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We prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function.
Capacity problems for linear machines
Thomas M. Cover · 1968
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Lower bounds for approximation by nonlinear manifolds
Hugh E. Warren · 1968
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On the uniform convergence of relative frequencies of events to their probabilities
V. N. Vapnik and A. Ya. Chervonenkis · 1971
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What size net gives valid generalization?
Eric B. Baum and David Haussler · 1989
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Learnability and the Vapnik-Chervonenkis dimension
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth · 1989
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Empirical Processes: Theory and Applications , volume 2
David Pollard · 1990
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Feedback stabilization using two-hidden-layer nets
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Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers
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Why deep neural networks for function approximation?, 2017
Shyu Liang and R. Srikant · 2017
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Depth-width tradeoffs in approximating natural functions with neural networks, 2017
I. Safran and O. Shamir · 2017
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Error bounds for approximations with deep ReLU networks, 2017
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On the expressive power of deep learning: A tensor analysis
N. Cohen, O. Sharir, and A. Shashua · 2016
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Dmitry Yarotsky · 2017
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