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The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of...

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Autores principales: Hu, Yu, Sompolinsky, Haim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9345493/
https://www.ncbi.nlm.nih.gov/pubmed/35862445
http://dx.doi.org/10.1371/journal.pcbi.1010327
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author Hu, Yu
Sompolinsky, Haim
author_facet Hu, Yu
Sompolinsky, Haim
author_sort Hu, Yu
collection PubMed
description A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics’ Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include second-order connectivity motifs and discuss extensions to excitatory-inhibitory networks. The theoretical results are compared with those from finite-size networks and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.
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spelling pubmed-93454932022-08-03 The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics Hu, Yu Sompolinsky, Haim PLoS Comput Biol Research Article A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics’ Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include second-order connectivity motifs and discuss extensions to excitatory-inhibitory networks. The theoretical results are compared with those from finite-size networks and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data. Public Library of Science 2022-07-21 /pmc/articles/PMC9345493/ /pubmed/35862445 http://dx.doi.org/10.1371/journal.pcbi.1010327 Text en © 2022 Hu, Sompolinsky 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
Hu, Yu
Sompolinsky, Haim
The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
title The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
title_full The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
title_fullStr The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
title_full_unstemmed The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
title_short The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
title_sort spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9345493/
https://www.ncbi.nlm.nih.gov/pubmed/35862445
http://dx.doi.org/10.1371/journal.pcbi.1010327
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