# Shaping dynamics with multiple populations in low-rank recurrent networks

arXiv: https://arxiv.org/abs/2007.02062 · HTML: https://mlsanity.com/paper/2007.02062/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [Inferring stochastic low-rank recurrent neural networks from neural data](https://mlsanity.com/paper/2406.16749/) (2024)
- [A ghost mechanism: An analytical model of abrupt learning in recurrent networks](https://mlsanity.com/paper/2501.02378/) (2025)
- [A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity](https://mlsanity.com/paper/2511.13899/) (2025)
- [Learning reveals invisible structure in low-rank RNNs](https://mlsanity.com/paper/2605.04115/) (2026)
- [Measuring and Controlling Solution Degeneracy across Task-Trained Recurrent Neural Networks](https://mlsanity.com/paper/2410.03972/) (2024)
- [Storing overlapping associative memories on latent manifolds in low-rank spiking networks](https://mlsanity.com/paper/2411.17485/) (2024)
- [JEDI: Jointly Embedded Inference of Neural Dynamics](https://mlsanity.com/paper/2603.10489/) (2026)
- [Identifying Connectivity Distributions from Neural Dynamics Using Flows](https://mlsanity.com/paper/2603.26506/) (2026)
- [Dynamics and Representation Structure of Local Approximations to Gradient-Based Learning in Linear Recurrent Neural Networks](https://mlsanity.com/paper/2606.00243/) (2026)
- [Auditing Finite-Lag Statistics of Recurrent Representations](https://mlsanity.com/paper/2607.01746/) (2026)

## Abstract (arXiv)

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.