A normative principle governing memory transfer in cerebellar motor learning

The cerebellum, consisting of the cerebellar cortex and nuclei, plays a crucial role in motor learning and exhibits a phenomenon known as systems consolidation, where memory traces are transferred from the cortex to the nuclei. However, the underlying principles and mechanisms governing this memory transfer remain unclear. In this study, we propose a normative framework extending the bias-variance tradeoff that predicts task difficulty as a key factor regulating memory transfer. We model the cerebellum as a dual learning system composed of a complex cortical network and simpler nuclear network, with a cost function that trades off bias, variance, and overhead costs. Computational simulations and in-vivo optogenetic experiments in male mice demonstrate that easier tasks promote greater transfer to the simpler system during consolidation, while harder tasks favor retention in the complex system. Moreover, task difficulty correlates with the specificity of the learned response to untrained stimulus conditions. Our findings provide a unifying framework that explains previously disparate experimental observations and generates testable predictions regarding cerebellar learning and memory consolidation.