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This is close to the slowest decay, meaning the most high-dimensional code, that still keeps the response a smooth function of the image, and which circuit mechanism sets it is unknown.","posed_since":"2019","precise":"In mouse primary visual cortex, principal-component variances of responses to natural images follow $\\lambda_n \\sim n^{-\\alpha}$ with $\\alpha \\sim 1$ (Stringer and co-workers, 2019), near the bound $\\alpha > 1 + 2/d$ required for a smooth representation of d-dimensional inputs. Identify the circuit mechanism (recurrent dynamics, plasticity, input statistics) that yields $\\alpha \\sim 1$, and explain why alpha stays near the bound $1 + 2/d$ for low-dimensional stimulus sets, as measured.","problem_ref":null,"references":"","settled_by":"A circuit model with measured connectivity statistics that predicts $\\alpha$ for several stimulus ensembles, confirmed by recordings.","status_note":"","title":"Origin of the 1/n spectrum of cortical population 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