On the Magnitude of Weights and Thresholds of Multithreshold Neural Units

We treat the problem of the evaluation of the memory capacity sufficient to store all weights and thresholds of a multithreshold neural network without loss of its capability to recognize set of patterns in n-dimensional space. We give the bounds on the magnitude of the integer weight and threshold vectors, respectively, of a multithreshold neuron, which hold for binary-valued neurons as well as multi-valued ones. The refinement of these bounds in the case of binary inputs is also presented. It allows us to evaluate the memory capacity of the multithreshold network. The estimation of average memory capacity for such networks is also considered. We established O(n2 + kn) lower bound on the capacity of the memory that is necessary to store weight coefficients and thresholds of almost all k-threshold neural units proceeding with k-threshold Boolean functions.