Deep learning methods for discovering interpretable latent dynamics in high-dimensional neural data

Abstract

Many fields of science are being revolutionized by new techniques from deep learning to discover dynamics underlying complex high-dimensional data. Adapting these powerful new methods to the challenges of neuroscience, however, is still in its early stages. Here we describe the development of our deep learning method over the years for discovering the nonlinear dynamics of neurons in large populations using only a few latent dimensions. Unlike prominent existing methods, the low-dimensionality of our approach makes the learned dynamical system easier to interpret, even allowing explicit visualization of the vector fields and attractor structures of the system. Our approach leverages neural differential equations (NDEs), a class of deep recurrent neural network models that can implement more complex computations in lower dimensions compared to classical recurrent neural networks. This increased complexity in lower dimensions subsequently helps in extracting interpretable, effective low-dimensional dynamics that may underlie a dataset or task. We address several technical challenges in applying NDEs to neural data, and develop a neural dynamics discovery method called FINDR (Flow-field Inference from Neural Data using deep Recurrent networks) that is built on the backbone of NDEs. To demonstrate its scientific use, we apply FINDR to a variety of neural population datasets, including data from frontal cortex and striatum of rats performing a perceptual decision-making task. We discovered that neural trajectories evolve in two sequential regimes, the first driven by sensory inputs, and the second driven by dynamics internal to the system. The initial regime mediates evidence accumulation, while the subsequent regime subserves decision commitment. This regime transition is coupled to a rapid reorganization in the representation of the decision process in the neural population (a change in the ``neural mode'' along which the process develops). Our results show that the formation of a perceptual choice involves a rapid, coordinated transition in both the dynamical regime and the neural mode of the decision process. Overall, FINDR shows promise as a powerful method for revealing the low-dimensional dynamics of neural populations, and provides a general, interpretable framework for investigating neural computation through the lens of dynamical systems.