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Metastable spiking networks in the replica-mean-field limit

Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of infinitely many replicas of the finite network of interest, but...

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Autores principales: Yu, Luyan, Taillefumier, Thibaud O.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9246178/
https://www.ncbi.nlm.nih.gov/pubmed/35714155
http://dx.doi.org/10.1371/journal.pcbi.1010215
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author Yu, Luyan
Taillefumier, Thibaud O.
author_facet Yu, Luyan
Taillefumier, Thibaud O.
author_sort Yu, Luyan
collection PubMed
description Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of infinitely many replicas of the finite network of interest, but with randomized interactions across replicas. Such randomization renders certain excitatory networks fully tractable at the cost of neglecting activity correlations, but with explicit dependence on the finite size of the neural constituents. However, metastable dynamics typically unfold in networks with mixed inhibition and excitation. Here, we extend the RMF computational framework to point-process-based neural network models with exponential stochastic intensities, allowing for mixed excitation and inhibition. Within this setting, we show that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. Technically, these stationary rates are determined as the solutions of a set of delayed differential equations under certain regularity conditions that any physical solutions shall satisfy. We solve this original problem by combining the resolvent formalism and singular-perturbation theory. Importantly, we find that these rates specify probabilistic pseudo-equilibria which accurately capture the neural variability observed in the original finite-size network. We also discuss the emergence of metastability as a stochastic bifurcation, which can be interpreted as a static phase transition in the RMF limits. In turn, we expect to leverage the static picture of RMF limits to infer purely dynamical features of metastable finite-size networks, such as the transition rates between pseudo-equilibria.
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spelling pubmed-92461782022-07-01 Metastable spiking networks in the replica-mean-field limit Yu, Luyan Taillefumier, Thibaud O. PLoS Comput Biol Research Article Characterizing metastable neural dynamics in finite-size spiking networks remains a daunting challenge. We propose to address this challenge in the recently introduced replica-mean-field (RMF) limit. In this limit, networks are made of infinitely many replicas of the finite network of interest, but with randomized interactions across replicas. Such randomization renders certain excitatory networks fully tractable at the cost of neglecting activity correlations, but with explicit dependence on the finite size of the neural constituents. However, metastable dynamics typically unfold in networks with mixed inhibition and excitation. Here, we extend the RMF computational framework to point-process-based neural network models with exponential stochastic intensities, allowing for mixed excitation and inhibition. Within this setting, we show that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. Technically, these stationary rates are determined as the solutions of a set of delayed differential equations under certain regularity conditions that any physical solutions shall satisfy. We solve this original problem by combining the resolvent formalism and singular-perturbation theory. Importantly, we find that these rates specify probabilistic pseudo-equilibria which accurately capture the neural variability observed in the original finite-size network. We also discuss the emergence of metastability as a stochastic bifurcation, which can be interpreted as a static phase transition in the RMF limits. In turn, we expect to leverage the static picture of RMF limits to infer purely dynamical features of metastable finite-size networks, such as the transition rates between pseudo-equilibria. Public Library of Science 2022-06-17 /pmc/articles/PMC9246178/ /pubmed/35714155 http://dx.doi.org/10.1371/journal.pcbi.1010215 Text en © 2022 Yu, Taillefumier https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Yu, Luyan
Taillefumier, Thibaud O.
Metastable spiking networks in the replica-mean-field limit
title Metastable spiking networks in the replica-mean-field limit
title_full Metastable spiking networks in the replica-mean-field limit
title_fullStr Metastable spiking networks in the replica-mean-field limit
title_full_unstemmed Metastable spiking networks in the replica-mean-field limit
title_short Metastable spiking networks in the replica-mean-field limit
title_sort metastable spiking networks in the replica-mean-field limit
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9246178/
https://www.ncbi.nlm.nih.gov/pubmed/35714155
http://dx.doi.org/10.1371/journal.pcbi.1010215
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