Field theory of self-organizing neural nets

A field theory is proposed as a mathematical method for analyzing learning and self-organizing nerve nets and systems in a unified manner. It is shown by the use of the theory that a nerve net has an ability for automatically forming categorizers or signal detecting cells for the signals which the net receives from its environment. Moreover, when the set of signals has a topological structure, the detectors are arranged in the nerve system (or field) to preserve the topology, so that the topographical structure is introduced in the nerve system by self-organization.