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TR96-034 | 28th March 1996 00:00

On Neural Networks with Minimal Weights


Authors: Vasken Bohossian, Jehoshua Bruck
Publication: 23rd May 1996 19:47
Downloads: 1914


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.

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