  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 trial-to-trial variability.
