Linking network- and neuron-level correlations by renormalized field theory

Physical Review Research, vol. 6

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 analog 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. Published by the American Physical Society 2024

Authors 3

1. M.I. Dick corresponding Aachen

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Jülich Research Centre

   Peter Grünberg Institut (PGI-1) and Institute for Advanced Simulation (IAS-1)

   RWTH Aachen University

2. Alexander van Meegen

   Forschungszentrum Jülich · University of Cologne

   Affiliation as printed

   Jülich Research Centre

   University of Cologne

3. Moritz Helias Aachen

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Jülich Research Centre

   RWTH Aachen University