Stochastic mean field formulation of the dynamics of diluted neural networks

TL;DR

This paper introduces a stochastic mean field approach to model the dynamics of diluted neural networks, capturing chaos and fluctuations through additive noise in a globally coupled system.

Contribution

It demonstrates that fluctuations in diluted neural networks can be effectively modeled as noise in a mean field framework, reproducing key dynamical features and stability properties.

Findings

Fluctuations induce chaos in neural networks.

Stochastic approximation reproduces microscopic and macroscopic dynamics.

Lyapunov exponents match between deterministic and stochastic models.

Abstract

We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the microscopic level. Our main aim is to mimic the effect of the dilution as a noise source acting on the dynamics of a globally coupled non-chaotic system. Indeed, the evolution of a diluted neural network can be well approximated as a fully pulse coupled network, where each neuron is driven by a mean synaptic current plus additive noise. These terms represent the average and the fluctuations of the synaptic currents acting on the single neurons in the diluted system. The main microscopic and macroscopic dynamical features can be retrieved with this stochastic approximation. Furthermore, the microscopic stability of the diluted network can be also reproduced, as demonstrated from the almost coincidence of the measured Lyapunov exponents in the deterministic and stochastic cases for an ample range of system sizes. Our results strongly suggest that the fluctuations in the synaptic currents are responsible for the emergence of chaos in this class of pulse coupled networks.