Conditioned response timing and integration in the cerebellum

Classical conditioning procedures instill knowledge about the temporal relationships between events. The unconditioned stimulus (US) is the event to be timed. The conditioned response (CR) is viewed as a prediction of the imminence of the US. Knowledge of the elapsed time between conditioned stimuli (CSs) and US delivery is expressed in the topological features of the CR. The peak amplitude of the CR coincides with the timing of the US. A simple connectionist network based on Sutton and Barto's Time Derivative (TD) Model of Pavlovian Reinforcement provides a mechanism that can account for and simulate CR timing in a variety of protocols. This article describes extensions of the model to predictive timing under temporal uncertainty. The model is expressed in terms of equations that operate in real time according to a competitive learning rule. The unfolding of time from the onsets and offsets of events such as CSs is represented by the propagation of activity along a sequence of time-tagged elements. The model can be aligned with anatomical circuits of the cerebellum and brain stem that are essential for learning and performance of conditioned eye-blink responses.