REPLICA SYMMETRY-BREAKING IN A DILUTED NETWORK WITH BINARY COUPLINGS

Abstract

We describe a one-stage replica-symmetry-breaking (RSB) calculation of the free energy of the annealed-dilution network with binary couplings. We locate the extremum of the free-energy functional through a systematic search in the space of order parameters. A genuine RSB extremum only exists for values of the storage ratio alpha greater than alpha(s), which is the value for which the RS entropy vanishes at T=0. The corresponding free energy always has a positive value from which we derive that the storage capacity is equal to alpha(s). The free energy also determines the fraction of errors when the loading of the network exceeds the storage capacity, Although the error fraction for weak overloading is remarkably small, the information content in the optimal coupling vector fails to grow above its value at saturation.