Pattern separation is a fundamental function of the brain. Divergent feedforward networks separate overlapping activity patterns by mapping them onto larger numbers of neurons, aiding learning in downstream circuits. However, the relationship between the synaptic connectivity within these circuits and their ability to separate patterns is poorly understood. To investigate this we built simplified and biologically detailed models of the cerebellar input layer and systematically varied the spatial correlation of their inputs and their synaptic connectivity. Performance was quantified by the learning speed of a classifier trained on either the mossy fiber input or granule cell output patterns. Our results establish that the extent of synaptic connectivity governs the pattern separation performance of feedforward networks by counteracting the beneficial effects of expanding coding space and threshold-mediated decorrelation. The sparse synaptic connectivity in the cerebellar input layer provides an optimal solution to this trade-off, enabling efficient pattern separation and faster learning.