Author

Jia Li

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Preprint Aug 2026

Sharp Approximation on the Sphere by Linearized Shallow Networks with Analytic Activations

The analysis connects spectral asymptotic asymptotics and lower bounds at the degrees where the ultraspherical coefficients do not vanish with Sobolev-norm approximation and coefficient control for fixed analytic activation functions.

Jia Li, Tong Mao, Jin-Chao Xu · 0 citations

Preprint Aug 2026

Sharp Sobolev Approximation on General Domains by Linearized Shallow Networks with Analytic Activations

It is proved that quasi-Chebyshev parameter sets with univariate resolution $m$ generate fixed feature spaces attaining the sharp $H^r$-to-to-H^s$ approximation order for a class of analytic activations satisfying a quantitative non-cancellation condition on their Taylor coefficients.

Jia Li, Tong Mao, Jin-Chao Xu · 2 citations