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This paper establishes the (nearly) optimal approximation error characterization of deep rectified linear unit (ReLU) networks for smooth functions in terms of both width and depth simultaneously.
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Optimal nonlinear approximation
Ronald A. Devore · 1989
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
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Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
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Efficient distribution-free learning of probabilistic concepts
Michael J. Kearns and Robert E. Schapire · 1994
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Almost linear VC-dimension bounds for piecewise polynomial networks
Peter Bartlett, Vitaly Maiorov, and Ron Meir · 1998
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Akito Sakurai · 1999
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton · 2012
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On the complexity of neural network classifiers: A comparison between shallow and deep architectures
M. Bianchini and F. Scarselli · 2014
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On the number of linear regions of deep neural networks
Guido F Montufar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio · 2014
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Shiyu Liang and R. Srikant · 2016
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Nearly-tight VC-dimension bounds for piecewise linear neural networks
Nick Harvey, Christopher Liaw, and Abbas Mehrabian · 2017
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Why and when can deep—but not shallow—networks avoid the curse of dimensionality: A review
T. Poggio, H. N. Mhaskar, L. Rosasco, B. Miranda, and Q. Liao · 2017
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Error bounds for approximations with deep ReLU networks
Dmitry Yarotsky · 2017
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Learning and generalization in overparameterized neural networks, going beyond two layers
Zeyuan Allen-Zhu, Yuanzhi Li, and Yingyu Liang · 2018
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Approximation and estimation for high-dimensional deep learning networks
Andrew R. Barron and Jason M. Klusowski · 2018
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Charles K. Chui, Shao-Bo Lin, and Ding-Xuan Zhou · 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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A priori estimates of the population risk for residual networks
Weinan E, Chao Ma, and Qingcan Wang · 2019
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A priori estimates of the population risk for two-layer neural networks
Weinan E, Chao Ma, and Lei Wu · 2019
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Approximation spaces of deep neural networks
Rémi Gribonval, Gitta Kutyniok, Morten Nielsen, and Felix Voigtlaender · 2019
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Error bounds for approximations with deep ReLU neural networks in W s , p W^{s,p} norms
Ingo Gühring, Gitta Kutyniok, and Philipp Petersen · 2019
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New error bounds for deep networks using sparse grids
Hadrien Montanelli and Qiang Du · 2019
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Neural tangent kernel: Convergence and generalization in neural networks
Arthur Jacot, Franck Gabriel, and Clément Hongler · 2018
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Optimal approximation of piecewise smooth functions using deep ReLU neural networks
Philipp Petersen and Felix Voigtlaender · 2018
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Optimal approximation of continuous functions by very deep ReLU networks
Dmitry Yarotsky · 2018
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Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks
Sanjeev Arora, Simon S. Du, Wei Hu, Zhiyuan Li, and Ruosong Wang · 2019
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Approximation analysis of convolutional neural networks
Chenglong Bao, Qianxiao Li, Zuowei Shen, Cheng Tai, Lei Wu, and Xueshuang Xiang · 2019
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Optimal approximation with sparsely connected deep neural networks
Helmut. Bölcskei, Philipp. Grohs, Gitta. Kutyniok, and Philipp. Petersen · 2019
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Generalization bounds of stochastic gradient descent for wide and deep neural networks
Yuan Cao and Quanquan Gu · 2019
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Deep ReLU networks overcome the curse of dimensionality for bandlimited functions
Hadrien Montanelli, Haizhao Yang, and Qiang Du · 2019
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Exponential ReLU DNN expression of holomorphic maps in high dimension
J. A. A. Opschoor, Ch. Schwab, and J. Zech · 2019
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Nonlinear approximation via compositions
Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2019
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Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality
Taiji Suzuki · 2019
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Ziwei Ji and Matus Telgarsky · 2020
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Error bounds for deep ReLU networks using the Kolmogorov–Arnold superposition theorem
Hadrien Montanelli and Haizhao Yang · 2020
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Deep network approximation characterized by number of neurons
Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
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The phase diagram of approximation rates for deep neural networks
Dmitry Yarotsky and Anton Zhevnerchuk · 2020
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Universality of deep convolutional neural networks
Ding-Xuan Zhou · 2020
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