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Neural Computing and Applications

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01-01-2014 | ICONIP 2012

Analyses for L ^p[a, b]-norm approximation capability of flexible approximate identity neural networks

Authors: Saeed Panahian Fard, Zarita Zainuddin

Published in: Neural Computing and Applications | Issue 1/2014

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Abstract

This study investigates the universal approximation capability of a three-layered feedforward flexible approximate identity neural networks under the L ^p[a, b]-norm. We are motivated to study such a problem by the fact that the L ^p[a, b]-norm has the capability of improving approximation performance significantly. Using flexible approximate identity functions as introduced in our previous study, we prove that any Lebesgue integrable function on the closed and bounded real interval [a, b] will converge to itself under the L ^p[a, b]-norm if it convolves with flexible approximate identity functions. Using this result, we also establish a main theorem. The proof of the main theorem is in the framework of the theory of \(\epsilon\)-net.

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Title: Analyses for L p [a, b]-norm approximation capability of flexible approximate identity neural networks
Authors: Saeed Panahian Fard
Zarita Zainuddin
Publication date: 01-01-2014
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 1/2014
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-013-1493-9

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