Associative Memory and Its Statistical Neurodynamical Analysis

A neural network is a complex system consisting of a large number of mutually connected elements having a simple input-output relation. Its behavior is highly non-linear, so that it is in general difficult to analyze its dynamical behavior of information processing. In order to elucidate a typical behavior, we study a network whose connection weights or synaptic efficacies of connections are randomly generated and then fixed. Given a probability law of connection weights, we have an ensemble of randomly generated networks. Statistical neurodynamics provides a theoretical method to search for macroscopic behaviors which are shared by all typical random networks in the ensemble, i.e. those networks generated by the same probability law.

[1]  Shun-ichi Amari,et al.  Statistical neurodynamics of associative memory , 1988, Neural Networks.

[2]  J Nagumo,et al.  [A model of associative memory]. , 1972, Iyo denshi to seitai kogaku. Japanese journal of medical electronics and biological engineering.

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

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

[5]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[6]  Sompolinsky,et al.  Spin-glass models of neural networks. , 1985, Physical review. A, General physics.

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

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

[9]  W. Kinzel Learning and pattern recognition in spin glass models , 1985 .

[10]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Teuvo Kohonen,et al.  Correlation Matrix Memories , 1972, IEEE Transactions on Computers.

[12]  Meir,et al.  Exact solution of a layered neural network model. , 1987, Physical review letters.

[13]  Santosh S. Venkatesh,et al.  The capacity of the Hopfield associative memory , 1987, IEEE Trans. Inf. Theory.

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