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 (Unpublished) http://resolver.caltech.edu/CaltechPARADISE:1995.ETR005
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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:||Report or Paper (Technical Report)|
|Group:||Parallel and Distributed Systems Group|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechPARADISE|
|Deposited On:||04 Sep 2002|
|Last Modified:||26 Dec 2012 13:52|
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