Asymmetric Hopfield-type networks: Theory and applications

Neural Networks

Volumn 9, Issue 3, 1996, Pages 483-501

  Xu, Zong Ben ^a   Hu, Guo Qing ^b   Kwong, Chung Ping ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b NONE

Author keywords

Asymmetric Hopfield type networks; Classification theory on energy functions; Combinatorial optimization; Convergence principle; Maximal independent set problem; Regular and normal correspondence

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; MATHEMATICAL MODELS; OPTIMIZATION; RELIABILITY;

ASYMMETRIC HOPFIELD TYPE NETWORKS; CLASSIFICATION THEORY ON ENERGY FUNCTIONS; COMBINATORIAL OPTIMIZATION; CONVERGENCE PRINCIPLE; CORRESPONDENCE; MAXIMAL INDEPENDENT SET PROBLEM;

NEURAL NETWORKS;

ALGORITHM; ARTIFICIAL NEURAL NETWORK; COMPUTER MODEL; PRIORITY JOURNAL; REVIEW;

EID: 0030130743     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/0893-6080(95)00114-X     Document Type: Article

References (43)

1. Aiyer, S. V. B., Niranjan, M., & Fallside, F. (1990). A theoretical investigation into the performance of the Hopfield model. IEEE Transactions on Neural Networks, 1. 204-215.
2. Amit, D., Gutfreund, H., & Sompolinsky, H. (1985). Spin-glass models of neural networks, Physical Review A, 32, 1007-1018.
3. Bondy, J. A., & Murty, U. S. R. (1976). Graph theory with applications. London: The Macmillan Press.
4. Bruck, J., (1990). On the convergence properties of the Hopfield model. Proceedings of the IEEE, 78, 1579-1585.
5. Bruck, J., & Goodman, J. W. (1988). A generalized convergence theorem for neural networks. IEEE Transactions on Information Theory, 34, 1089-1092.
6. Bruck, J., & Blaum, M. (1989). Neural networks, error correcting codes and polynomials over binary n-cubes. IEEE Transactions on Information Theory, 35, 976-987.
7. Bruck, J., & Roychowdhury, V. P. (1989). On the number of spurious memories in the Hopfield Model. IEEE Transactions on Information Theory, 36, 393-397.
8. Chiueh, T. D., & Goodman, R. M. (1991). Recurrent correlation associative memories. IEEE Transactions on Neural Networks, 2, 275-284.
9. Coolen, T., & Sherrington, D (1993). Dynamics of attractor neural networks. In J. G. Taylor (Ed.), Mathematical approaches to neural networks. Amsterdam: Elsevier.
10. Cottrel, M. (1988). Stability and attractiveness in associative memory networks. Biological Cybernetics, 58, 129-139.
11. Crisanti, A., & Sompolinsky, H. (1987). Dynamics of spin systems with randomly asymmetric bonds: Langevin dynamics and a spherical model. Physical Review A, 36, 4922-4936.
12. Dahl, E. D. (1988). Neural network algorithms for an NP-complete problem: Map and graph coloring. Proceedings of International Conference on Neural Networks, (III, pp. 113-120).
13. Dasgupta, S., Ghosh, A., & Cuykendall, R. (1989). Convergence in neural memories. IEEE Transactions on Information Theory, 35, 1069-1072.
14. Derrida, B., Gardner, E., & Zippelius, A. (1987). An exactly soluble asymmetric neural network model. Europhysics Letters, 4, 167-173.
15. Goles, E. (1986). Antisymmetrical neural networks. Discrete Applied Mathematics, 13, 97-100.
16. Goles, E., Fogelman, F., & Pellegrin, D. (1985). Decreasing energy functions as a tool for studying threshold networks. Discrete Applied Mathematics, 12, 261-277.
17. Guez, A., Protopopescu, V., & Barhen, J. (1988). On the stability, storage capacity and design of nonlinear continuous neural networks. IEEE Transactions on System, Man, Cybernetics, 18, 80-87.
18. Hertz, J. A., Grinstein, G., & Solla, S. (1986). Memory networks with asymmetric bonds. In J. S. Denker (Ed.), Neural networks for computing (pp. 212-218). New York: American Institute of Physics.
19. Hertz, J. A., Krogh, A., & Palmer, R. G. (1991). Introduction to the theory of neural computation. Reading, MA: Addison-Wesley.
20. Hinton, G. E., & Sejnowski, T. J. (1983). Optimal perceptual inference. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Washington 1983 (pp. 448-453). New York: IEEE.
21. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational ability. Proceedings of the National Academy of Sciences, USA, 79, 2554-2558.
22. Hopfield, J. J., & Tank, D. W. (1985). Neural computation of decisions in optimization problems. Biological Cybernetics, 52, 141-152.
23. Kanter, I., & Sompolinsky, H. (1987). Associative recall of memory without errors. Physical Review A, 35, 308-392.
24. Kohonen, T. (1974). An adaptive associative memory principle. IEEE Transaction on computers, C-23, 444-445.
25. Kohonen, T. (1989). Self-organization and associative memory (3rd ed.). Berlin: Springer-Verlag.
26. Kohring, G. A. (1993). On the Q-state neuron problem in attractor neural networks. Neural Networks, 6, 573-581.
27. Kosko, B. (1988). Bidirectional associative memories. IEEE Transactions on System, Man, Cybernetics, 18, 49-60.
28. Little, W. A. (1974). The existence of persistent states in the brain. Mathematical Biosciences, 19, 101-120.
29. Mazumadar, P., & Yih, J. S. (1989). Neural computing for built in self repair of embedded memory arrays. Proceedings of the 19th International Symposium on Fault Tolerant Computing, pp. 480-487.
30. McEliece, R. J., Posner, E. C., Rodemich, E. R., & Venkatesh, S. S. (1987). The capacity of the Hopfield associative memory. IEEE Transactions on Information Theory, 33, 461-482.
31. Parisi, G. (1986). Asymetric neural networks and process of learning. Journal of Physics, 19, L675-L680.
32. Personnaz, L., Guyon, I., & Dreyfus, G. (1985). Information storage and retrieval in spin-glass-like neural networks. Journal de Physiue Letters (paries), 46, 359-365.
33. Porat, S. (1989). Stability and looping in connectionist models with asymmetric weights. Biological Cybernetics, 60, 335-344.
34. Pramanick, I. (1991). Parallel dynamic interaction - An inherently parallel problem solving methodology. Ph.D. Thesis, Department of ECE, University of Iowa (May).
35. Shrivastava, Y., Dasgupta, S., & Reddy, S. M. (1992). Guaranteed convergence in a class of Hopfield networks. IEEE Transactions on Neural Networks, 3, 951-961.
36. Sompolinsky, H. (1987). The theory of neural networks: The Hebb rules and beyond. In J. L. van Hermmen & I. Morgenstern (Eds.), Heidelberg Colloquium on Glassy Dynamics (Heidelberg 1986), (pp. 485-527). Berlin: Springer-Verlag.
37. Sompolinsky, H., & Kanter, I. (1986). Temporal association in asymmetric neural networks. Physical Review Letters, 57, 2861-2864.
38. van Hemmen, J. L., & Kühn, R. (1986). Nonlinear neural networks. Physical Review Letters, 57, 913-916.
39. Wilson, V., & Pawley, G. S. (1988). On the stability of the TSP problem algorithm of Hopfield and Tank. Biological Cybernetics, 58, 63-70.
40. Xu, Z. B., & Kwong, C. P. (1995a). Global convergence and asymptotic stability of asymmetric Hopfield neural networks. Journal of Mathematical Analysis and Applications, 191, 405-427.
41. Xu, Z. B., & Kwong, C. P. (1995b). A decomposition principle for complexity reduction of artificial neural networks. Neural Networks (in press).
42. Xu, Z. B., Leung, Y., & He, X. W. (1994). Asymmetric bi-directional associative memories. IEEE Transactions on System, Man, Cybernetics, 24, 1558-1564.
43. Xu, Z. B., Hu, G. Q., & Kwong, C. P. (1996). Some efficient strategies for improving the eigenstructure method in synthesis of feedback neural networks. IEEE Transactions on Neural Networks, 7, 233-245.