196 citations · 1.4k across the 75 of their papers we have counts for
18 papers · 1 filter
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives
Yahong Yang, Haizhao Yang, Yang Xiang
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural network…
Finite Expression Methods for Discovering Physical Laws from Data
Zhongyi Jiang, Chunmei Wang, Haizhao Yang
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics…
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Ke Chen, Chunmei Wang, Haizhao Yang
Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an e…
A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
Qiyuan Pang, Haizhao Yang
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of…
Reinforced Inverse Scattering
Hanyang Jiang, Yuehaw Khoo, Haizhao Yang
Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in di…
Neural Network Architecture Beyond Width and Depth
Zuowei Shen, Haizhao Yang, Shijun Zhang
This paper proposes a new neural network architecture by introducing an additional dimension called height beyond width and depth. Neural network architectures with height, width,…
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
Yong Zheng Ong, Zuowei Shen, Haizhao Yang
Discretization invariant learning aims at learning in the infinite-dimensional function spaces with the capacity to process heterogeneous discrete representations of functions as i…
Deep Network Approximation in Terms of Intrinsic Parameters
Zuowei Shen, Haizhao Yang, Shijun Zhang
One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive…
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…
Reproducing Activation Function for Deep Learning
Senwei Liang, Liyao Lyu, Chunmei Wang +1
We propose reproducing activation functions (RAFs) to improve deep learning accuracy for various applications ranging from computer vision to scientific computing. The idea is to e…
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…
Instance Enhancement Batch Normalization: an Adaptive Regulator of Batch Noise
Senwei Liang, Zhongzhan Huang, Mingfu Liang +1
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of…
CASS: Cross Adversarial Source Separation via Autoencoder
Yong Zheng Ong, Charles K. Chui, Haizhao Yang
This paper introduces a cross adversarial source separation (CASS) framework via autoencoder, a new model that aims at separating an input signal consisting of a mixture of multipl…
SelectNet: Learning to Sample from the Wild for Imbalanced Data Training
Yunru Liu, Tingran Gao, Haizhao Yang
Supervised learning from training data with imbalanced class sizes, a commonly encountered scenario in real applications such as anomaly/fraud detection, has long been considered a…
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…