Supported by a decade of primate electrophysiological experiments, the prevailing theory of neural motor control holds that movement generation is accomplished by a preparatory process that progressively steers the state of the motor cortex into a movement-specific optimal subspace prior to movement onset. The state of the cortex then evolves from these optimal subspaces, producing patterns of neural activity that serve as control inputs to the musculature. This theory, however, does not address the following questions: what characterizes the optimal subspace and what are the neural mechanisms that underlie the preparatory process? We address these questions with a circuit model of movement preparation and control. Specifically, we propose that preparation can be achieved by optimal feedback control (OFC) of the cortical state via a thalamo-cortical loop. Under OFC, the state of the cortex is selectively controlled along state-space directions that have future motor consequences, and not in other inconsequential ones. We show that OFC enables fast movement preparation and explains the observed orthogonality between preparatory and movement-related monkey motor cortex activity. This illustrates the importance of constraining new theories of neural function with experimental data. However, as recording technologies continue to improve, a key challenge is to extract meaningful insights from increasingly large-scale neural recordings. Latent variable models (LVMs) are powerful tools for addressing this challenge due to their ability to identify the low-dimensional latent variables that best explain these large data sets. One shortcoming of most LVMs, however, is that they assume a Euclidean latent space, while many kinematic variables, such as head rotations and the configuration of an arm, are naturally described by variables that live on non-Euclidean latent spaces (e.g., SO(3) and tori). To address this shortcoming, we propose the Manifold Gaussian Process Latent Variable Model, a method for simultaneously inferring nonparametric tuning curves and latent variables on non-Euclidean latent spaces. We show that our method is able to correctly infer the latent ring topology of the fly and mouse head direction circuits.This work was supported by a Trinity-Henry Barlow scholarship and a scholarship from the Ministry of Education, ROC Taiwan
