PATTERN LEARNING BY SELF-ORGANIZING NETS OF THRESHOLD ELEMENTS.

The output of a nerve cell is a complex nonlinear function of the weighted sum of a large number of inputs. The threshold element is a simple model of the nerve cell, in which spatial summation and the threshold effect are taken in into account. A self-organizing net of threshold elements alters its parameters depending on the sequences of stimulus patterns applied from the outside. The net, learning from these patterns or pattern sequences, remembers some of the patterns as stable equilibrium states or state-transition sequences by self-organization. The stability of their remembrance as well as of their recall is investigated theoretically. The stability of state transition in an autonomous logical net of threshold elements is studied by using various stability numbers. From the results the following conditions are given explicitly: i) the condition that the net stores many patterns in memory as stable states; ii) the condition that the net remembers many sequences of patterns as state-transition sequences; and iii) the condition that the net forms a representative pattern as a stable state from a given set of patterns. Their stability is also shown. The author states that study provides a theoretical basis for self-organizing nets such as the four-layer perceptron, the associatron, etc.