Geometric determinants of time series learning and attractor stability in closed-loop circuits

Skilled volitional behaviours arise from recurrent circuits, which can sustain structured neural activity in the absence of external drive, through internal feedback. But how such autonomous activity is learned and stability maintained in distributed motor circuits is poorly understood. To investigate the relationship between neural representations and learning we compared a cortex-like recurrent neural network (RNN) and a cortico-cerebellar-like circuit with a feed-forward layer (RNN+FFL), both in a closed-loop configuration. RNN+FFL circuits learned periodic target signals that parameter-matched RNNs could not, due to a failure to form attractor states. Decomposing population activity by frequency, rather than variance, separated the task-relevant and task-irrelevant subspaces. Quantifying their geometric arrangement revealed that the feed-forward layer improved learning and stabilised attractor states by increasing the angles within and between these subspaces. Our results show that task-specific representational geometry is a better predictor of periodic time series learning in recurrent circuits than classical global measures such as dimensionality.