Editing Neural network (machine learning) (section)

===Computational power===
The [[multilayer perceptron]] is a [[UTM theorem|universal function]] approximator, as proven by the [[universal approximation theorem]]. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters.

A specific recurrent architecture with [[rational number|rational]]-valued weights (as opposed to full precision real number-valued weights) has the power of a [[universal Turing machine]],<ref>{{Cite journal | title = Turing computability with neural nets | url = http://www.math.rutgers.edu/~sontag/FTPDIR/aml-turing.pdf | year = 1991 | journal = Appl. Math. Lett. | pages = 77–80 | volume = 4 | issue = 6 | last1 = Siegelmann | first1 = H.T. | last2 = Sontag | first2 = E.D. | doi = 10.1016/0893-9659(91)90080-F | access-date = 10 January 2017 | archive-date = 19 May 2024 | archive-url = https://web.archive.org/web/20240519082138/http://www.math.rutgers.edu/~sontag/FTPDIR/aml-turing.pdf | url-status = live }}</ref> using a finite number of neurons and standard linear connections. Further, the use of [[Irrational number|irrational]] values for weights results in a machine with [[Hypercomputation|super-Turing]] power.<ref>{{cite news |title=Analog computer trumps Turing model |first=Sunny |last=Bains |date=3 November 1998 |work=EE Times |url=https://www.eetimes.com/analog-computer-trumps-turing-model/ |access-date=11 May 2023 |archive-date=11 May 2023 |archive-url=https://web.archive.org/web/20230511152308/https://www.eetimes.com/analog-computer-trumps-turing-model/ |url-status=live }}</ref><ref>{{cite journal |last1=Balcázar |first1=José |title=Computational Power of Neural Networks: A Kolmogorov Complexity Characterization |journal=IEEE Transactions on Information Theory|date=July 1997 |volume=43 |issue=4 |pages=1175–1183 |doi=10.1109/18.605580 |citeseerx=10.1.1.411.7782 }}</ref>{{Failed verification|date=May 2023}}