Large Deviations Approach to Random Recurrent Neuronal Networks: Parameter Inference and Fluctuation-Induced Transitions

TL;DR

This paper integrates field theory and large deviations to analyze random recurrent neuronal networks, enabling parameter inference and revealing fluctuation-induced transitions beyond mean-field approximations.

Contribution

It introduces a unified framework combining field theory and large deviations for neuronal networks, deriving a rate function as a Kullback-Leibler divergence for data-driven inference.

Findings

Effective action equals the rate function derived via field theory.

The rate function is expressed as a Kullback-Leibler divergence.

Identification of fluctuation-induced transitions between mean-field solutions.

Abstract

We here unify the field theoretical approach to neuronal networks with large deviations theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action is identical to the rate function and derive the latter using field theory. This rate function takes the form of a Kullback-Leibler divergence which enables data-driven inference of model parameters and calculation of fluctuations beyond mean-field theory. Lastly, we expose a regime with fluctuation-induced transitions between mean-field solutions.