Optimal Degrees of Synaptic Connectivity

Synaptic connectivity varies widely across neuronal types. Cerebellar granule cells receive five orders of magnitude fewer inputs than the Purkinje cells they innervate, and cerebellum-like circuits, including the insect mushroom body, also exhibit large divergences in connectivity. In contrast, the number of inputs per neuron in cerebral cortex is more uniform and large. We investigate how the dimension of a representation formed by a population of neurons depends on how many inputs each neuron receives and what this implies for learning associations. Our theory predicts that the dimensions of the cerebellar granule-cell and Drosophila Kenyon-cell representations are maximized at degrees of synaptic connectivity that match those observed anatomically, showing that sparse connectivity is sometimes superior to dense connectivity. When input synapses are subject to supervised plasticity, however, dense wiring becomes advantageous, suggesting that the type of plasticity exhibited by a set of synapses is a major determinant of connection density. •Sparse synaptic wiring can optimize a neural representation for associative learning•Maximizing dimension predicts the degree of connectivity for cerebellum-like circuits•Supervised plasticity of input connections is needed to exploit dense wiring•Performance of a Hebbian readout neuron is formally related to dimension The number of inputs a neuron receives varies widely across different neural circuits. Using analytic calculations, Litwin-Kumar et al. relate this degree of connectivity to the ability of neuronal populations to produce high-dimensional stimulus representations and support associative learning.