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Related papers: Approximation Properties of Deep ReLU CNNs

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This paper introduces deep super ReLU networks (DSRNs) as a method for approximating functions in Sobolev spaces measured by Sobolev norms $W^{m,p}$ for $m\in\mathbb{N}$ with $m\ge 2$ and $1\le p\le +\infty$. Standard ReLU deep neural…

Numerical Analysis · Mathematics 2025-09-03 Yahong Yang , Yue Wu , Haizhao Yang , Yang Xiang

In this paper we propose a novel decomposition method based on filter group approximation, which can significantly reduce the redundancy of deep convolutional neural networks (CNNs) while maintaining the majority of feature representation.…

Computer Vision and Pattern Recognition · Computer Science 2018-08-01 Bo Peng , Wenming Tan , Zheyang Li , Shun Zhang , Di Xie , Shiliang Pu

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we…

Machine Learning · Computer Science 2020-01-09 Gao Huang , Zhuang Liu , Geoff Pleiss , Laurens van der Maaten , Kilian Q. Weinberger

We consider approximations of general continuous functions on finite-dimensional cubes by general deep ReLU neural networks and study the approximation rates with respect to the modulus of continuity of the function and the total number of…

Neural and Evolutionary Computing · Computer Science 2018-06-08 Dmitry Yarotsky

An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular,…

Machine Learning · Statistics 2026-05-13 Anthony Lee

With the impressive capability to capture visual content, deep convolutional neural networks (CNN) have demon- strated promising performance in various vision-based ap- plications, such as classification, recognition, and objec- t…

Computer Vision and Pattern Recognition · Computer Science 2015-09-16 Zhen Liu

A deep convolutional neural network (CNN) has been widely used in image classification and gives better classification accuracy than the other techniques. The softmax cross-entropy loss function is often used for classification tasks. There…

Computer Vision and Pattern Recognition · Computer Science 2020-04-20 Motoshi Abe , Junichi Miyao , Takio Kurita

Deep convolutional neural networks (CNNs) have brought breakthroughs in processing clinical electrocardiograms (ECGs), speaker-independent speech and complex images. However, typical CNNs require a fixed input size while it is common to…

Machine Learning · Computer Science 2022-10-07 Linpeng Jin

This research project studies the impact of convolutional neural networks (CNN) in image classification tasks. We explore different architectures and training configurations with the use of ReLUs, Nesterov's accelerated gradient, dropout…

Computer Vision and Pattern Recognition · Computer Science 2019-10-30 Anderson de Andrade

Feature spaces in the deep layers of convolutional neural networks (CNNs) are often very high-dimensional and difficult to interpret. However, convolutional layers consist of multiple channels that are activated by different types of…

Machine Learning · Computer Science 2021-10-25 David Bonet , Antonio Ortega , Javier Ruiz-Hidalgo , Sarath Shekkizhar

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called…

Machine Learning · Computer Science 2020-07-10 Xingyu Xie , Hao Kong , Jianlong Wu , Wayne Zhang , Guangcan Liu , Zhouchen Lin

We propose a local modelling approach using deep convolutional neural networks (CNNs) for fine-grained image classification. Recently, deep CNNs trained from large datasets have considerably improved the performance of object recognition.…

Computer Vision and Pattern Recognition · Computer Science 2015-03-02 ZongYuan Ge , Chris McCool , Conrad Sanderson , Peter Corke

A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these…

Machine Learning · Computer Science 2020-12-04 Ben Sattelberg , Renzo Cavalieri , Michael Kirby , Chris Peterson , Ross Beveridge

We show that deep convolutional neural networks (CNN) can massively outperform traditional densely-connected neural networks (both deep or shallow) in predicting eigenvalue problems in mechanics. In this sense, we strike out in a new…

Computational Physics · Physics 2018-07-19 David Finol , Yan Lu , Vijay Mahadevan , Ankit Srivastava

Image search can be tackled using deep features from pre-trained Convolutional Neural Networks (CNN). The feature map from the last convolutional layer of a CNN encodes descriptive information from which a discriminative global descriptor…

Computer Vision and Pattern Recognition · Computer Science 2021-06-11 J. I. Forcen , Miguel Pagola , Edurne Barrenechea , Humberto Bustince

Reaction-diffusion systems represent one of the most fundamental formulations used to describe a wide range of physical, chemical, and biological processes. With the increasing adoption of neural networks, recent research has focused on…

Machine Learning · Computer Science 2025-10-17 Haotian Feng

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

Machine Learning · Statistics 2022-06-10 Hao Liu , Minshuo Chen , Siawpeng Er , Wenjing Liao , Tong Zhang , Tuo Zhao

Many classic methods have shown non-local self-similarity in natural images to be an effective prior for image restoration. However, it remains unclear and challenging to make use of this intrinsic property via deep networks. In this paper,…

Computer Vision and Pattern Recognition · Computer Science 2018-12-12 Ding Liu , Bihan Wen , Yuchen Fan , Chen Change Loy , Thomas S. Huang

Recently there has been much interest in understanding why deep neural networks are preferred to shallow networks. We show that, for a large class of piecewise smooth functions, the number of neurons needed by a shallow network to…

Machine Learning · Computer Science 2017-03-07 Shiyu Liang , R. Srikant

Convolutional neural networks (CNNs) have shown great capability of solving various artificial intelligence tasks. However, the increasing model size has raised challenges in employing them in resource-limited applications. In this work, we…

Computer Vision and Pattern Recognition · Computer Science 2018-09-06 Hongyang Gao , Zhengyang Wang , Shuiwang Ji