(and Their Possible Relation to Neural Networks) Mutsumi Nakamura, Ray Mines, ...  Home/Search
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Abstract: In 1987, R. Hecht-Nielsen noticed that a theorem that was proved by Kolmogorov in 1957 as a solution to one of Hilbert's problems, actually shows that an arbitrary function f can be implemented by a 3-layer neural network with appropriate activation functions / and . The more accurately we implement these functions, the better approximation to f we get. (Update)
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BibTeX entry: (Update)
@misc{ possible-guaranteed,
author = "And Their Possible",
title = "Guaranteed Intervals for Kolmogorov's Theorem",
url = "citeseer.ist.psu.edu/697218.html" }
Citations (may not include all citations):623 Multilayer Feedforward Networks are Universal Approximators (context) - Hornik, Stinchcombe et al. - 1989
99 Foundations of Constructive Analysis (context) - Bishop - 1967
75 Constructive Analysis (context) - Bishop, Bridges - 1985
28 the Representation of Continuous Functions of Several Variab.. (context) - Kolmogorov - 1957
18 A History of Mathematics (context) - Boyer, Merzbach - 1991
17 Constructive Functional Analysis (context) - Bridges - 1979
17 the Structure of Continuous Functions of Several Variables (context) - Sprecher - 1965
16 Kolmogorov's Theorem and Multilayer Neural Networks (context) - Kurkova - 1992
14 Approximate Representation of Functions of Several Variables.. (context) - Frisch, Borzi et al. - 1989
13 Kolmogorov's Theorem Is Relevant (context) - Kurkova - 1991
9 Kolmogorov's Mapping Neural Network Existence Theorem (context) - Hecht-Nielsen - 1987
7 Approximative versions of Kolmogorov's superposition theorem (context) - Ness - 1993
5 Representation Properties of Networks: Kolmogorov's Theorem .. (context) - Girosi, Poggio - 1989
3 An Improvement in the Superposition Theorem of Kolmogorov (context) - Sprecher - 1972
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