155 citations · 379 across the 24 of their papers we have counts for
7 papers · 1 filter
Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain Ridge Integral Spaces for ReLU Networks
Juncai He, Zitong Tian
We develop the space and approximation theory for shallow neural networks with activations. The central object is the Radon-domain space $\mathcal{R}L…
Divergence-free Linearized Neural Networks: Integral Representation and Optimal Approximation Rates
Juncai He, Xinliang Liu, Zitong Tian
This paper studies the numerical approximation of divergence-free vector fields by linearized shallow neural networks, also referred to as random feature models or finite neuron sp…
Deep Neural Networks and Finite Elements of Any Order on Arbitrary Dimensions
Juncai He, Jinchao Xu
In this study, we establish that deep neural networks employing ReLU and ReLU activation functions can effectively represent Lagrange finite element functions of any order on v…
ReLU Deep Neural Networks from the Hierarchical Basis Perspective
Juncai He, Lin Li, Jinchao Xu
We study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods. First, we show that the approximation sch…
Power Series Expansion Neural Network
Qipin Chen, Wenrui Hao, Juncai He
In this paper, we develop a new neural network family based on power series expansion, which is proved to achieve a better approximation accuracy in comparison with existing neural…
ReLU Deep Neural Networks and Linear Finite Elements
Juncai He, Lin Li, Jinchao Xu +1
In this paper, we investigate the relationship between deep neural networks (DNN) with rectified linear unit (ReLU) function as the activation function and continuous piecewise lin…
Generalized Gaffney inequality and discrete compactness for discrete differential forms
Juncai He, Kaibo Hu, Jinchao Xu
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on -regular domains, including general Lipschitz domains. In computa…