Self-regulated emergence of heavy-tailed weight distributions in evolving complex network architectures

The nervous system continuously adjusts connection strengths and reorganizes its structure to form and maintain complex connectivity patterns with heavy-tailed weight distributions. We propose a parsimonious model in which structural and synaptic plasticity are driven by common diffusion dynamics. Synaptic plasticity alone generates heavy-tailed weight distributions, but only when activity spreading remains predominantly local.

However, when combined with structural plasticity through adaptive rewiring, the model also generates these distributions with more extensive activity flow. Furthermore, adaptive rewiring produces complex network structures with convergent-divergent circuits. These circuits contain motifs that are pervasive in nervous systems and are responsible for context-sensitive signal propagation and enhanced signal-to-noise ratios.

Our model robustly reproduces these results across diverse dynamical regimes while capturing key connectivity features of both C. elegans and mouse brain networks. These findings suggest that the underlying principles are shared across species of varying complexity. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government.

The research was supported by an Odysseus grant (G.0003.12) from the Flemish Organization for Science (F.W.O) to Cees van Leeuwen. Brain and Cognition, KU Leuven, Leuven, Belgium Center for Cognitive Science, University of Kaiserslautern-Landau, Kaiserslautern, Germany NICE Research Group, Computer Science Research Centre, University of Surrey, Guildford, UK Surrey Institute for People-Centred Artificial Intelligence, University of Surrey, Guildford, UK Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Paris, France The authors declare no competing interests. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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