Musicians can perform at different tempos, speakers can control the cadence of their speech, and children can flexibly vary their temporal expectations of events. To understand the neural basis of such flexible timing, we recorded from the medial frontal cortex of primates trained to produce different time intervals with different effectors. The activity of neurons was heterogeneous, nonlinear and complex. However, responses were unified under a remarkable form of invariance: firing rate profiles were temporally stretched for longer intervals and compressed for short ones. At the network level, this phenomenon was evident by flexible changes in the speed with which the population activity traced an invariant trajectory. To identify the origin of speed control, we recorded from both downstream caudate neurons and thalamic neurons projecting to the medial frontal cortex. Speed adjustments were a prominent feature in the caudate but not in the thalamus suggesting that this phenomenon originates within cortical networks. To understand the underlying mechanisms, we created recurrent neural network models at different levels of complexity that could explain flexible timing with speed control. Analysis of the models revealed that the key to flexible speed control was the action of an external input upon the nonlinearities of individual neurons whose recurrent interactions set the network relaxation dynamics. These findings demonstrate a simple and general mechanism for conferring temporal flexibility upon sensorimotor and cognitive functions.
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