An emerging paradigm proposes that neural computations can be understood at the level of dynamic systems that govern low-dimensional trajectories of collective neural activity. How the connectivity structure of a network determines the emergent dynamical system, however, remains to be clarified. Here we consider a novel class of models, gaussian-mixture, low-rank recurrent networks in which the rank of the connectivity matrix and the number of statistically defined populations are independent hyperparameters. We show that the resulting collective dynamics form a dynamical system, where the rank sets the dimensionality and the population structure shapes the dynamics. In particular, the collective dynamics can be described in terms of a simplified effective circuit of interacting latent variables. While having a single global population strongly restricts the possible dynamics, we demonstrate that if the number of populations is large enough, a rank network can approximate any -dimensional dynamical system.
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June 2021
May 13 2021
Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks
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Manuel Beiran,
Manuel Beiran
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France manuel.beiran@ens.fr
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Alexis Dubreuil,
Alexis Dubreuil
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France alexis.dubreuil@gmail.com
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Adrian Valente,
Adrian Valente
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France adrian.valente@ens.fr
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Francesca Mastrogiuseppe,
Francesca Mastrogiuseppe
Gatsby Computational Neuroscience Unit, UCL, London W1T 4JG, U.K. f.mastrogiuseppe@ucl.ac.uk
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Srdjan Ostojic
Srdjan Ostojic
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France srdjan.ostojic@ens.fr
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Manuel Beiran
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France manuel.beiran@ens.fr
Alexis Dubreuil
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France alexis.dubreuil@gmail.com
Adrian Valente
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France adrian.valente@ens.fr
Francesca Mastrogiuseppe
Gatsby Computational Neuroscience Unit, UCL, London W1T 4JG, U.K. f.mastrogiuseppe@ucl.ac.uk
Srdjan Ostojic
Laboratoire de Neurosciences Cognitives et Computationnelles, INSERM U960, Ecole Normale Superieure. PSL University, 75005 Paris, France srdjan.ostojic@ens.fr
Received:
July 21 2020
Accepted:
December 17 2020
Online Issn: 1530-888X
Print Issn: 0899-7667
© 2021 Massachusetts Institute of Technology
2021
Massachusetts Institute of Technology
Neural Computation (2021) 33 (6): 1572–1615.
Article history
Received:
July 21 2020
Accepted:
December 17 2020
Citation
Manuel Beiran, Alexis Dubreuil, Adrian Valente, Francesca Mastrogiuseppe, Srdjan Ostojic; Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks. Neural Comput 2021; 33 (6): 1572–1615. doi: https://doi.org/10.1162/neco_a_01381
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