On the conditions for the existence of Perfect Learning and power law in learning from stochastic examples by Ising perceptrons

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In a previous letter, we studied learning from stochastic examples by perceptrons with Ising weights in the framework of statistical mechanics. Under the one-step replica symmetry breaking ansatz, the behaviours of learning curves were classified according to some local property of the rules by which examples were drawn. Further, the conditions for the existence of the Perfect Learning together with other behaviors of the learning curves were given. In this paper, we give the detailed derivation about these results and further argument about the Perfect Learning together with extensive numerical calculations.