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Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness.
Deep network approximation characterized by number of neurons
Shen, Z · 1906
Earlier work this paper cites.
Adaptive approximation and estimation of deep neural network to intrinsic dimensionality
Nakada, R · 1907
Earlier work this paper cites.
Nonparametric regression on low-dimensional manifolds using deep relu networks
Chen, M · 1908
Earlier work this paper cites.
Deep relu network approximation of functions on a manifold
Schmidt-Hieber, J · 1908
Earlier work this paper cites.
Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic besov space
Suzuki, T · 1910
Earlier work this paper cites.
Generalized sobolev spaces and their applications to boundary value problems of partial differential equations, leningrad
Slobodeckij, L · 1958
Earlier work this paper cites.
Curvature measures
Federer, H · 1959
Earlier work this paper cites.
Singular Integrals and Differentiability Properties of Functions
Stein, E. M · 1970
Earlier work this paper cites.
A comprehensive introduction to differential geometry
Spivak, M · 1973
Earlier work this paper cites.
Sphere packings, lattices and groups
Conway, J · 1988
Earlier work this paper cites.
Capabilities of three-layered perceptrons
Irie, B · 1988
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
Cybenko, G · 1989
Earlier work this paper cites.
On the approximate realization of continuous mappings by neural networks
Funahashi, K.-I · 1989
Earlier work this paper cites.
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
Hornik, K · 1990
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
Hornik, K · 1991
Earlier work this paper cites.
Approximation of a function and its derivative with a neural network
Cardaliaguet, P · 1992
Earlier work this paper cites.
Approximation by ridge functions and neural networks with one hidden layer
Chui, C. K · 1992
Earlier work this paper cites.
Universal approximation bounds for superpositions of a sigmoidal function
Barron, A. R · 1993
Earlier work this paper cites.
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Leshno, M · 1993
Earlier work this paper cites.
Virtual adversarial training: a regularization method for supervised and semi-supervised learning
Miyato, T · 1993
Earlier work this paper cites.
Neural networks for optimal approximation of smooth and analytic functions
Mhaskar, H. N · 1996
Cited alongside, same era.
Nonlinear dimensionality reduction by locally linear embedding
Roweis, S. T · 2000
Cited alongside, same era.
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Tenenbaum, J. B · 2000
Cited alongside, same era.
Analysis tools with applications
Driver, B. K · 2003
Cited alongside, same era.
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Cited alongside, same era.
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Cited alongside, same era.
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Later among the works it cites.
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Later among the works it cites.
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Shaham, U · 2018
Later among the works it cites.
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Uesato, J · 2018
Later among the works it cites.
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Cited alongside, same era.
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Cited alongside, same era.
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