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In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs).
An algorithm for finding intrinsic dimensionality of data
Keinosuke Fukunaga and David R Olsen · 1971
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Andrew R Barron · 1993
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Andrew R Barron · 1994
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Aad W van der Vaart and Jon A Wellner · 1996
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Jörg Bruske and Gerald Sommer · 1998
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A global geometric framework for nonlinear dimensionality reduction
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Martin Anthony and Peter L Bartlett · 2009
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Diederick P Kingma and Jimmy Ba · 2015
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Hadrien Montanelli and Qiang Du · 2017
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Taiji Suzuki · 2017
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Dmitry Yarotsky · 2017
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Stronger generalization bounds for deep nets via a compression approach
Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang · 2018
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