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 the neocortex1,2, which accelerate learning by constraining neural activity to task-relevant axes3. Conversely, context separation is attributed to neural expansion layers that can project information into high-dimensional feature spaces4,5, most famously cerebellar granule cells (GrCs)6-8. To investigate the generalization-separation tradeoff, we simultaneously imaged key nodes in the universal cortico-cerebellar pathway9--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, despite stable cortico-cerebellar coupling, L5PT activity patterns generalized while GrC patterns temporally remapped. But rather than independently scrambling, GrC populations remapped coherently: their low-dimensional trajectories "rotated" apart between tasks, separating the contexts while preserving the cortical geometry of each. Moreover, GrC trajectories diverged most strongly in expert animals. This suggests a fundamental architectural division of labor: the cortex provides invariant dynamic primitives for smooth generalization, while cerebellar activity reconfigures them to drive context-specific output.