On the capacity per synapse

The optimal storage capacity of a perceptron with a finite fraction of sign constrained weights, which are prescribed a priori, is examined. The storage capacity is calculated by considering the fractional volume of weights which can store a set of alpha N random patterns, where N is the size of the input. It is found that in the case where (1-s) N weights are sign constrained the capacity is (1+s)/2 alpha ^G_c(k), where alpha ^G _c(k) is the maximal storage capacity in Gardner's case and k is a stability parameter.