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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).
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Iterative methods by space decomposition and subspace correction
Jinchao Xu · 1992
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Universal approximation bounds for superpositions of a sigmoidal function
Andrew R Barron · 1993
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Aspects of the numerical analysis of neural networks
SW Ellacott · 1994
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Iterative solution of large sparse systems of equations , volume 95
Wolfgang Hackbusch · 1994
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Gradient-based learning applied to document recognition
Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner · 1998
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Approximation theory of the mlp model in neural networks
Allan Pinkus · 1999
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The method of alternating projections and the method of subspace corrections in Hilbert space
Jinchao Xu and Ludmil Zikatanov · 2002
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Imagenet: A large-scale hierarchical image database
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei · 2009
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Learning multiple layers of features from tiny images
Alex Krizhevsky and Geoffrey Hinton · 2009
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Rectified linear units improve restricted boltzmann machines
Vinod Nair and Geoffrey E Hinton · 2010
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Matrix computations , volume 3
Gene H Golub and Charles F Van Loan · 2012
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton · 2012
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Multi-grid methods and applications , volume 4
Wolfgang Hackbusch · 2013
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Very deep convolutional networks for large-scale image recognition
Karen Simonyan and Andrew Zisserman · 2014
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
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Batch normalization: Accelerating deep network training by reducing internal covariate shift
Sergey Ioffe and Christian Szegedy · 2015
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Deep learning
Yann LeCun, Yoshua Bengio, and Geoffrey Hinton · 2015
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Learning deconvolution network for semantic segmentation
Hyeonwoo Noh, Seunghoon Hong, and Bohyung Han · 2015
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U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
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Going deeper with convolutions
Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, and Andrew Rabinovich · 2015
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Deep multigrid: learning prolongation and restriction matrices
Alexandr Katrutsa, Talgat Daulbaev, and Ivan Oseledets · 2017
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A flow model of neural networks
Zhen Li and Zuoqiang Shi · 2017
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Feature pyramid networks for object detection
Tsung-Yi Lin, Piotr Dollár, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie · 2017
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When image denoising meets high-level vision tasks: A deep learning approach
Ding Liu, Bihan Wen, Xianming Liu, and Thomas S. Huang · 2017
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Deep relu networks lessen the curse of dimensionality
Hadrien Montanelli and Qiang Du · 2017
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Tsung-Wei Ke, Michael Maire, and X Yu Stella · 2016
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Fractalnet: Ultra-deep neural networks without residuals
Gustav Larsson, Michael Maire, and Gregory Shakhnarovich · 2016
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Image restoration using very deep convolutional encoder-decoder networks with symmetric skip connections
Xiao-Jiao Mao, Chunhua Shen, and Yu-Bin Yang · 2016
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V-net: Fully convolutional neural networks for volumetric medical image segmentation
F. Milletari, N. Navab, and S. A. Ahmadi · 2016
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Wide residual networks
Sergey Zagoruyko and Nikos Komodakis · 2016
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Multi-level residual networks from dynamical systems view
Bo Chang, Lili Meng, Eldad Haber, Frederick Tung, and David Begert · 2017
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Dual path networks
Yunpeng Chen, Jianan Li, Huaxin Xiao, Xiaojie Jin, Shuicheng Yan, and Jiashi Feng · 2017
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Algebraic multigrid methods
Jinchao Xu and Ludmil Zikatanov · 2017
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Polynet: A pursuit of structural diversity in very deep networks
Xingcheng Zhang, Zhizhong Li, Chen Change Loy, and Dahua Lin · 2017
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Optimization methods for large-scale machine learning
Léon Bottou, Frank E Curtis, and Jorge Nocedal · 2018
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Exponential convergence of the deep neural network approximation for analytic functions
Weinan E and Qingcan Wang · 2018
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Relu deep neural networks and linear finite elements
Juncai He, Lin Li, Jinchao Xu, and Chunyue Zheng · 2018
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Learning neural pde solvers with convergence guarantees
Jun-Ting Hsieh, Shengjia Zhao, Stephan Eismann, Lucia Mirabella, and Stefano Ermon · 2018
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Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations
Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong · 2018
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Provable approximation properties for deep neural networks
Uri Shaham, Alexander Cloninger, and Ronald R Coifman · 2018
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Universality of deep convolutional neural networks
Ding-Xuan Zhou · 2018
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On the approximation properties of neural networks
Jonathan W Siegel and Jinchao Xu · 2019
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The Finite Element Methods
Jinchao Xu · 2019
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