Tensor Analysis and the Dynamics of Motor Cortex

Neural data often span multiple indices, such as neuron, experimental condition, trial, and time, resulting in a tensor or multidimensional array. Standard approaches to neural data analysis often rely on matrix factorization techniques, such as principal component analysis or nonnegative matrix factorization. Any inherent tensor structure in the data is lost when flattened into a matrix. Here, we analyze datasets from primary motor cortex from the perspective of tensor analysis, and develop a theory for how tensor structure relates to certain computational properties of the underlying system. Applied to the motor cortex datasets, we reveal that neural activity is best described by condition-independent dynamics as opposed to condition-dependent relations to external movement variables. Motivated by this result, we pursue one further tensor-related analysis, and two further dynamical systems-related analyses. First, we show how tensor decompositions can be used to denoise neural signals. Second, we apply system identification to the cortex- to-muscle transformation to reveal the intermediate spinal dynamics. Third, we fit recurrent neural networks to muscle activations and show that the geometric properties observed in motor cortex are naturally recapitulated in the network model. Taken together, these results emphasize (on the data analysis side) the role of tensor structure in data and (on the theoretical side) the role of motor cortex as a dynamical system.