期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1996
卷号：1996
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：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.
