Inferring stochastic low-rank recurrent neural networks from neural data

TL;DR

This paper introduces a variational sequential Monte Carlo method to fit stochastic low-rank RNNs to neural data, enabling interpretable, low-dimensional dynamical models that match observed neural variability and efficiently identify fixed points.

Contribution

It presents a novel fitting method for stochastic low-rank RNNs using variational sequential Monte Carlo, improving interpretability and computational efficiency in analyzing neural data.

Findings

Lower-dimensional latent dynamics achieved compared to existing methods.

Efficient polynomial-time fixed point identification for piecewise linear RNNs.

Validated on continuous and spiking neural datasets.

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.