Linking Network and Neuron-level Correlations by Renormalized Field Theory

arXiv (Cornell University)

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.

Authors 3

1. Michael J. Dick
2. Alexander van Meegen
3. Moritz Helias Aachen Department of Physics Faculty 1

   RWTH Aachen University

   Affiliation as printed

   Department of Physics , Faculty 1 , RWTH Aachen University , Aachen , Germany

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-