Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

TL;DR

This paper applies the Equation-Free multiscale approach to analyze neural network dynamics on random graphs, enabling equilibrium and rare-events analysis without explicit macroscopic models.

Contribution

It introduces a novel multiscale computational framework for neural networks that bypasses the need for explicit macroscopic equations, using microscopic simulations and simulated annealing.

Findings

Computed equilibrium bifurcation diagrams for neural interactions.

Analyzed stability of stationary states in neural networks.

Performed rare-events analysis with effective Fokker-Planck equations.

Abstract

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables.