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 chi is accompanied by a teacher's decision omega (omega epsilon(1,...,M)). The pairs (chi[n], omega[n]) appear in successive steps independently according to some unknown stationary distribution p(chi, omega). 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(chi,omega))K of distributions p(chi, omega), an optimal decision rule stabilizes after a finite number of steps. These classes (p(chi, omega))K also contain distributions describing learning processes with perturbations.