Inferring stochastic low-rank recurrent neural networks from neural data

Matthijs Pals, A Erdem Sağtekin, Felix C Pei, Manuel Gloeckler, Jakob H. Macke

Keywords: Low-rank RNNs, dynamical systems, variational inference, sequential monte carlo, neural data

TL;DR: We fit low-rank RNNs to neural data using variational SMC, and obtain models that are both generative and have tractable low-dimensional dynamics.

Abstract: A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well. Low-rank recurrent neural networks (RNNs) exhibit such interpretability by having tractable dynamics. However, it is unclear how to best fit low-rank RNNs to data consisting of noisy observations of an underlying stochastic system. Here, we propose to fit stochastic low-rank RNNs with variational sequential Monte Carlo methods. We validate our method on several datasets consisting of both continuous and spiking neural data, where we obtain lower dimensional latent dynamics than current state of the art methods. Additionally, for low-rank models with piecewise linear nonlinearities, we show how to efficiently identify all fixed points in polynomial rather than exponential cost in the number of units, making analysis of the inferred dynamics tractable for large RNNs. Our method both elucidates the dynamical systems underlying experimental recordings and provides a generative model whose trajectories match observed variability.

Primary Area: Neuroscience and cognitive science (neural coding, brain-computer interfaces)

Submission Number: 19365