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