Learning and pattern recognition in spin glass models

Spin glass models have a complex phase space which may be used to store information. By an asynchronous relaxational dynamics noisy patterns are recognized very fast. In particular the Hopfield model which may be a simple model for neural networks is analyzed in detail. By numerical simulations and analytical approximations the number of patterns to be stored and the amount of noise to be recognized is calculated. It is demonstrated that a random network can learn patterns by reducing frustrated bonds.

[1]  S. Kirkpatrick,et al.  Solvable Model of a Spin-Glass , 1975 .

[2]  A class of exactly soluble random spin systems , 1976 .

[3]  D. Mattis Solvable spin systems with random interactions , 1976 .

[4]  Kurt Binder,et al.  Phase transitions of a nearest-neighbor Ising-model spin glass , 1976 .

[5]  W. Kinzel Remanent magnetization in spin-glasses , 1979 .

[6]  K. Binder Monte Carlo methods in statistical physics , 1979 .

[7]  M. Azbel' Quantum Particle in One-Dimensional Potentials with Incommensurate Periods , 1979 .

[8]  D. Purves,et al.  Elimination of synapses in the developing nervous system. , 1980, Science.

[9]  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.

[10]  K. Fischer Spin glasses (I) , 1983 .

[11]  J. Provost,et al.  Ergodicity of the Coupling Constants and the Symmetric n -Replicas Trick for a Class of Mean-Field Spin-Glass Models , 1983 .

[12]  The van Hemmen model-a true spin glass? , 1984 .

[13]  M. Mézard,et al.  Nature of the Spin-Glass Phase , 1984 .

[14]  B. A. Huberman,et al.  Adaptation and self-repair in parallel computing structures , 1984 .

[15]  I. Guyon,et al.  Information storage and retrieval in spin-glass like neural networks , 1985 .

[16]  Sompolinsky,et al.  Storing infinite numbers of patterns in a spin-glass model of neural networks. , 1985, Physical review letters.