155 citations · 987 across the 104 of their papers we have counts for
6 papers · 1 filter
Constrained Linear Data-feature Mapping for Image Classification
Juncai He, Yuyan Chen, Lian Zhang +1
In this paper, we propose a constrained linear data-feature mapping model as an interpretable mathematical model for image classification using convolutional neural network (CNN) s…
An Extended Galerkin Analysis for Elliptic Problems
Qingguo Hong, Shuonan Wu, Jinchao Xu
A general analysis framework is presented in this paper for many different types of finite element methods (including various discontinuous Galerkin methods). For second order elli…
Extended Regularized Dual Averaging Methods for Stochastic Optimization
Jonathan W. Siegel, Jinchao Xu
We introduce a new algorithm, extended regularized dual averaging (XRDA), for solving regularized stochastic optimization problems, which generalizes the regularized dual averaging…
Approximation Rates for Neural Networks with General Activation Functions
Jonathan W. Siegel, Jinchao Xu
We prove some new results concerning the approximation rate of neural networks with general activation functions. Our first result concerns the rate of approximation of a two layer…
A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry
Fei Wang, Shuonan Wu, Jinchao Xu
In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in -dimension ($d…
MgNet: A Unified Framework of Multigrid and Convolutional Neural Network
Juncai He, Jinchao Xu
We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving di…