Feed-forward correction of neural timing errors through fluctuating scalar input

Complex learned behaviors like playing piano often rely on precise timing control. However, it remains unknown how the nervous system generates precise timing, in particular among multiple motor components that must synchronize for long periods (e.g. two hands). Motivated by the songbird brain, where the putative sequence-generating nuclei governing left and right vocal muscle timing do not connect (birds have no corpus callosum) but could receive shared low-dimensional input, we present a model in which neural sequence generators are synchronized simply by a scalar modulatory input. We show that feed-forward scalar modulation alone can correct timing errors if (1) the modulation fluctuates in time and (2) it is spread non-uniformly over positions in the sequence so as to reflect its timecourse spatially. This yields attractor sequences within a spatiotemporal landscape of propagation speeds toward which delayed sequences advance and advanced sequences slow down. We give a mathematical recipe for constructing an appropriate spatial profile given the temporal structure of the modulation and show how it can correct sizable timing errors in a songbird-inspired neural network. This work reveals a simple mechanism for ongoing correction of timing errors in neural motor signals.