math.NA · 2026-09-08 · No. 109

Numerical Analysis, 2026-09-08.

1 new papers in math.NA. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

1 entries
  1. 01

    Shallow neural network approximation in mixed Sobolev spaces

    Yuwen Li, Guozhi Zhang

    math.NA · cs.LG

    We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions. We first establish an activation-independent Fourier-block principle: if an activation has univariate approximation order $ρ$ in the sense of the Fourier-block property, then the global approximation rate has algebraic order $\min\{α,ρ\}$ for target functions of mixed smoothness $α$, up to explicit...

    arxiv.org/abs/2609.05263 · PDF

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