3 citations · 3 across the 9 of their papers we have counts for
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Sharp Sobolev Approximation on General Domains by Linearized Shallow Networks with Analytic Activations
Jia Li, Tong Mao, Jinchao Xu
We study Sobolev approximation on bounded domains by linearized shallow neural networks whose inner parameters are prescribed independently of the target function. Our main step is…
Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples
Xinliang Liu, Tong Mao, Jinchao Xu
We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations using linearized ReLU neural networks on the sp…
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…
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…
Configuration-Dependent Lower Bounds for Approximation by Shallow ReLU Networks on the Sphere
Tong Mao, Jinchao Xu
We establish two related but logically distinct results for shallow ReLU neural networks on the unit sphere $\SS^d$. First, for an arbitrary set of inner neural-network paramet…
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…