Shaping dynamics with multiple populations in low-rank recurrent networks

TL;DR

This paper introduces Gaussian-mixture low-rank recurrent networks, revealing how connectivity structure and population diversity shape neural dynamics, enabling approximation of complex R-dimensional systems with multiple populations.

Contribution

It presents a novel class of low-rank recurrent networks with independent hyper-parameters for rank and population number, elucidating their role in shaping neural dynamics.

Findings

Population structure influences the shape of neural dynamics.

Large enough populations allow approximation of any R-dimensional system.

The dynamics can be simplified to an effective circuit of latent variables.

Abstract

An emerging paradigm proposes that neural computations can be understood at the level of dynamical 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 hyper-parameters. 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.