Granule cells reorient cortical manifolds to separate contexts but preserve their geometry

To learn effectively, animals must generalize across yet distinguish between related contexts. Generalization relies on low-dimensional neural manifolds found throughout neocortex^1-3, which accelerate learning by constraining neural activity to task-relevant axes^4,5. Conversely, context separation is attributed to neural expansion layers that can project information into high-dimensional feature spaces^6-8, most famously cerebellar granule cells (GrCs)^9-11. To investigate the generalization-separation tradeoff, we simultaneously imaged key nodes in the universal cortico-cerebellar pathway^12,13-premotor layer 5 pyramidal tract (L5PT) and GrCs-during parallel learning of two distinct skills with shared temporal structure. Rather than expanding the cortical representations, GrCs retained their low-rank encoding of each task. Across contexts, however, despite stable cortico-cerebellar coupling, L5PT activity patterns generalized while GrC patterns temporally remapped. Mechanistically, GrCs used affine transformations that rotated the cortical manifolds apart but preserved their intrinsic low-dimensional geometry. Moreover, GrCs decorrelated cortical trajectories most strongly in expert animals. This reveals a fundamental architectural division of labor: the cortex generates invariant dynamic primitives for smooth generalization, while the cerebellum reconfigures them to drive context-specific output.