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On Neural Networks with Minimal Weights

Bohossian, Vasken and Bruck, Jehoshua (1996) On Neural Networks with Minimal Weights. In: Advances in Neural Information Processing Systems 8 (NIPS 1995). Advances in Neural Information Processing Systems. No.8. MIT Press , Cambridge, MA, pp. 246-252. ISBN 0-262-20107-0. http://resolver.caltech.edu/CaltechAUTHORS:20160223-114401229

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Abstract

Linear threshold elements are the basic building blocks of artificial neural networks. A linear threshold element computes a function that is a sign of a weighted sum of the input variables. The weights are arbitrary integers; actually, they can be very big integers-exponential in the number of the input variables. However, in practice, it is difficult to implement big weights. In the present literature a distinction is made between the two extreme cases: linear threshold functions with polynomial-size weights as opposed to those with exponential-size weights. The main contribution of this paper is to fill up the gap by further refining that separation. Namely, we prove that the class of linear threshold functions with polynomial-size weights can be divided into subclasses according to the degree of the polynomial. In fact, we prove a more general result- that there exists a minimal weight linear threshold function for any arbitrary number of inputs and any weight size. To prove those results we have developed a novel technique for constructing linear threshold functions with minimal weights.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://papers.nips.cc/paper/1066-on-neural-networks-with-minimal-weightsOrganizationPaper
http://resolver.caltech.edu/CaltechPARADISE:1995.ETR005Related ItemTechnical Report
Additional Information:© 1996 Massachusetts Institute of Technology. This work was supported in part by the NSF Young Investigator Award CCR-9457811, by the Sloan Research Fellowship, by a grant from the IBM Almaden Research Center, San Jose, California, by a grant from the AT&T Foundation and by the center for Neuromorphic Systems Engineering as a part of the National Science Foundation Engineering Research Center Program; and by the California Trade and Commerce Agency, Office of Strategic Technology.
Funders:
Funding AgencyGrant Number
NSFCCR-9457811
Alfred P. Sloan FoundationUNSPECIFIED
IBM Almaden Research CenterUNSPECIFIED
AT&T FoundationUNSPECIFIED
California Trade and Commerce Agency, Office of Strategic TechnologyUNSPECIFIED
Record Number:CaltechAUTHORS:20160223-114401229
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160223-114401229
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ID Code:64678
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Deposited By: Kristin Buxton
Deposited On:23 Feb 2016 21:59
Last Modified:23 Feb 2016 21:59

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