structure–function coupling. We show that HOI can promote the persistence time of self-sustained activity across diverse network topologies, governed by two key predictors: the average higher-order degree and the higher-order E/I composition ratio. Simulations on four empirical connectome-derived topologies (C. elegans, Drosophila, mouse, and rhesus) reproduce the structural trends observed in idealized networks. A reduced LIF-based rate analysis identifies a model-level critical HOI threshold and captures the qualitative dependence on network rewiring and higher-order structural statistics observed in the HH simulations. Together, these results reveal the mechanism of higher-order structure–function coupling in neural systems and provide theoretical insight into how HOI can shape persistent activity relevant for working-memory related processes and brain-inspired computation.