TR96-034 Authors: Vasken Bohossian, Jehoshua Bruck

Publication: 23rd May 1996 19:47

Downloads: 1075

Keywords:

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.