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math.ST updates on arXiv.org

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Dimension lower bounds for linear approaches to function approximation
Daniel Hsu · 2025-08-19 · via math.ST updates on arXiv.org

This short note presents a linear algebraic approach to proving dimension lower bounds for linear methods that solve $L^2$ function approximation problems. The basic argument has appeared in the literature before (e.g., Barron, 1993) for establishing lower bounds on Kolmogorov $n$-widths. The argument is applied to give sample size lower bounds for kernel methods.

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