Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks - Archive ouverte HAL
Article Dans Une Revue Neural Computation Année : 2021

Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks

Résumé

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.
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Dates et versions

hal-03433734 , version 1 (14-10-2022)

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Manuel Beiran, Alexis Dubreuil, Adrian Valente, Francesca Mastrogiuseppe, Srdjan Ostojic. Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks. Neural Computation, 2021, 33 (6), pp.1572-1615. ⟨10.1162/neco_a_01381⟩. ⟨hal-03433734⟩

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