Heterogeneous Mean Field for neural networks with short term plasticity

TL;DR

This paper introduces a Heterogeneous Mean-Field approach to analyze the dynamics of leaky-integrate-and-fire neurons with short-term plasticity on random networks, enabling phase characterization and network topology reconstruction.

Contribution

The study develops a novel mean-field formulation that captures dynamical phases and allows inverse reconstruction of network topology from activity data.

Findings

The mean-field model reproduces quasi-synchronous events.

The in-degree distribution can be reconstructed from global activity.

The approach remains robust under noise and disorder.

Abstract

We report about the main dynamical features of a model of leaky-integrate-and fire excitatory neurons with short term plasticity defined on random massive networks. We investigate the dynamics by a Heterogeneous Mean-Field formulation of the model, that is able to reproduce dynamical phases characterized by the presence of quasi-synchronous events. This formulation allows one to solve also the inverse problem of reconstructing the in-degree distribution for different network topologies from the knowledge of the global activity field. We study the robustness of this inversion procedure, by providing numerical evidence that the in-degree distribution can be recovered also in the presence of noise and disorder in the external currents. Finally, we discuss the validity of the heterogeneous mean-field approach for sparse networks, with a sufficiently large average in-degree.