Scaling behaviour in probabilistic neuronal cellular automata

TL;DR

This paper investigates the critical behavior of a neural network modeled as stochastic cellular automata, analyzing activity avalanches and their scaling properties, and finds agreement with mean-field theory at the critical point.

Contribution

It provides a detailed numerical analysis of activity avalanches in a probabilistic neural cellular automaton and compares the results with mean-field predictions.

Findings

Avalanche size and duration distributions follow power-law scaling.

Scaling exponents match mean-field theory predictions at criticality.

Critical point varies with stochasticity or temperature.

Abstract

We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean--field theory.