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Universal approximation theorem

In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate any continuous function to any desired degree of accuracy. These theorems provide a mathematical justification for using neural networks, assuring researchers that a sufficiently large or deep…

History, Arbitrary-depth case & Arbitrary-width case

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Arbitrary-width case

Arbitrary-depth case

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Universal approximation theorem

Nodes63
Edges62
Triples50
Avg. degree1.97
Density0.031746
Components1

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Universal approximation theorem

Top relations

related to Arbitrary-depth case · 13
Universal approximation theorem → Bochner, For, In, It, L1, Lebesgue, Lebesgue-integrable, Moreover, ReLU, The, They, Universal, Zhou Lu
related to Kolmogorov network · 9
Universal approximation theorem → Arnold, In, Indeed, Kolmogorov, Robert Hecht-Nielsen, The Kolmogorov, This, Vugar Ismailov, Ziming Liu
related to Bounded depth and bounded width case · 7
Universal approximation theorem → For, Maiorov, Pinkus, The, Their, There, Universal
related to Arbitrary-width case · 5
Universal approximation theorem → George Cybenko, In, Kurt Hornik, See, The
related to Setup · 4
Universal approximation theorem → Artificial, In, Most, The

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function displaystyle networks approximation universal neural activation width network functions depth theorem arbitrary also mathbb approximate continuous relu hidden layer

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SubjectPredicateObjectConfidenceSrc
Gustaf Gripenberg in 2003instance ofMoshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary…0.80text
Dmitry Yarotskyinstance ofMoshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary…0.80text
Zhou Lu et al in 2017instance ofMoshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary…0.80text
Boris Hanininstance ofMoshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary…0.80text
Mark Sellke in 2018 who focused on neural networks with ReLU activation functioninstance ofMoshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function.Arbitrary…0.80text
Gustaf Gripenberg in 2003instance ofArbitrary depthThe arbitrary depth case was also studied by a number of authors0.80text
Dmitry Yarotskyinstance ofArbitrary depthThe arbitrary depth case was also studied by a number of authors0.80text
Zhou Lu et al in 2017instance ofArbitrary depthThe arbitrary depth case was also studied by a number of authors0.80text
Boris Hanininstance ofArbitrary depthThe arbitrary depth case was also studied by a number of authors0.80text
Mark Sellke in 2018 who focused on neural networks with ReLU activation functioninstance ofArbitrary depthThe arbitrary depth case was also studied by a number of authors0.80text
the step function can be approximated by continuous activation functionsinstance ofcertain non-continuous activation functions0.80text
which then allows the approximation result to apply to those functionsinstance ofcertain non-continuous activation functions0.80text

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