Linking Network and Neuron-level Correlations by Renormalized Field Theory

Michael Dick; Alexander van Meegen; Moritz Helias

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arXiv · 2309.14973

Linking Network and Neuron-level Correlations by Renormalized Field Theory

Michael Dick·Alexander van Meegen·Moritz Helias

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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.

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Michael Dick, Alexander van Meegen, Moritz Helias. 2024-01-27. Linking Network and Neuron-level Correlations by Renormalized Field Theory. https://arxiv.org/abs/2309.14973

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