title: Optimal Degrees of Synaptic Connectivity.
abstract: 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.
authors.affiliation: Mortimer B. Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, NY 10027, USA. Electronic address: ak3625@columbia.edu.
authors.forename: Ashok
authors.initials: A
authors.lastname: Litwin-Kumar
authors.affiliation: Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA.
authors.forename: Kameron Decker
authors.initials: KD
authors.lastname: Harris
authors.affiliation: Mortimer B. Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, NY 10027, USA; Department of Biochemistry and Molecular Biophysics, Columbia University, New York, NY 10032, USA; Howard Hughes Medical Institute, Columbia University, New York, NY 10032, USA.
authors.forename: Richard
authors.initials: R
authors.lastname: Axel
authors.affiliation: Edmond and Lily Safra Center for Brain Sciences, Hebrew University, Jerusalem 91904, Israel; Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel; Center for Brain Science, Harvard University, Cambridge, MA 02138, USA.
authors.forename: Haim
authors.initials: H
authors.lastname: Sompolinsky
authors.affiliation: Mortimer B. Zuckerman Mind Brain Behavior Institute, Department of Neuroscience, Columbia University, New York, NY 10027, USA; Department of Physiology and Cellular Biophysics, Columbia University, New York, NY 10032, USA.
authors.forename: L F
authors.initials: LF
authors.lastname: Abbott
mesh_terms: D000818:Animals; D002531:Cerebellum / Q000502:physiology; D002540:Cerebral Cortex / Q000502:physiology; D004331:Drosophila melanogaster; D008959:Models, Neurological; D024521:Mushroom Bodies / Q000502:physiology; D009473:Neuronal Plasticity / Q000502:physiology*; D011689:Purkinje Cells / Q000502:physiology*; D013569:Synapses / Q000502:physiology*