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

## TL;DR

This paper presents a unified model of synaptic and structural plasticity that explains the emergence of heavy-tailed weight distributions and complex network structures in biological neural systems, aligning with observations across species.

## Contribution

It introduces a novel model combining Hebbian plasticity and homeostatic regulation that reproduces key neural connectivity features and network architectures.

## Key findings

- Heavy-tailed weight distributions arise with synaptic plasticity when activity beyond neighbors is discarded.
- Combining Hebbian structural plasticity with weight adjustment produces realistic network structures.
- The model explains connectivity patterns observed in C. elegans and mice.

## Abstract

Synaptic plasticity typically produces heavy-tailed distributions of synaptic strengths, consisting of a few strong connections among many weaker ones. Meanwhile, structural plasticity relies on distinct signaling cascades to reshape network topology. We propose a model in which both types of plasticity adhere to the Hebbian principle while operating within homeostatically regulated activity. Synaptic plasticity alone generates heavy-tailed weight distributions, but only when any activity spreading beyond neighboring units is discarded. However, when combined with Hebbian structural plasticity, i.e., adaptive rewiring, heavy-tailed weight distributions also arise with more extensive activity flow. Furthermore, adaptive rewiring provides complex network structures with convergent-divergent circuits similar to those that facilitate signal transmission throughout the nervous system. Having adaptive weight adjustment and rewiring driven by the same homeostatic dynamics gives our model a parsimonious and robust framework that simultaneously produces heavy-tailed weight distributions and convergent-divergent units under a wide range of dynamical regimes. Consequently, the model accounts for key connectivity structures in both C. elegans and the mouse, suggesting that its principles are shared across species of different complexities.

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Source: https://tomesphere.com/paper/2508.21445