Inferring structural complexity from dynamical measures

Abstract

Complexity, commonly defined as the coexistence of integration and differentiation, is a fundamental property of thalamocortical networks and is regarded as a prerequisite for adaptive brain function and consciousness. A variety of metrics have been developed to estimate neural complexity from recorded activity and are increasingly employed in both research and clinical settings. Yet, the extent to which these measures reflect specific architectural features of the underlying circuits remains poorly understood. Here, we used Wilson-Cowan mean-field equations to simulate neural dynamics across networks spanning a broad range of architectures. By systematically rewiring connectivity, we generated graded variations in the structural integration-differentiation balance and assessed a panel of complexity measures derived either from spontaneous activity (observational metrics) or from responses to external perturbations (perturbational metrics). Observational measures exhibited markedly heterogeneous behavior: some were primarily sensitive to network integration, others to differentiation, whereas some showed limited sensitivity to architectural manipulations. In contrast, perturbational measures robustly peaked at intermediate rewiring steps and scaled with small-worldness, consistent with architectures that combine local recurrence and distributed communication. Moreover, perturbational metrics proved robust to common-driver confounds and were highest in a wake-like regime near critical instability, declining as sleep-like dynamics became more widespread across the network. Taken together, these findings map widely used empirical complexity measures onto specific network architectures, reveal dynamical factors that can bias observational estimates, and provide guidance for inferring complexity in systems whose internal organization is inaccessible, unconventional, or only partially known, including brain organoids, non-human nervous systems, and synthetic neural networks.