Abstract
Introducing a finite correlationρ 0 between any two learned patterns (others remaining uncorrelated), we observe in a numerical simulation that the Hopfield model stores these two patterns with correlationρ f such thatρ f⩾ρ0 for any loading capacityα. The patterns are memorized perfectly (withρ f=ρ 0) up to α-0.05 for finite correlationsρ 0 not exceeding a valueρ c(α), whereρ c(α) decreases continuously to zero at α-0.05.
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References
J. J. Hopfield,Proc. Natl. Acad. Sci. USA 79:2554 (1982).
D. J. Amit, H. Gutfreund, and H. Sompolinsky,Ann. Phys. 170:30 (1987).
D. J. Amit, H. Gutfreund, and H. Sompolinsky,Phys. Rev. A 35:2293 (1987); F. Pazmandi and T. Geszti,Europhys. Lett. 13:673 (1990).
H. Gutfreund,Phys. Rev. A 37:570 (1987); M. V. Feigelman and B. Ioffe,Int. J. Mod. Phys. B 1:51 (1987).
B. Derrida, E. Gardner, and A. Zippelius,Europhys. Lett. 4:167 (1987).
J. F. Fontanari and R. Koberle,J. Phys. A 21:2477 (1988).
A. Rau, K. Y. M. Wong, and D. Sherrington, preprint (1991).
T. J. P. Penna and P. M. C. de Oliviera,J. Phys. A 22:L719 (1989).
F. A. Tamarit and E. M. F. Curado,J. Stat. Phys. 62:473 (1991).
R. Meir and E. Domany,Phys. Rev. A 37:2660 (1988).
P. Sen and B. K. Chakrabarti,Phys. Rev. A 40:4700 (1989).
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Sen, P. Growth of correlation in the Hopfield model. J Stat Phys 67, 413–417 (1992). https://doi.org/10.1007/BF01049042
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DOI: https://doi.org/10.1007/BF01049042