On the Size of Weights for Bithreshold Neurons and Networks

The paper deals with the issues concerning the memory capacity sufficient to store all coefficients of a bithre-shold neurons and networks without loss of their capability to solve classification tasks. The magnitude of integer weight coefficients of bithreshold neurons and networks providing desired binary classification of the finite set in n-dimensional space is studied. We give the bounds on the size of the norm of the integer weight vector of bithreshold neurons realizing bithreshold Boolean functions. The problem of average memory capacity is also considered. We prove the quadratic (on the number of inputs) lower bounds on the capacity of the memory that is necessary to store the parameters of threshold and bithreshold neurons for almost all threshold and bithreshold functions.