196 citations · 688 across the 10 of their papers we have counts for
10 papers
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
Baicheng Li, Haizhao Yang, Shijun Zhang
In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2…
Multigrade Neural Network Approximation
Shijun Zhang, Zuowei Shen, Yuesheng Xu
We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now…
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions
Shijun Zhang, Jianfeng Lu, Hongkai Zhao
This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set is defined to encompass the m…
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These…
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper concentrates on the approximation power of deep feed-forward neural networks in terms of width and depth. It is proved by construction that ReLU networks with width $\ma…
Neural Network Approximation: Three Hidden Layers Are Enough
Zuowei Shen, Haizhao Yang, Shijun Zhang
A three-hidden-layer neural network with super approximation power is introduced. This network is built with the floor function (), the exponential function ($2^x…
Deep Network with Approximation Error Being Reciprocal of Width to Power of Square Root of Depth
Zuowei Shen, Haizhao Yang, Shijun Zhang
A new network with super approximation power is introduced. This network is built with Floor () or ReLU () activation function in each neuron and hen…
Deep Network Approximation for Smooth Functions
Jianfeng Lu, Zuowei Shen, Haizhao Yang +1
This paper establishes the (nearly) optimal approximation error characterization of deep rectified linear unit (ReLU) networks for smooth functions in terms of both width and depth…
Deep Network Approximation Characterized by Number of Neurons
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper quantitatively characterizes the approximation power of deep feed-forward neural networks (FNNs) in terms of the number of neurons. It is shown by construction that ReLU…
Nonlinear Approximation via Compositions
Zuowei Shen, Haizhao Yang, Shijun Zhang
Given a function dictionary and an approximation budget , nonlinear approximation seeks the linear combination of the best terms $\{T_n\}_{1\le n\le…