3 citations · 3 across the 11 of their papers we have counts for
6 papers · 1 filter
Convergence of Least Squares Methods for PDEs on R^d with Shallow ReLU^k Networks
Tong Mao, Lei Shi, Hanfei Zhou
We establish inverse inequalities in Gaussian Sobolev norms for shallow trial spaces. The estimates identify the sharp regularity threshold and quantify the depen…
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…
Sharp Approximation on the Sphere by Linearized Shallow Networks with Analytic Activations
Jia Li, Tong Mao, Jinchao Xu
We study the spectral behavior and approximation properties of linearized shallow networks with analytic activation functions on the unit sphere . Motivated by earlier…
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…
Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
Tong Mao, Jinchao Xu
Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom. However, practical computation operates under finite precisi…
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…