Learning processes in multilayer threshold nets

Abstract

An algorithm of learning in multilayer threshold nets without feedbacks is proposed. The net is. built of threshold elements with binary inputs. During a learning process each input vector x is accompanied by a teacher's decision ω (ωε{1,...,M}). The pairs (x[n], ω[n]) appear in successive steps independently according to some unknown stationary distribution p(x,ω). The problem of learning of a threshold net has been decomposed to a series of problems of learning of the threshold elements. The proposed learning algorithm of the threshold elements has a perceptron-like form. It was proven that a decision rule of the threshold net stabilizes after a finite number of steps. For definite classes {p(x, ω)} ^K_* of distributions p(x,ω), an optimal decision rule stabilizes after a finite number of steps. These classes {p(x, ω)} ^K_* also contain distributions describing learning processes with perturbations.