Statistical Mechanics of Neural Networks

Some recent results on the cooperative behaviour of networks of interconnected two state elements are presented. Such networks have an infinite number of attractors in the phase space of the binary elements, which may be used for pattern retrieval. The statistical mechanics of pattern retrieval and learning is introduced and discussed.

[1]  D. Amit,et al.  Statistical mechanics of neural networks near saturation , 1987 .

[2]  J. Nadal,et al.  Learning and forgetting on asymmetric, diluted neural networks , 1987 .

[3]  Kanter,et al.  Associative recall of memory without errors. , 1987, Physical review. A, General physics.

[4]  Gutfreund,et al.  Processing of temporal sequences in neural networks. , 1988, Physical review letters.

[5]  Meir,et al.  Layered feed-forward neural network with exactly soluble dynamics. , 1988, Physical review. A, General physics.

[6]  Wolfgang Kinzel,et al.  Metastable states of the SK model of spin glasses , 1987 .

[7]  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.

[8]  E. Gardner Structure of metastable states in the Hopfield model , 1986 .

[9]  Heinz Horner Dynamics of Spin Glasses and Related Models of Neural Networks , 1987 .

[10]  E. Gardner,et al.  Optimal storage properties of neural network models , 1988 .

[11]  Sompolinsky,et al.  Neural networks with nonlinear synapses and a static noise. , 1986, Physical review. A, General physics.

[12]  I. Morgenstern,et al.  Heidelberg Colloquium on Glassy Dynamics , 1987 .

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

[14]  J. L. Hemmen,et al.  Nonlinear neural networks. , 1986, Physical review letters.

[15]  L. Personnaz,et al.  Collective computational properties of neural networks: New learning mechanisms. , 1986, Physical review. A, General physics.

[16]  J. Chayes,et al.  The phase boundary in dilute and random Ising and Potts ferromagnets , 1987 .

[17]  Eytan Domany,et al.  Stochastic dynamics of a layered neural network. Exact solution , 1987 .

[18]  Sompolinsky,et al.  Dynamics of spin systems with randomly asymmetric bonds: Ising spins and Glauber dynamics. , 1988, Physical review. A, General physics.

[19]  W. Kinzel The remanent magnetisation and energy of spin glasses , 1988 .

[20]  E. Gardner,et al.  An Exactly Solvable Asymmetric Neural Network Model , 1987 .

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

[22]  U. Krey,et al.  Dynamical Learning Process for Recognition of Correlated Patterns in Symmetric Spin Glass Models , 1987 .

[23]  P. Leath,et al.  The failure distribution in percolation models of breakdown , 1987 .

[24]  J. Hemmen Nonlinear neural networks near saturation. , 1987 .

[25]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[26]  H. Gutfreund,et al.  The nature of attractors in an asymmetric spin glass with deterministic dynamics , 1988 .

[27]  Opper,et al.  Learning of correlated patterns in spin-glass networks by local learning rules. , 1987, Physical review letters.

[28]  Kinzel Remanent magnetization of the infinite-range Ising spin glass. , 1986, Physical review. B, Condensed matter.

[29]  W. Krauth,et al.  Learning algorithms with optimal stability in neural networks , 1987 .

[30]  E. Gardner The space of interactions in neural network models , 1988 .

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

[32]  Opper Learning times of neural networks: Exact solution for a PERCEPTRON algorithm. , 1988, Physical review. A, General physics.

[33]  Spingläser und Hirngespinste: Physikalische Modelle des Lernens und Erkennens , 1988 .

[34]  J. J. Hopfield,et al.  ‘Unlearning’ has a stabilizing effect in collective memories , 1983, Nature.