Learning strategies for the maximally stable diluted binary perceptron
I show analytically that an optimally chosen continuous precursor J in the hypercube is highly correlated to the maximally stable diluted binary perceptron which solves the same storage problem. J allows the construction of a diluted binary perceptron D by a simple rule. Performing simulations for perceptrons of size N=100 I demonstrate that D is highly stable and can be improved in an efficient manner by partial enumeration thereby incorporating information from the precursor components. The precursor highlights the vector components on which partial enumeration improves the stability of the vector most efficiently. Moreover, it discriminates for each vector component i at least one of the three possible values D(i)=-1,0,1 as being extremely unlikely.