Marr [J. Physiol. (1969) 202, 437-470] and Albus [Math. Biosci. (1971) 10, 25-61] hypothesized that cerebellar learning is facilitated by a granule cell sparse code, i.e. a neural code in which the fraction of active neurons is low at any one time. In this paper, we re-examine this hypothesis in light of recent experimental and theoretical findings. We argue that cerebellar motor learning is enhanced by a sparse code that simultaneously maximizes information transfer between mossy fibers and granule cells, minimizes redundancies between granule cell discharges, and re-codes the mossy fiber inputs with an adaptive resolution such that inputs corresponding to large errors are finely encoded. We then propose that a set of biologically plausible unsupervised learning rules can produce such a code. To maintain a low mean firing rate compatible with a sparse code, an activity-dependent homeostatic mechanism sets the cells' thresholds. Then, to maximize information transfer, the mossy fiber--granule cell synapses are adjusted by a Hebbian rule. Furthermore, to minimize redundancies between granule cell discharges, the inhibitory Golgi cell--granule cell synapses are tuned by an anti-Hebbian rule. Finally, to allow adaptive resolution, a performance-based neuromodulator-like signal gates these three plastic processes. We integrate these gated learning rules into a simplified model of the cerebellum for arm movement control, and show that unsupervised learning of granule cell sparse codes greatly improves cerebellar adaptive motor control in comparison to a "fixed" Marr--Albus-type model. Until recently, activity-dependent cerebellar plasticity was thought to be largely confined to the granule cell--Purkinje cell synapses. This static view of the cerebellum is, however, quickly being replaced by an extremely dynamic view in which plasticity is omnipresent. The present theoretical study shows how several forms of plasticity in the granular layer of the cerebellum can produce fast, accurate and stable cerebellar learning.