Beyond storage capacity in a single model neuron: Continuous replica symmetry breaking

Journal of Statistical Physics

Volumn 101, Issue 1-2, 2000, Pages 679-702

  Gyorgyi G ^a   Reimann, P ^b  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Neural networks; Perceptron; Replica method; Storage capacity

Indexed keywords

EID: 0034288238     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1026441500710     Document Type: Article

References (39)

1. J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79:2554 (1982).
2. W. A. Little, Math. Biosci. 19:101 (1974).
3. W. S. McCulloch and W. Pitts, Bull. Mathem. Biophys. 5:115 (1943).
4. E. Gardner, J. Phys. A 21:257 (1988).
5. J. Hertz, A. Krogh, and R. G. Palmer, Introduction to the Theory of Neural Computation (Addison Wesley, Reading, MA. 1991).
6. M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
7. K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, UK, 1991).
8. F. Rosenblatt, Principles of Neurodynamics (Spartan, New York, 1962).
9. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, Nuture 323:533 (1986).
10. T. L. H. Watkin, A. Rau, and M. Biehl, Rev. Mod. Phys. 65:499 (1993).
11. S. Amari, Neural Computation 10:251 (1998).
12. E. Gardner and B. Derrida, J. Phys. A 21:271 (1988).
13. M. L. Minsky and S. A. Papert, Perceptrous (MIT Press, Cambridge, MA, 1969).
14. M. Biehl and N. Caticha, in The Handbook of Brain Theory and Neural Networks, 2nd edn., M. A. Arbib, ed. (MIT Press, Cambridge, MA, 1999).
15. D. Malzahn, A. Engel, and I. Kanter, Phys. Rev. E 55:7369 (1997).
16. B. Schottky, J. Phys. A 28:4515 (1995).
17. A. H. L. West and D. Saad, J. Phys. A 31:8977 (1998).
18. O. Winther, B. Lautrup, and J.-B. Zhang, Phys. Rev. E 55:836 (1997).
19. W. Whyte and D. Sherrington, J. Phys. A 29:3063 (1996).
20. M. Opper and W. Kinzel, in Models of Neural Networks, Vol. III, E. Domany, J. L. van Hemmen, and K. Schulten, eds. (Springer-Verlag, New York, 1996).
21. G. Györgyi and N. Tishby, Statistical mechanics of learning a rule, in Proceedings of the STATPHYS-17 Workshop on Neural Networks ami Spin Glasses, W. K. Theumann and R. Köberle, eds. (Singapore-Teaneck, NJ-Hongkong, 1990, World Scientific).
22. P. Majer, A. Engel, and A. Zippelius, J. Phys. A 26:7405 (1993).
23. R. Erichsen and W. K. Theumann, J. Phys. A 26:L61 (1993).
24. G. Györgyi and P. Reimann, Phys. Rev: Lett. 79:2746 (1997).
25. M. Griniasty and H. Gutfreund, J. Phys. A 24:715 (1991).
26. M. Aizenman, J. L. Lebowitz, and D. Ruelle, Comm. Math. Phys. 112:3 (1987).
27. G. Györgyi, Phys. Rep., to be published.
28. M. Bouten, J. Phys. A 27:6021 (1994).
29. G. Parisi, J. Phys. A 13:L115 (1980).
30. J. R. L. de Almeida and E. J. S. Lage, J. Phys. C 16:939 (1983).
31. H.-J. Sommers and W. Dupont, J. Phys. C 17:5785 (1984).
32. H. Sompolinsky and A. Zippelius, Phys. Rev. Lett. 47:935 (1981).
33. M. Mézard and M. A. Virasoro, J. Phys. France 46:1293 (1985).
34. T. Temesvári, C. De Dominicis, and I. Kondor, J. Phys. A 27:7569 (1994).
35. C. De Dominicis, T. Temesvári, and I. Kondor, J. Phys. IV France 8:Pr6-13 (1998).
36. Th. M. Nieuwenhuizen, Phys. Rev. Lett. 74:4289 (1995).
37. A. Engel has pointed out this fact to us.
38. A. Wendemuth, J. Phys. A 28:5423 (1995).
39. A. Wendemuth, J. Phys. A 28:5485 (1995).