Linking Network and Neuron-level Correlations by Renormalized Field Theory

Michael Dick, Alexander van Meegen, Moritz Helias
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)
2023-09-25 16:00:00
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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