3 papers
math.NA2026
Solving High-Dimensional PDEs Using Linearized Neural Networks
Tong Mao, Jinchao Xu, Xiaofeng Xu
Linearized shallow neural networks that are constructed by fixing the hidden-layer parameters have recently shown strong performance in solving partial differential equations (PDEs…
math.NA2025
Condition Numbers and Eigenvalue Spectra of Shallow Networks on Spheres
Xinliang Liu, Tong Mao, Jinchao Xu
We present an estimation of the condition numbers of the \emph{mass} and \emph{stiffness} matrices arising from shallow ReLU neural networks defined on the unit sphere~$\mathbb…
math.NA2025
Integral Representations of Sobolev Spaces via ReLU Activation Function and Optimal Error Estimates for Linearized Networks
Xinliang Liu, Tong Mao, Jinchao Xu
This paper presents two main theoretical results concerning shallow neural networks with ReLU activation functions. We establish a novel integral representation for Sobolev spa…