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08/10/2023
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 d...
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07/05/2023
Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions
In this paper, we study linear regression applied to data structured on ...
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02/02/2023
FV-MgNet: Fully Connected V-cycle MgNet for Interpretable Time Series Forecasting
By investigating iterative methods for a constrained linear model, we pr...
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02/02/2023
An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations
This study used a multigrid-based convolutional neural network architect...
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03/01/2022
Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space
The low dimensional manifold hypothesis posits that the data found in ma...
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12/14/2021
An Interpretive Constrained Linear Model for ResNet and MgNet
We propose a constrained linear data-feature-mapping model as an interpr...
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09/01/2021
Approximation Properties of Deep ReLU CNNs
This paper is devoted to establishing L^2 approximation properties for d...
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09/01/2021
A Weight Initialization Based on the Linear Product Structure for Neural Networks
Weight initialization plays an important role in training neural network...
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05/18/2021
Make $\ell_1$ Regularization Effective in Training Sparse CNN
Compressed Sensing using 𝓁1 regularization is among the most powerful an...
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05/18/2021
ReLU Deep Neural Networks and linear Finite Elements
In this paper, we investigate the relationship between deep neural netwo...
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05/10/2021
ReLU Deep Neural Networks from the Hierarchical Basis Perspective
We study ReLU deep neural networks (DNNs) by investigating their connect...
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02/25/2021
Power series expansion neural network
In this paper, we develop a new neural network family based on power ser...
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11/23/2019
Constrained Linear Data-feature Mapping for Image Classification
In this paper, we propose a constrained linear data-feature mapping mode...
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01/29/2019
MgNet: A Unified Framework of Multigrid and Convolutional Neural Network
We develop a unified model, known as MgNet, that simultaneously recovers...
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07/11/2018