🤖 AI Summary
This study addresses the core challenge in computational neuroscience of inferring latent low-dimensional dynamical systems from noisy neural recordings (continuous or spiking). We propose an interpretable, high-fidelity stochastic low-rank recurrent neural network (RNN) modeling framework. Methodologically, we introduce variational sequential Monte Carlo (VSMC) for parameter learning in stochastic low-rank RNNs—its first application to this class—and design a polynomial-time fixed-point enumeration algorithm, overcoming the traditional exponential computational bottleneck. Our contributions are threefold: (1) superior extraction of lower-dimensional, more interpretable latent dynamics across multiple real neural datasets; (2) accurate generative reproduction of the statistical variability observed in neural signals; and (3) acceleration of fixed-point analysis from exponential to polynomial time complexity, thereby ensuring both model parsimony and computational scalability.
📝 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.