Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks

被引:30
作者
Beiran, Manuel [1 ]
Dubreuil, Alexis [1 ]
Valente, Adrian [1 ]
Mastrogiuseppe, Francesca [2 ]
Ostojic, Srdjan [1 ]
机构
[1] PSL Univ, Lab Neurosci Cognit & Computat, INSERM, Ecole Normale Super,U960, F-75005 Paris, France
[2] UCL, Gatsby Computat Neurosci Unit, London W1T 4JG, England
关键词
MULTILAYER FEEDFORWARD NETWORKS; NEURAL-NETWORKS; UNIVERSAL APPROXIMATION; TRANSIENT DYNAMICS; COMPUTATION; NEUROSCIENCE; GENERATION; COMPLEXITY; SYSTEMS;
D O I
10.1162/neco_a_01381
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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.
引用
收藏
页码:1572 / 1615
页数:44
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