Bohossian, Vasken and Bruck, Jehoshua (1995) On Neural Networks with Minimal Weights. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechPARADISE:1995.ETR005

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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 polynomialsize weights as opposed to those with exponentialsize 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 polynomialsize weights can be divided into subclasses according to the degree of the polynomial. In fact we prove a more general resultthat 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:  Report or Paper (Technical Report)  

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Group:  Parallel and Distributed Systems Group  
Record Number:  CaltechPARADISE:1995.ETR005  
Persistent URL:  http://resolver.caltech.edu/CaltechPARADISE:1995.ETR005  
Usage Policy:  You are granted permission for individual, educational, research and noncommercial reproduction, distribution, display and performance of this work in any format.  
ID Code:  26069  
Collection:  CaltechPARADISE  
Deposited By:  Imported from CaltechPARADISE  
Deposited On:  04 Sep 2002  
Last Modified:  26 Dec 2012 13:52 
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