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.

An important problem in systems neuroscience is to identify the latent dynamics underlying neural population activity. Here we address this problem by introducing a low-dimensional nonlinear model for latent neural population dynamics using neural ordinary differential equations (neural ODEs), with noisy sensory inputs and Poisson spike train outputs. We refer to this as the Poisson Latent Neural Differential Equations (PLNDE) model. We apply the PLNDE framework to a variety of synthetic datasets, and show that it accurately infers the phase portraits and fixed points of nonlinear systems augmented to produce spike train data, including the FitzHugh-Nagumo oscillator, a 3-dimensional nonlinear spiral, and a nonlinear sensory decision-making model with attractor dynamics. Our model significantly outperforms existing methods at inferring single-trial neural firing rates and the corresponding latent trajectories that generated them, especially in the regime where the spike counts and number of trials are low. We then apply our model to multi-region neural population recordings from medial frontal cortex of rats performing an auditory decision-making task. Our model provides a general, interpretable framework for investigating the neural mechanisms of decision-making and other cognitive computations through the lens of dynamical systems.