DETERMINANTS OF TIME-SERIES LEARNING AND STABILITY IN CLOSED-LOOP NETWORKS

To acquire new motor skills, animals must learn to precisely control their muscles. But how distributed motor circuits, which are interconnected through multiple feedback loops, learn the time-series commands required for coordinated movements remains poorly understood. To explore the principles underlying time series learning we studied simple rate-based models inspired by the cortico-cerebellar system, consisting of a recurrent neural network (RNN) and a two-layer perceptron with closed-loop feedback. Intriguingly, we found that combined perceptron and RNN circuits outperformed equivalent closed-loop RNNs when learning complex periodic signals. Analysis of the neural representations using a frequency-based dimensionality reduction approach revealed two subspaces that were naturally associated with the learning task: a signal space, spanned by frequency components inherent in the target signal and a noise space, spanned by frequency components absent from the target signal. These subspaces could not be distinguished by Principal Component Analysis. Orthogonalization of the angles between components within the signal space and the principal angles between the signal and noise spaces improved the range and extent of stable learning. The relationships between these geometrical properties and network learning and stability was further explored by mimicking nonlinear network properties with linear circuits with added noise components. Our frequency-based dimensionality-reduction framework reveals key determinants of time series learning in closed loop networks and extend classical theories of cerebellar recoding, by showing how orthogonalizing cortical representations in the frequency domain could improve the fidelity and stability of learned motor commands.