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  1. Throughout mammalian neocortex, layer 5 pyramidal (L5) cells project via the pons to a vast number of cerebellar granule cells (GrCs), forming a fundamental pathway. Yet, it is unknown how neuronal dynamics are transformed through the L5/GrC pathway. Here, by directly comparing premotor L5 and GrC activity during a forelimb movement task usingdual-site two-photon Ca2+ imaging, we found that in expert mice, L5 and GrC dynamics were highly similar. L5 cells and GrCs shared a common set of task-encoding activity patterns, possessed similar diversity of responses, and exhibited high correlations comparable to local correlations among L5 cells. Chronic imaging revealed that these dynamics co-emerged in cortex and cerebellum over learning: as behavioral performance improved, initially dissimilar L5 cells and GrCs converged onto a shared, low dimensional, task-encoding set of neural activity patterns. Thus, a key function of cortico-cerebellar communication is the propagation of shared dynamics that emerge during learning. 
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