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

Abstract: Brain networks continually adjust the weights of their connections, resulting in heavy-tailed distributions of their connection weights, a few strong connections among many weaker ones. At the same time, these connections undergo structural plasticity, forming a complex network topology. Although mechanisms producing either heavy-tailed distributions or complex topologies have been proposed, it has remained unclear whether a single mechanism can produce both. We consider homeostasis as the driving principle and propose a Hebbian inspired model that adaptively adjusts weights and rewires directed connections based on homeostatic dynamics. Without adaptive rewiring, weight adjustment alone still generates heavy-tailed weight distributions, as long as activity does not spread beyond locally neighboring units. However, when combined with adaptive rewiring, the homeostatic dynamics create a synergy that produces heavy-tailed weight distributions also for more extended activity flow. Furthermore, the model generates complex network structures that encompass convergent-divergent circuits similar to those that facilitate signal transmission throughout the nervous system. By combining adaptive weight adjustment and rewiring based on the same homeostatic dynamics, our model provides a parsimonious and robust mechanism that simultaneously produces heavy-tailed weight distributions and convergent-divergent units under a wide range of dynamical regimes.