Generalization in the programed teaching of a perceptron

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=αN 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 Y₀(α), which diverges for α→0 and remains nonzero while α<α_c≊5.7. That suggests programed learning: easy examples should be taught first.