The retrieval phase of the Hopfield model: A rigorous analysis of the overlap distribution

Probability Theory and Related Fields

Volumn 107, Issue 1, 1997, Pages 61-98

  Bovier, Anton ^a   Gayrard, Véronique ^b  

^a Weierstra Inst Angew Anal/S   (Germany)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030673431     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050077     Document Type: Article

References (21)

1. Amit, D.J., Gutfreund, H., Sompolinsky, H.: Statistical mechanics of neural networks near saturation. Ann. Phys. 173, 30-67 (1987)
2. Bovier, A., Gayrard, V.: The thermodynamics of the Curie-Weiss model with random couplings. J. Stat. Phys. 72, 643-664 (1993)
3. Bovier, A., Gayrard, V.: An almost sure large deviation principle for the Hopfield model. WIAS-Preprint 146; Ann. Probab. (to appear 1996)
4. Bovier, A., Gayrard, V., Picco, P.: Gibbs states of the Hopfield model in the regime of perfect memory. Probab. Theory Relat. Fields 100, 329-363 (1994)
5. Bovier, A., Gayrard, V., Picco, P.: Gibbs states of the Hopfield model with extensively many patterns. J. Stat. Phys. 79, 395-414 (1995)
6. Geman, S.: A limit theorem for the norms of random matrices. Ann. Probab. 8, 252-261 (1980)
7. Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. USA 79, 2554-2558 (1982)
8. Hubbard, J.: Calculation of partition functions. Phys. Rev. Lett. 3, 77-78 (1959)
9. Koch, H.: A free energy bound for the Hopfield model. J. Phys. A 26, L353-L355 (1993)
10. Komlós, J., Paturi, R.: Convergence results in an autoassociative memory model. Neural Networks 1, 239-250 (1988)
11. Ledoux, M., Talagrand, M.: Probability in Banach spaces. Berlin Heidelberg New York: Springer, 1991
12. Newman, Ch.M.: Memory capacity in neural network models: Rigorous lower bounds. Neural Networks 1, 223-238 (1988)
13. Pastur, L.A., Figotin, A.L.: Exactly soluble model of a spin glass. Sov. J. Low Temp. Phys. 3(6), 378-383 (1977)
14. Petritis, D.: Thermodynamic formalism of neural computing. Preprint Université de Rennes (1995)
15. Shcherbina, M., Tirozzi, B.: The free energy for a class of Hopfield models. J. Stat. Phys. 72, 113-125 (1992)
16. Stratonovich, R.L.: On a method of calculating quantum distribution functions. Dok. Akad. Nauk SSSR 115, 1097 (1957); in English: soviet Phys. Doklady 2, 416-419 (1958)
17. Stratonovich, R.L.: On a method of calculating quantum distribution functions. Dok. Akad. Nauk SSSR 115, 1097 (1957); in English: soviet Phys. Doklady 2, 416-419 (1958)
18. Szarek, S.: On the best constant in the Khintchine inequality. Studia Math. 58, 197-208 (1976)
19. Talagrand, M.: A new look at independence. Probab. Theory Relat. Fields 24, 1-34 (1996)
20. Talagrand, M.: Résultats rigoureux pour le modèle de Hopfield. C. R. Acad. Sci. Paris Série I, 321, 109-112 (1995)
21. Bovier, A., Gayrard, V.: Hopfield models as generalized random mean field models. WIAS-Preprint 253 (1996)