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Dimension lower bounds for linear approaches to function approximation

arXiv 2508.13346 ↗First posted 18 Aug 2025cs.LG math.ST stat.THcited by 0

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Abstract (arXiv)

This short note presents a linear algebraic approach to proving dimension lower bounds for linear methods that solve L2 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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 4 of its 17 references that are in the map. First posted on arXiv 18 Aug 2025.

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References · 4

  1. 2018Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernelcited by 131
  2. 2020Learning Parities with Neural Networkscited by 78
  3. 2021On the Approximation Power of Two-Layer Networks of Random ReLUscited by 29
  4. 2020Approximate is Good Enough: Probabilistic Variants of Dimensional and Margin Complexitycited by 25

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