Generalization in the programed teaching of a perceptron
Imre Derényi, Tamás Geszti, G. Györgyi · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1994
According to a widely used model of learning and generalization in neural networks, a single neuron (perceptron) can learn from examples to imitate another neuron, called the teacher perceptron. We introduce a variant of this model in which examples within a layer of thickness 2Y around the decision surface are excluded from teaching. That restriction transmits global information about the teacher's rule. Therefore for a given number p=\ensuremath{\alpha}N of presented examples (i.e., those outside of the layer) the generalization performance obtained by Boltzmannian learning is improved by setting Y to an optimum value ${\mathit{Y}}_{0}$(\ensuremath{\alpha}), which diverges for \ensuremath{\alpha}\ensuremath{\rightarrow}0 and remains nonzero while \ensuremath{\alpha}${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$\ensuremath{\approxeq}5.7. That suggests programed learning: easy examples should be taught first.