Title: Identifying Feedforward and Feedback Controllable Subspaces of Neural Population Dynamics
Primary area: applications to neuroscience & cognitive science
Keywords: Control Theory, Dimensionality Reduction, Neural Population Dynamics

Abstract: There is overwhelming evidence that cognition, perception, and action rely on feedback control. In neuroscience control is traditionally considered in the context of the brain controlling the body (i.e., the plant) dynamics, here we propose that neural population dynamics themselves should be controllable by, e.g., the activity of other brain areas. However, if and how neural population dynamics are amenable to different control strategies is poorly understood, in large part because machine learning methods to directly assess controllability in neural population dynamics are lacking. To address this gap, we developed a novel dimensionality reduction method, Feedback Controllability Components Analysis (FCCA), that identifies subspaces of linear dynamical systems that are most feedback controllable based on a new measure of feedback controllability. We further show that PCA identifies subspaces of linear dynamical systems that maximize a measure of feedforward controllability. As such, FCCA and PCA are data-driven methods to identify subspaces of neural population data (approximated as linear dynamical systems) that are most feedback and feedforward controllable respectively, and are thus natural contrasts for hypothesis testing. We developed new theory proving that non-normality of underlying dynamics determines the divergence between FCCA and PCA solutions, and confirmed this in numerical simulations of diverse linear and non-linear dynamical systems. To evaluate the degree to which different control strategies extract unsupervised subspaces relevant for task variables, we applied FCCA to diverse neural population recordings, and find that feedback controllable dynamics are geometrically distinct from PCA subspaces and are better predictors of animal behavior. These methods provide a novel approach towards analyzing neural population dynamics from a control theoretic perspective, and indicate that feedback controllable subspaces are important for behavior, providing insight into principles of neural computation.