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Algebraic Techniques for Constructing Minimal Weight Threshold Functions

Bohossian, Vasken and Bruck, Jehoshua (1996) Algebraic Techniques for Constructing Minimal Weight Threshold Functions. California Institute of Technology . (Unpublished)

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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. While in the present literature a distinction is made between the two extreme cases of linear threshold functions with polynomial-size weights as opposed to those with exponential-size weights, the best known lower bounds on the size of threshold circuits are for depth-2 circuits with small weights. Our main contributions are devising two distinct methods for constructing threshold functions with minimal weights and filling up the gap between polynomial and exponential weight growth by further refining the 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.

Item Type:Report or Paper (Technical Report)
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URLURL TypeDescription
Bruck, Jehoshua0000-0001-8474-0812
Group:Parallel and Distributed Systems Group
Record Number:CaltechPARADISE:1996.ETR015
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Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:26059
Deposited By: Imported from CaltechPARADISE
Deposited On:04 Sep 2002
Last Modified:22 Nov 2019 09:58

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