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...

Full description

Saved in:
Bibliographic Details
Published in:PLoS computational biology 2022-07, Vol.18 (7), p.e1010327-e1010327
Main Authors: Hu, Yu, Sompolinsky, Haim
Format: Article
Language:English
Subjects:
Biology and Life Sciences
Charitable foundations
Computational neuroscience
Computer and Information Sciences
Covariance matrix
Dynamic structural analysis
Dynamics
Eigenvalues
Fluctuations
Linear systems
Mathematical analysis
Matrices
Nervous system
Neural networks
Neuroimaging
Neurons
Neurosciences
Physical Sciences
Population
Principal components analysis
Research and Analysis Methods
Stochasticity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1553-7358
1553-734X
1553-7358
DOI:10.1371/journal.pcbi.1010327