On-line Learning of Unlearnable True Teacher through Mobile Ensemble Teachers

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The on-line learning of a hierarchical learning model is studied by a method based on statistical mechanics. In our model, a student of a simple perceptron learns from not a true teacher directly, but ensemble teachers who learn from a true teacher with a perceptron learning rule. Since the true teacher and ensemble teachers are expressed as nonmonotonic and simple perceptrons, respectively, the ensemble teachers go around the unlearnable true teacher with the distance between them fixed in an asymptotic steady state. The generalization performance of the student is shown to exceed that of the ensemble teachers in a transient state, as was shown in similar ensemble-teachers models. Furthermore, it is found that moving the ensemble teachers even in the steady state, in contrast to the fixed ensemble teachers, is efficient for the performance of the student.