Feb 2026· arXiv.org· Vol abs/2602.19381· 3 citations· 23 references
MathematicsComputer Science
TL;DR
A regularity theorem is established for second-order elliptic PDEs on $\mathbb{R}^{d}$ in spectral Barron spaces under mild ellipticity and smallness assumptions, and a class of PDEs whose solutions can be approximated by two-layer neural networks with cosine activation functions, where the width of the neural network is independent of the spatial dimension.
Abstract
We establish a regularity theorem for second-order elliptic PDEs on $\mathbb{R}^{d}$ in spectral Barron spaces. Under mild ellipticity and smallness assumptions, the solution gains two additional orders of Barron regularity. As a corollary, we identify a class of PDEs whose solutions can be approximated by two-layer neural networks with cosine activation functions, where the width of the neural network is independent of the spatial dimension.
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