Redpath, Stuart Frederick (2010) Universal approximation properties of feedforward artificial neural networks. Masters thesis, Rhodes University.
In this thesis we summarise several results in the literature which show the approximation capabilities of multilayer feedforward articial neural networks.We show that multilayer feedforward articial neural networks are capable of approximating continuous and measurable functions from Rn ! R to any degree of accuracy under certain conditions. In particular making use of the Stone-Weierstrass and Hahn-Banach theorems,we show that a multilayer feedforward articial neural network can approximate any continuous function to any degree of accuracy, by using either an arbitrary squashing function or any continuous sigmoidal function for activation. Making use of the Stone-Weirstrass Theorem again, we extend these approximation capabilities of multilayer feedforward articial neural networks to the space of measurable functions under any probability measure.
|Item Type:||Thesis (Masters)|
|Uncontrolled Keywords:||Neural networks (Computer science), Artificial intelligence, Biological applications, Neural networks (Neurobiology), Functional analysis, Weierstrass-Stone theorem, Banach-Hahn theorem|
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||Faculty > Faculty of Science|
|Deposited By:||Madireng Monyela|
|Deposited On:||07 Nov 2011 09:31|
|Last Modified:||06 Jan 2012 16:22|
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