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Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks

Beiran, M; Dubreuil, AM; Valente, A; Mastrogiuseppe, F; Ostojic, S; (2021) Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks. Neural Computation , 33 (6) pp. 1572-1615. 10.1162/neco_a_01381. Green open access

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Abstract

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 R network can approximate any R-dimensional dynamical system.

Type: Article
Title: Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks
Open access status: An open access version is available from UCL Discovery
DOI: 10.1162/neco_a_01381
Publisher version: https://doi.org/10.1162/neco_a_01381
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit
URI: https://discovery.ucl.ac.uk/id/eprint/10129036
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