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Neural networks and rational functions efficiently approximate each other.
Rational approximation to | x | |x|
Newman, D. J · 1964
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Log depth circuits for division and related problems
Beame, Paul, Cook, Stephen A., and Hoover, H. James · 1986
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Rational approximation of real functions
Petrushev, P. P. Penco Petrov and Popov, Vasil A · 1987
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Approximation by superpositions of a sigmoidal function
Cybenko, George · 1989
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Splines, rational functions and neural networks
Williamson, Robert C. and Bartlett, Peter L · 1991
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Approximating threshold circuits by rational functions
Paturi, Ramamohan and Saks, Michael E · 1994
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Constructive approximation : advanced problems
Lorentz, G. G., Golitschek, Manfred von, and Makovoz, Yuly · 1996
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Neural Network Learning: Theoretical Foundations
Anthony, Martin and Bartlett, Peter L · 1999
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Representation benefits of deep feedforward networks
Telgarsky, Matus · 2015
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On the expressive power of deep learning: A tensor analysis
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The power of depth for feedforward neural networks
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Depth separation in relu networks for approximating smooth non-linear functions
Benefits of depth in neural networks
Telgarsky, Matus · 2016
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Error bounds for approximations with deep relu networks
Yarotsky, Dmitry · 2016
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Reliably learning the relu in polynomial time
Goel, Surbhi, Kanade, Varun, Klivans, Adam, and Thaler, Justin · 2017
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Why deep neural networks for function approximation?
Liang, Shiyu and Srikant, R · 2017
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Why and when can deep – but not shallow – networks avoid the curse of dimensionality: a review
Poggio, Tomaso, Mhaskar, Hrushikesh, Rosasco, Lorenzo, Miranda, Brando, and Liao, Qianli · 2017
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Safran, Itay and Shamir, Ohad · 2016
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Application of elliptic functions to the problem of the functions of the least and most deviation from zero
Zolotarev, E.I
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