2 citations · 6 across the 12 of their papers we have counts for
13 papers
Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension
Jianfei Li, Shuo Huang, Han Feng +2
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter diffic…
Spherical Analysis of Learning Nonlinear Functionals
Zhenyu Yang, Shuo Huang, Han Feng +1
In recent years, there has been growing interest in the field of functional neural networks. They have been proposed and studied with the aim of approximating continuous functional…
Bridging Smoothness and Approximation: Theoretical Insights into Over-Smoothing in Graph Neural Networks
Guangrui Yang, Jianfei Li, Ming Li +2
In this paper, we explore the approximation theory of functions defined on graphs. Our study builds upon the approximation results derived from the -functional. We establish a t…
Convergence Analysis for Deep Sparse Coding via Convolutional Neural Networks
Jianfei Li, Han Feng, Ding-Xuan Zhou
In this work, we explore the intersection of sparse coding theory and deep learning to enhance our understanding of feature extraction capabilities in advanced neural network archi…
On the rates of convergence for learning with convolutional neural networks
Yunfei Yang, Han Feng, Ding-Xuan Zhou
We study approximation and learning capacities of convolutional neural networks (CNNs) with one-side zero-padding and multiple channels. Our first result proves a new approximation…
Permutation Equivariant Graph Framelets for Heterophilous Graph Learning
Jianfei Li, Ruigang Zheng, Han Feng +2
The nature of heterophilous graphs is significantly different from that of homophilous graphs, which causes difficulties in early graph neural network models and suggests aggregati…
Fine-grained Analysis of Non-parametric Estimation for Pairwise Learning
Junyu Zhou, Shuo Huang, Han Feng +2
In this paper, we are concerned with the generalization performance of non-parametric estimation for pairwise learning. Most of the existing work requires the hypothesis space to b…
SignReLU neural network and its approximation ability
Jianfei Li, Han Feng, Ding-Xuan Zhou
Deep neural networks (DNNs) have garnered significant attention in various fields of science and technology in recent years. Activation functions define how neurons in DNNs process…
Approximation analysis of CNNs from a feature extraction view
Jianfei Li, Han Feng, Ding-Xuan Zhou
Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures…
Convolutional Neural Networks for Spherical Signal Processing via Spherical Haar Tight Framelets
Jianfei Li, Han Feng, Xiaosheng Zhuang
In this paper, we develop a general theoretical framework for constructing Haar-type tight framelets on any compact set with a hierarchical partition. In particular, we construct a…
Radial Basis Function Approximation with Distributively Stored Data on Spheres
Han Feng, Shao-Bo Lin, Ding-Xuan Zhou
This paper proposes a distributed weighted regularized least squares algorithm (DWRLS) based on spherical radial basis functions and spherical quadrature rules to tackle spherical…
Theory of Deep Convolutional Neural Networks II: Spherical Analysis
Zhiying Fang, Han Feng, Shuo Huang +1
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications.…
Best polynomial approximation on the triangle
Han Feng, Christian Krattenthaler, Yuan Xu
Let denote the error of best approximation by polynomials of degree at most in the space on the triangle $\{(x,y): x, y \ge 0, x+y \le 1\…