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We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN).
Iterative methods by space decomposition and subspace correction
Jinchao Xu · 1992
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Iterative Solution of Large Sparse Systems of Equations
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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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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Learning fast approximations of sparse coding
Karol Gregor and Yann LeCun · 2010
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Matrix Computations
Gene H Golub and Charles F Van Loan · 2012
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Optimization and dynamical systems
Uwe Helmke and John B Moore · 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
Wolfgang Hackbusch · 2013
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Dropout: a simple way to prevent neural networks from overfitting
Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov · 2014
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Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding
Song Han, Huizi Mao, and William J Dally · 2015
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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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U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
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Imagenet large scale visual recognition challenge
Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al · 2015
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Very deep convolutional networks for large-scale image recognition
Karen Simonyan and Andrew Zisserman · 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 residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Identity mappings in deep residual networks
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Multigrid neural architectures
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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Aggregated residual transformations for deep neural networks
Saining Xie, Ross Girshick, Piotr Dollár, Zhuowen Tu, and Kaiming He · 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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Neural ordinary differential equations
Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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Learning deep resnet blocks sequentially using boosting theory
Furong Huang, Jordan Ash, John Langford, and Robert Schapire · 2018
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Optimization algorithm inspired deep neural network structure design
Huan Li, Yibo Yang, Dongmin Chen, and Zhouchen Lin · 2018
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Etai Littwin and Lior Wolf · 2016
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V-net: Fully convolutional neural networks for volumetric medical image segmentation
Fausto Milletari, Nassir Navab, and Seyed-Ahmad Ahmadi · 2016
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Deep admm-net for compressive sensing mri
Jian Sun, Huibin Li, Zongben Xu, et al · 2016
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Residual networks behave like ensembles of relatively shallow networks
Andreas Veit, Michael J Wilber, and Serge Belongie · 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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A proposal on machine learning via dynamical systems
Weinan E · 2017
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Resnet with one-neuron hidden layers is a universal approximator
Hongzhou Lin and Stefanie Jegelka · 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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Functional gradient boosting based on residual network perception
Atsushi Nitanda and Taiji Suzuki · 2018
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What can resnet learn efficiently, going beyond kernels?
Zeyuan Allen-Zhu and Yuanzhi Li · 2019
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Mgnet: A unified framework of multigrid and convolutional neural network
Juncai He and Jinchao Xu · 2019
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Learning neural pde solvers with convergence guarantees
Jun-Ting Hsieh, Shengjia Zhao, Stephan Eismann, Lucia Mirabella, and Stefano Ermon · 2019
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Pytorch: An imperative style, high-performance deep learning library
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala · 2019
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Scan: A scalable neural networks framework towards compact and efficient models
Linfeng Zhang, Zhanhong Tan, Jiebo Song, Jingwei Chen, Chenglong Bao, and Kaisheng Ma · 2019
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Make ℓ 1 \ell_{1} regularization effective in training sparse cnn
Juncai He, Xiaodong Jia, Jinchao Xu, Lian Zhang, and Liang Zhao · 2020
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Why do deep residual networks generalize better than deep feedforward networks?—a neural tangent kernel perspective
Kaixuan Huang, Yuqing Wang, Molei Tao, and Tuo Zhao · 2020
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Approximation properties of deep relu cnns
Juncai He, Lin Li, and Jinchao Xu · 2022
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Kernel-based smoothness analysis of residual networks
Tom Tirer, Joan Bruna, and Raja Giryes · 2022
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