REPLICA-SYMMETRY BREAKING IN PERCEPTRONS

In the problem of optimization of pattern stabilization in perceptrons the replica-symmetric ansatz is known to be mathematically unstable f or storage capacities alpha greater than some alpha(c). In this paper we demonstrate that for alpha greater than alpha(c) the one-step repli ca-symmetry broken (RSB) solution is also unstable. We further show th at in this region, full RSB is necessary for an exact solution. Direct evaluation of the two-step RSB solution yields a minimum storage erro r which is only slightly greater than the one-step RSB, which itself i s greater than that given by the (unstable) replica-symmetric ansatz b y a much larger amount.