One-step replica-symmetry-breaking solution for a perceptron learning with weight mismatch
Kibeom Park, Chulan Kwon, YoungAh Park · Journal of Physics A Mathematical and General · 1996
We investigate the properties of the one-step replica-symmetry-breaking (1RSB) solution for a perceptron learning from examples with weight mismatch where the entropy zero line crosses the Almeida - Thouless (AT) line of the RS solution. For a small number of examples we find the optimal 1RSB solution which has the maximum free energy, non-negative entropy and satisfies the stability condition, the AT criterion for the 1RSB solution. The transition from RS to 1RSB is continuous or discontinuous depending on whether the RS AT line is above or below the zero entropy line. However, for a relatively large number of examples, the 1RSB solution which maximizes the free energy becomes unstable, and should be replaced by higher-step RSB solutions. We also obtain the AT line for the 1RSB solution.