Linking Network and Neuron-level Correlations by Renormalized Field Theory

TL;DR

This paper develops a renormalized field theory for cortical networks, linking neuron and network correlations, and explains various autocorrelation functions through self-consistent equations derived from a model exhibiting critical dynamics.

Contribution

It introduces a renormalized theory that captures fluctuations neglected by mean-field approximations, connecting network and neuron-level correlations in critical neural systems.

Findings

Explains population and single-unit autocorrelation functions with multiple temporal scales.

Derives self-consistency equations for Greens functions revealing activity-heterogeneity coupling.

Provides a quantitative framework for critical neural dynamics.

Abstract

It is frequently hypothesized that cortical networks operate close to a critical point. Advantages of criticality include rich dynamics well-suited for computation and critical slowing down, which may offer a mechanism for dynamic memory. However, mean-field approximations, while versatile and popular, inherently neglect the fluctuations responsible for such critical dynamics. Thus, a renormalized theory is necessary. We consider the Sompolinsky-Crisanti-Sommers model which displays a well studied chaotic as well as a magnetic transition. Based on the analogue of a quantum effective action, we derive self-consistency equations for the first two renormalized Greens functions. Their self-consistent solution reveals a coupling between the population level activity and single neuron heterogeneity. The quantitative theory explains the population autocorrelation function, the single-unit autocorrelation function with its multiple temporal scales, and cross correlations.