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Harmonic Analysis And The Complexity Of Computing With Threshold (Neural) Elements

Bruck, Jehoshua and Smolensky, Roman (1991) Harmonic Analysis And The Complexity Of Computing With Threshold (Neural) Elements. In: 1991 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, p. 86. ISBN 0-7803-0056-4 http://resolver.caltech.edu/CaltechAUTHORS:20120417-094637010

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Abstract

The main purpose of this talk is to introduce a useful tool for the analysis of discrete neural networks in which every node is a Boolean threshold gate. The difficulty in the analysis of neural networks arises from the fact that the basic processing elements (linear threshold gates) are nonlinear. The key idea in harmonic analysis of threshold functions is to represent the functions as polynomials over the field of real numbers. Answering different questions regarding neural networks becomes equivalent to answering questions related to the coefficients of these polynomials. We have applied these techniques and obtained many interesting and surprising results [1, 2, 3, 4]. The focus of this talk will be on presenting a theorem that characterizes-using spetral norms-the complexity of computing a Boolean function with threshold circuits [2, 3]. This result establishes the first known link between harmonic analysis and the complexity of computing with neural networks.


Item Type:Book Section
Related URLs:
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http://dx.doi.org/10.1109/ISIT.1991.695142DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=695142PublisherUNSPECIFIED
Additional Information:© 1991 IEEE. Date of Current Version: 06 August 2002.
Record Number:CaltechAUTHORS:20120417-094637010
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120417-094637010
Official Citation:Bruck, J.; Smolensky, R.; , "Harmonic Analysis And The Complexity Of Computing With Threshold (Neural) Elements," Information Theory, 1991 (papers in summary form only received), Proceedings. 1991 IEEE International Symposium on (Cat. No.91CH3003-1) , vol., no., pp.86, 24-28 Jun 1991 doi: 10.1109/ISIT.1991.695142 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=695142&isnumber=4025
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30124
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Apr 2012 17:52
Last Modified:26 Dec 2012 15:04

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