Dimension lower bounds for linear approaches to function approximation

Daniel Hsu

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arXiv · 2508.13346

Dimension lower bounds for linear approaches to function approximation

Daniel Hsu

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Abstract

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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Daniel Hsu. 2025-08-18. Dimension lower bounds for linear approaches to function approximation. https://arxiv.org/abs/2508.13346

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