Neural computations underlying processes such as decision-making, working memory, and motor control are thought to emerge from neural population dynamics. But estimating these dynamics remains a significant challenge. Here we introduce Flow-field Inference from Neural Data using deep Recurrent networks (FINDR), an unsupervised deep learning method for inferring low-dimensional, nonlinear, stochastic dynamics underlying neural population activity. Using spike train data from frontal brain regions of rats performing an auditory decision-making task, we demonstrate that FINDR performs competitively with existing methods in capturing the heterogeneous responses of individual neurons. When trained to disentangle task-relevant and irrelevant activity, FINDR uncovers interpretable low-dimensional dynamics. These dynamics can be visualized as flow fields and attractors, enabling direct tests of attractor-based theories of neural computation. We suggest FINDR as a powerful method for revealing the low-dimensional task-relevant dynamics of neural populations and their associated computations.

Neurons work together in large groups to solve tasks---like deciding whether to buy a laptop or not based on online reviews. A central premise in neuroscience is that the brain's algorithm for doing such tasks can be succinctly represented as a differential equation describing how this group activity changes over time. In this work, we present a method called FINDR that aims to discover what this differential equation is, using real brain activity data from animals doing specific tasks. The method does this in two main steps:1) It separates the brain activity that is relevant to the task from activity that isn't.2) Then it learns the most likely differential equation that is consistent with the task-relevant brain activity.We show that this approach performs competitively with existing methods in predicting neural activity, while being better at discovering differential equations that neuroscientists can interpret.