Linking Network and Neuron-level Correlations by Renormalized Field Theory
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.
Cite
@article{arxiv.2309.14973,
title = {Linking Network and Neuron-level Correlations by Renormalized Field Theory},
author = {Michael Dick and Alexander van Meegen and Moritz Helias},
journal= {arXiv preprint arXiv:2309.14973},
year = {2024}
}