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.

[1]  D. N. Spinelli,et al.  Visual Experience Modifies Distribution of Horizontally and Vertically Oriented Receptive Fields in Cats , 1970, Science.

[2]  Teuvo Kohonen,et al.  A Simple Paradigm for the Self-Organized Formation of Structured Feature Maps , 1982 .

[3]  S. Amari,et al.  Characteristics of Random Nets of Analog Neuron-Like Elements , 1972, IEEE Trans. Syst. Man Cybern..

[4]  S. Amari.  Topographic organization of nerve fields , 1979, Neuroscience Letters.

[5]  Kaoru Nakano,et al.  Associatron-A Model of Associative Memory , 1972, IEEE Trans. Syst. Man Cybern..

[6]  James A. Anderson,et al.  A simple neural network generating an interactive memory , 1972 .

[7]  M. Arbib,et al.  Systems Matching and Topographic Maps: The Branch-Arrow Model (BAM) , 1982 .

[8]  Shun-ichi Amari,et al.  Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements , 1972, IEEE Transactions on Computers.

[9]  Shun-ichi Amari,et al.  Characteristics of randomly connected threshold-element networks and network systems , 1971 .

[10]  G. F. Cooper,et al.  Development of the Brain depends on the Visual Environment , 1970, Nature.

[11]  R. M. Gaze,et al.  The arrow model: retinotectal specificity and map formation in the goldfish visual system , 1976, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[12]  D. Marr.  A theory of cerebellar cortex , 1969, The Journal of physiology.

[13]  M. Yoon.  Reorganization of retinotectal projection following surgical operations on the optic tectum in goldfish. , 1971, Experimental neurology.

[14]  Shun-ichi Amari,et al.  Chapter XIV A Mathematical Theory of Self-Organizing Nerve Systems , 1982 .

[15]  D. Hubel,et al.  Receptive fields of single neurones in the cat's striate cortex , 1959, The Journal of physiology.

[16]  S. Amari,et al.  A Mathematical Foundation for Statistical Neurodynamics , 1977 .

[17]  S. Geman.  SOME AVERAGING AND STABILITY RESULTS FOR RANDOM DIFFERENTIAL EQUATIONS , 1979 .

[18]  A. A. Mullin,et al.  Principles of neurodynamics , 1962 .

[19]  GrossbergS..  Adaptive pattern classification and universal recoding , 1976 .

[20]  S. Amari,et al.  Competition and Cooperation in Neural Nets , 1982 .