Universal approximation properties of feedforward artificial neural networks.

Redpath, Stuart Frederick

Title: Universal approximation properties of feedforward artificial neural networks.
Creator: Redpath, Stuart Frederick
Subject: Neural networks (Computer science)
Subject: Artificial intelligence -- Biological applications
Subject: Functional analysis
Subject: Weierstrass-Stone Theorem
Subject: Banach-Hahn theorem
Date Issued: 2011
Date: 2011
Type: Thesis
Type: Masters
Type: MSc
Identifier: vital:5430
Identifier: http://hdl.handle.net/10962/d1015869
Description: In this thesis we summarise several results in the literature which show the approximation capabilities of multilayer feedforward artificial neural networks. We show that multilayer feedforward artificial neural networks are capable of approximating continuous and measurable functions from Rn to 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 artificial 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 artificial neural networks to the space of measurable functions under any probability measure.
Format: 107 p.
Format: pdf
Publisher: Rhodes University
Publisher: Faculty of Science, Mathematics
Language: English
Rights: Redpath, Stuart Frederick

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Universal approximation propertiesof feedforward artificialneural networks.

Universal approximation properties
of feedforward artificial
neural networks.