Search Results for author:
Found 19 papers, 2 papers with code
Data-induced multiscale losses and efficient multirate gradient descent schemes
This paper investigates the impact of multiscale data on machine learning algorithms, particularly in the context of deep learning.
Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss
Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question.
Expressivity and Approximation Properties of Deep Neural Networks with ReLU$^k$ Activation
Additionally, through an exploration of the representation power of deep ReLU$^k$ networks for shallow networks, we reveal that deep ReLU$^k$ networks can approximate functions from a range of variation spaces, extending beyond those generated solely by the ReLU$^k$ activation function.
Deep Neural Networks and Finite Elements of Any Order on Arbitrary Dimensions
In this study, we establish that deep neural networks employing ReLU and ReLU$^2$ activation functions can effectively represent Lagrange finite element functions of any order on various simplicial meshes in arbitrary dimensions.
MgNO: Efficient Parameterization of Linear Operators via Multigrid
In this work, we propose a concise neural operator architecture for operator learning.
AceGPT, Localizing Large Language Models in Arabic
This paper is devoted to the development of a localized Large Language Model (LLM) specifically for Arabic, a language imbued with unique cultural characteristics inadequately addressed by current mainstream models.
On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem
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.
Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions
We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic geometry on the regression.
FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting
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 the most difficult tasks in forecasting.
An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs).
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space
In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.
An Interpretive Constrained Linear Model for ResNet and MgNet
We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN).
Approximation Properties of Deep ReLU CNNs
This paper focuses on establishing $L^2$ approximation properties for deep ReLU convolutional neural networks (CNNs) in two-dimensional space.
A Weight Initialization Based on the Linear Product Structure for Neural Networks
To address this challenge, we study neural networks from a nonlinear computation point of view and propose a novel weight initialization strategy that is based on the linear product structure (LPS) of neural networks.
ReLU Deep Neural Networks from the Hierarchical Basis Perspective
We study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods.
Constrained Linear Data-feature Mapping for Image Classification
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) such as the ResNet.
iRDA Method for Sparse Convolutional Neural Networks
We propose a new approach, known as the iterative regularized dual averaging (iRDA), to improve the efficiency of convolutional neural networks (CNN) by significantly reducing the redundancy of the model without reducing its accuracy.
MgNet: A Unified Framework of Multigrid and Convolutional Neural Network
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 discretized partial differential equations (PDEs).
Make $\ell_1$ Regularization Effective in Training Sparse CNN
Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)?
