The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

The preBötzinger Complex (preBötC), a key primary generator of the inspiratory breathing rhythm, contains neurons that project directly to facial nucleus (7n) motoneurons to coordinate orofacial and nasofacial activity. To further understand the identity of 7n-projecting preBötC neurons, we used a combination of optogenetic viral transgenic approaches to demonstrate that selective photoinhibition of these neurons affects mystacial pad activity, with minimal effects on breathing. These effects are altered by the type of anesthetic employed and also between anesthetised and conscious states. The population of 7n-projecting preBötC neurons we transduced consisted of both excitatory and inhibitory neurons that also send collaterals to multiple brainstem nuclei involved with the regulation of autonomic activity. We show that modulation of subgroups of preBötC neurons, based on their axonal projections, is a useful strategy to improve our understanding of the mechanisms that coordinate and integrate breathing with different motor and physiological behaviours. This is of fundamental importance, given that abnormal respiratory modulation of autonomic activity and orofacial behaviours have been associated with the development and progression of diseases.