Decomposed Linear Dynamical Systems (dLDS) for identifying the latent dynamics underlying high-dimensional time-series

Noga Mudrik, Yenho Chen, Eva Yezerets, Christopher John Rozell, Adam Shabti Charles

Track: Extended abstract

Keywords: nonstationary dynamics, nonlinearity, manifold embedding, dynamical systems, sparsity, neuroscience

TL;DR: We propose a model to describe nonlinear and non-stationary dynamics in latent space through a time-varying sparse decomposition of interpretable global linear dynamics.

Abstract: Learning interpretable representations of neural population dynamics is a crucial step to understanding how brain activity relates to behavior. Models of neural dynamics often focus on either low-dimensional projections that overlook the temporal relationships within the data, oversimplify the dynamics to linear and stationary patterns, or provide un-interpretable representations. Here, we consider dynamical systems as representative of flows on a low-dimensional manifold, and propose a new decomposed Linear Dynamical Systems (dLDS) model that captures complex nonstationary dynamics. dLDS models the latent state's evolution as following a sparse combination of simple interpretable components identified through a dictionary learning procedure. Importantly, the decomposed nature of the dynamics enables identifying overlapping co-active processes—a feature unavailable to other methods. Through several examples, we demonstrate our model's ability to learn interpretable representations of multiple systems and demix population dynamics of multiple sub-networks. Finally, when applying our model to neural recordings of *C. elegans*, we identified unique patterns of dynamics emerging across behavioral states, which are obscured by other methods.

Submission Number: 20