{"ID":2881299,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13346","arxiv_id":"2508.13346","title":"Dimension lower bounds for linear approaches to function approximation","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.","short_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 giv...","url_abs":"https://arxiv.org/abs/2508.13346","url_pdf":"https://arxiv.org/pdf/2508.13346v1","authors":"[\"Daniel Hsu\"]","published":"2025-08-18T20:04:46Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.ST\"]","methods":"[]","has_code":false}