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Neural computation of arithmetic functions

Siu, Kai-Yeung and Bruck, Jehoshua (1990) Neural computation of arithmetic functions. Proceedings of the IEEE, 78 (10). pp. 1669-1675. ISSN 0018-9219. http://resolver.caltech.edu/CaltechAUTHORS:20120503-090033553

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Abstract

A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n -bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/5.58350DOIUNSPECIFIED
http://dx.doi.org/10.1109/5.58350PublisherUNSPECIFIED
Additional Information:© 1990 IEEE. Manuscript received Nov. 14, 1989; revised March 14, 1990. This work was done while K.-Y. Siu was a research student associate at IBM Almaden Research Center and was supported in part by the Joint Services Program at Stanford University (US Army, US Navy, US Air Force) under Contract DAAL03-88-C-0011, and the Department of the Navy (NAVELEX) under Contract N00039-84-C-0211, NASA Headquarters, Center for Aeronautics and Space Information Sciences under Grant NAGW-419-S6. The first author would like to thank Prof. Thomas Kailath for his guidance, constant encouragement, and financial support.
Funders:
Funding AgencyGrant Number
Stanford University Joint Services Program DAAL03-88-C-0011
Department of the Navy (NAVALEX)N00039-84-C-0211
NASA Center for Aeronautics and Space Information SciencesNAGW-419-S6
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INSPEC Accession Number3796896
Record Number:CaltechAUTHORS:20120503-090033553
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120503-090033553
Official Citation:Siu, K.-Y.; Bruck, J.; , "Neural computation of arithmetic functions," Proceedings of the IEEE , vol.78, no.10, pp.1669-1675, Oct 1990 doi: 10.1109/5.58350 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=58350&isnumber=2116
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31288
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 May 2012 22:45
Last Modified:26 Dec 2012 15:09

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