Edge of chaos and avalanches in neural networks with heavy-tailed synaptic weight distribution

TL;DR

This paper introduces a neural network model with heavy-tailed synaptic weights that exhibits a continuous transition to chaos, reproduces biologically relevant activity patterns, and differs from Gaussian models which show a discontinuous transition.

Contribution

It presents an analytically tractable model with power-law synaptic weights that captures critical neural dynamics and activity patterns observed in biological systems.

Findings

Model exhibits a continuous transition to chaos.

Reproduces scale-free avalanches and low activity levels.

Heavy-tailed weights serve as a sparse connectivity prior.

Abstract

We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous transition to chaos and can reproduce biologically relevant low activity levels and scale-free avalanches, i.e. bursts of activity with power-law distributions of sizes and lifetimes. In contrast, the Gaussian counterpart exhibits a discontinuous transition to chaos and thus cannot be poised near the edge of chaos. We validate our predictions in simulations of networks of binary as well as leaky integrate-and-fire neurons. Our results suggest that heavy-tailed synaptic distribution may form a weakly informative sparse-connectivity prior that can be useful in biological and artificial adaptive systems.