Multifractality and percolation in the coupling space of perceptrons

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 4, 1997, Pages 4552-4561

  Weigt, M ^a   Engel, A ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007026929     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.4552     Document Type: Article

References (32)

1. E. Gardner, J. Phys. A21, 257 (1988);
2. E. Gardner and B. Derrida, J. Phys. Aibid. A21, 271 (1988).
3. M. Opper and W. Kinzel, in Models of Neural Networks III, edited by E. Domany, J. L. van Hemmen, and K. Schulten (Springer, New York, 1996).
4. T. L. M. Watkin, A. Rau and M. Biehl, Rev. Mod. Phys.65, 499 (1993).
5. T M. Cover, IEEE Trans. Electron. Comput.EC-14, 326 (1965).
6. D. Haussler, M. Kearns, and R. Schapire, Bounds on the Sample Complexity of Bayesian Learning Using Information Theory and the VC Dimension, Proceedings of the Conference on Computional Learning Theories '91 (Morgan Kaufmann, San Mateo, 1991).
7. B. Derrida, R B. Griffith and A. Prügel-Bennett, J. Phys. A24, 4907 (1991).
8. R. Monasson and D. O'Kane, Europhys. Lett.27, 85 (1994).
9. R. Monasson and R. Zecchina, Phys. Rev. Lett.75, 2432 (1995).
10. S. Cocco, R. Monasson and R. Zecchina, Phys. Rev. E54, 717 (1996).
11. A. Engel and M. Weigt, Phys. Rev. E53, R2064 (1996).
12. U. Frisch and G. Parisi, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by M. Ghil, R. Benzi, and G. Parisi (North Holland, Amsterdam, 1985).
13. T C. Halsey, M H. Jensen, L P. Kadanoff, I. Procaccia and B I. Shraiman, Phys. Rev. A33, 1141 (1986).
14. G. Parisi and M A. Virasoro, J. Phys. (Paris)50, 3317 (1989).
15. M. Biehl and M. Opper, in Neural Networks: The Statistical Mechanics Perspective, edited by Jong-Houn Oh, Chulan Kwon, and Sungzoon Cho (World Scientific, Singapore, 1995).
16. G. Györgyi and N. Tishby, in Workshop on Neural Networks and Spin Glasses, edited by K. Theumann and W. K. Koeberle (World Scientific, Singapore, 1990).
17. M. Opper and D. Haussler, Phys. Rev. Lett.66, 2677 (1991).
18. M. Mezard, G. Parisi, and M A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
19. V N. Vapnik and A Y. Chervonenkis, Theor. Prob. Appl.16, 264 (1971).
20. A. Engel, Mod. Phys. Lett. B8, 1683 (1994).
21. The simplest case is given by a pattern set in which one pattern occurs at least twice since it is, of course, impossible to map identical patterns to different outputs.
22. T. Bohr and T. Tél, in Directions in Chaos, edited by Hao-Bai-Lin (World Scientific, Singapore, 1988).
23. J. R. L. de Almeida and D. Thouless, J. Phys. A11, 983 (1978).
24. T. Temesvari, C. De Dominicis and I. Kondor, J. Phys. A27, 7569 (1994).
25. D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett.35, 1972 (1975).
26. W. Krauth and M. Mezard, J. Phys. France50, 3057 (1989).
27. G. Györgyi, Phys. Rev. Lett.64, 2957 (1990).
28. St. Mertens, J. Phys. A29, L199 (1996).
29. St. Mertens and A. Engel, Phys. Rev. E (to be published).
30. Stambke, diploma thesis, University of Giessen, 1992 (unpublished).
31. W. Krauth and M. Opper, J. Phys. A22, L519 (1989).
32. W H. Press, S A. Teukolsky, W T. Vetterling, and B P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, Cambridge, 1992).