Mathematics Colloquia and Seminars

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Many networks in the brain are sparsely connected, and the brain prunes connections during development, learning and, perhaps, sleep. Determining how the brain finds and maintains sparse network structure is important both to understanding the brain’s remarkable energy efficiency (and replicating it in artificial neural networks) and to understanding changes in connection density in disease and across the lifespan.

How could the brain decide which connections to prune? Determining the importance of a connection between two neurons is hard, depending on the role that both neurons play and on all possible pathways of information flow between them. Noise is ubiquitous in neural systems and often considered an irritant to be overcome, but I will suggest that the brain may use noise to probe network structure and will demonstrate a simple noise-driven learning rule that removes redundant network connections. For an important class of linear networks this rule provably preserves numerous properties of the original dynamics, even when the fraction of removed connections approaches 1.