155 citations · 379 across the 24 of their papers we have counts for
24 papers
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…
Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations
Shuang Chen, Juncai He, Xue-Cheng Tai
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition an…
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…
Self-composing neural operators for high-frequency and multiscale PDE surrogates
Juncai He, Xinliang Liu, Jinchao Xu
Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framew…
Alignment at Pre-training! Towards Native Alignment for Arabic LLMs
Juhao Liang, Zhenyang Cai, Jianqing Zhu +9
The alignment of large language models (LLMs) is critical for developing effective and safe language models. Traditional approaches focus on aligning models during the instruction…
Second Language (Arabic) Acquisition of LLMs via Progressive Vocabulary Expansion
Jianqing Zhu, Huang Huang, Zhihang Lin +18
This paper addresses the critical need for democratizing large language models (LLM) in the Arab world, a region that has seen slower progress in developing models comparable to st…
Expressivity and Approximation Properties of Deep Neural Networks with ReLU Activation
Juncai He, Tong Mao, Jinchao Xu
In this paper, we investigate the expressivity and approximation properties of deep neural networks employing the ReLU activation function for . Although deep ReLU ne…
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…
MgNO: Efficient Parameterization of Linear Operators via Multigrid
Juncai He, Xinliang Liu, Jinchao Xu
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural o…
On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem
Juncai He
This paper is devoted to studying the optimal expressive power of ReLU deep neural networks (DNNs) and its application in approximation via the Kolmogorov Superposition Theorem. We…
Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions
Liangchen Liu, Juncai He, Richard Tsai
In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objecti…
FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting
Jianqing Zhu, Juncai He, Lian Zhang +1
By investigating iterative methods for a constrained linear model, we propose a new class of fully connected V-cycle MgNet for long-term time series forecasting, which is one of th…
An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations
Jianqing Zhu, Juncai He, Qiumei Huang
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the…
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space
Juncai He, Richard Tsai, Rachel Ward
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low-dimensional manifolds em…
An Interpretive Constrained Linear Model for ResNet and MgNet
Juncai He, Jinchao Xu, Lian Zhang +1
We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN). From this vie…
A Weight Initialization Based on the Linear Product Structure for Neural Networks
Qipin Chen, Wenrui Hao, Juncai He
Weight initialization plays an important role in training neural networks and also affects tremendous deep learning applications. Various weight initialization strategies have alre…
Approximation Properties of Deep ReLU CNNs
Juncai He, Lin Li, Jinchao Xu
This paper focuses on establishing approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space. The analysis is based on a decomposit…
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…
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…
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…
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…
Make Regularization Effective in Training Sparse CNN
Juncai He, Xiaodong Jia, Jinchao Xu +2
Compressed Sensing using regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse…
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…