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New estimates for the population risk are established for two-layer neural networks.
Theory of reproducing kernels
Nachman Aronszajn · 1950
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Solutions of ill-posed problems
A. N. Tikhonov and Vasilii IAkovlevich Arsenin · 1977
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Universal approximation bounds for superpositions of a sigmoidal function
Andrew R. Barron · 1993
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Hinging hyperplanes for regression, classification, and function approximation
Leo Breiman · 1993
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Approximation and estimation bounds for artificial neural networks
Andrew R. Barron · 1994
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Information-theoretic determination of minimax rates of convergence
Yuhong Yang and Andrew Barron · 1999
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The finite element method for elliptic problems
Philippe G. Ciarlet · 2002
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Optimal rates for the regularized least-squares algorithm
Andrea Caponnetto and Ernesto De Vito · 2007
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Uniform approximation of functions with random bases
Ali Rahimi and Benjamin Recht · 2008
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Imagenet classification with deep convolutional neural networks
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton · 2012
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A probabilistic theory of pattern recognition
Luc Devroye, László Györfi, and Gábor Lugosi · 2013
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Understanding machine learning: From theory to algorithms
Shai Shalev-Shwartz and Shai Ben-David · 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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Adam: A method for stochastic optimization
Diederik P. Kingma and Jimmy Ba · 2015
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Norm-based capacity control in neural networks
Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2015
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Risk bounds for high-dimensional ridge function combinations including neural networks
Jason M Klusowski and Andrew R Barron · 2016
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On the quality of the initial basin in overspecified neural networks
Itay Safran and Ohad Shamir · 2016
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Spectrally-normalized margin bounds for neural networks
Peter L. Bartlett, Dylan J. Foster, and Matus J. Telgarsky · 2017
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SGD learns the conjugate kernel class of the network
Amit Daniely · 2017
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Computing nonvacuous generalization bounds for deep (stochastic) neural networks with many more parameters than training data
Size-independent sample complexity of neural networks
Noah Golowich, Alexander Rakhlin, and Ohad Shamir · 2018
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Approximation by combinations of relu and squared relu ridge functions with l1 and l0 controls
Jason M Klusowski and Andrew R Barron · 2018
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A mean field view of the landscape of two-layers neural networks
Song Mei, Andrea Montanari, and Phan-Minh Nguyen · 2018
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A PAC-bayesian approach to spectrally-normalized margin bounds for neural networks
Behnam Neyshabur, Srinadh Bhojanapalli, and Nathan Srebro · 2018
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On the margin theory of feedforward neural networks
Colin Wei, Jason D. Lee, Qiang Liu, and Tengyu Ma · 2018
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Topology and geometry of half-rectified network optimization
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Minimax lower bounds for ridge combinations including neural nets
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Exploring generalization in deep learning
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Learning and generalization in overparameterized neural networks, going beyond two layers
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Stronger generalization bounds for deep nets via a compression approach
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A generalization theory of gradient descent for learning over-parameterized deep relu networks
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Gradient descent provably optimizes over-parameterized neural networks
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A priori estimates of the population risk for residual networks
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Analysis of the gradient descent algorithm for a deep neural network model with skip-connections
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Barron spaces and compositional function spaces for neural network models
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The role of over-parametrization in generalization of neural networks
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