Universal approximation theorem: Difference between revisions

Revision as of 14:21, 10 June 2010

Revision as of 14:22, 10 June 2010

Line 5:

Kurt Hornik (1991) showed that it is not the specific choice of the activation function, but rather the multilayer feedforward architecture itself which gives neural networks the potential of being universal approximators. The output units are always assumed to be linear. For notational convenience we shall explicitly formulate our results only for the case where there is only one output unit. (The general case can easily be deduced from the simple case.)

The theorem<ref>G. Cybenko. Approximations by superpositions of sigmoidal functions. Mathematics of Control, Signals, and Systems, 2:303–314, no. 4 pp.&nbsp;303-314. [http://actcomm.dartmouth.edu/gvc/papers/approx_by_superposition.pdf electronic version], 1989.</ref><ref>

Kurt Hornik: Approximation Capabilities of Multilayer Feedforward Networks.

Neural Networks, vol. 4, 1991.</ref><ref>Haykin, Simon (1998). Neural Networks: A Comprehensive Foundation, 2, Prentice Hall. ISBN 0132733501.</ref><ref>Hassoun, M. (1995) ''Fundamentals of Artificial Neural Networks'' MIT Press, p.&nbsp;48</ref> in mathematical terms:

== Formal statement ==

Line 32:

==References==

{{Reflist}}

* [[George V. Cybenko|Cybenko, G.V.]] (1989). Approximation by Superpositions of a Sigmoidal function, ''Mathematics of Control, Signals and Systems'', vol. 2 no. 4 pp.&nbsp;303-314. [http://actcomm.dartmouth.edu/gvc/papers/approx_by_superposition.pdf electronic version]

* Hassoun, M. (1995) ''Fundamentals of Artificial Neural Networks'' MIT Press, p.&nbsp;48

{{DEFAULTSORT:Universal Approximation Theorem}}