摘要We construct a two-layer feedback neural network by a Monte Carlo based algorithm to store memories as fixed-point attractors or as limit-cycle attractors. Special attention is focused on comparing the dynamics of the network with limit-cycle attractors and with fixed-point attractors. It is found that the former has better retrieval property than the latter. Particularly, spurious memories may be suppressed completely when the memories are stored as a long-limit cycle. Potential application of limit-cycle-attractor networks is discussed briefly.
Abstract：We construct a two-layer feedback neural network by a Monte Carlo based algorithm to store memories as fixed-point attractors or as limit-cycle attractors. Special attention is focused on comparing the dynamics of the network with limit-cycle attractors and with fixed-point attractors. It is found that the former has better retrieval property than the latter. Particularly, spurious memories may be suppressed completely when the memories are stored as a long-limit cycle. Potential application of limit-cycle-attractor networks is discussed briefly.
[1] Hopfield J J 1982 Proc. Natl. Acad. Sci. U.S.A. 79 2554 [2] Hopfield J J 1984 Proc. Natl. Acad. Sci. U.S.A. 81 3088 [3] Amit D J 1989 Modeling Brain Function: The World of Attractor Neural Networks (New York: Cambridge University Press) chap 2 p58 [4] Haykin S 1998 Neural Networks: A Comprehensive Foundation (Upper Saddle River: Prentice Hall) chap 14 p664 [5] Mandan M G, Liang J and Noriyasu H 2003 Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory (Hoboken: Wiley--IEEE) chap 9 p 345 [6] Zhao H 2004 Phys. Rev. E 70 066137 [7] Zhou Z and Zhao H 2006 Chin. Phys. Lett. 23 1402 [8] Bauer U and Krey U 1990 Z. Phys. B 79 461 [9] Coolen A C C and Sherrington D 1992 J. Phys. A: Math. Gen. 25 5493 [10] Kawamura M and Okada M 2002 J. Phys. A: Math. Gen 35 253 [11] Miyoshi S, Yanai H F and Okada M 2002 arXiv:cond-mat/0209258 [12] Sompolinsky H and Kanter I 1986 Phys. Rev. Lett. 57 2861 [13] Amit D J, Gutfreund H and Sompolinsky H 1985 Phys. Rev. A 32 1007 [14] Amit D J, Gutfreund H and Sompolinsky H 1985 Phys. Rev. Lett. 55 1530 [15] Shuai J, Chen Z, Liu R and Wu B 1996 Chin. Phys. Lett. 13 185 [16] Hopfield J J and Tank D W 1985 Biological Cybernetics 52 141 [17] Tank D W and Hopfield J J 1986 IEEE Transactions on Circuits and Systems 33 533 [18] Jin T and Zhao H 2005 Phys. Rev. E 72 066111 [19] Zhang J and Xiao X 2000 Chin. Phys. Lett. 17 88 [20] Zhao H 2006 arXiv:physics/0607046
2008, Vol. 25 
