In this paper, a study of the Lyapunov Associative Memory (LYAM) is given. This system is constructed by a set of ordinary differential equations, and its stable equilibrium states store pattern cluster information. The study shows that the single-class system is always globally stable; the many-class system has many unstable activation states and at least one stable category state representing the learned information. A rigorous stability study of the many-class system is difficult, and it remains to be investigated.
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References
1.
Aizerman, M.A., E.M. Braverman and L.I. Rozonoer.1964a. "Theoretical Foundations of the Potential Function Method m Pattern Recognition Learning", Automation and Remote Control, 25(6):821-837.
2.
Aizerman, M.A., E.M. Braverman and L.I. Rozonoer.1964b. "The Probability Problem of Pattern Recognition Learning and the Method of Potential Functions", Automanon and Remote Control, 25(9):1175-1190.
3.
Amit, D.J., H. Gutfreund and H. Sompolinsky.1985. "Spin-Glass Models of Neural Networks", Physical Review A, 32(2):1007-1018.
4.
Cohen, M.A.1992. "The Construction of Arbitrary Stable Dynamics in Nonlinear Neural Networks'; Neural Networks , 5:83-103.
5.
Dembo, A. and O. Zeitoum.1988. "General Potential Surfaces and Neural Networks" , Physical Review A, 37:2134-2143.
6.
Haider, N.S. and M.R. Sayeh.1989. "A Discrete Lyapunov System as an Efficient Associative Memory", IJCNN, Washington, D.C., pp. 155-159.
7.
Han, J.Y., M.R. Sayeh and J. Zhang.1989. "Convergence and Limit Points of Neural Network and Its Application to Pattern Recognition", IEEE Transactions on Systems, Man, and Cybernetics, 19(5):1217-1222.
8.
Hopfield, J.J.1982. "Neural Networks and Physical Systems with Emergent Collective Computational Abilities", Proceedings of the National Academy of Sciences USA, 79:2554-2558.
9.
Sayeh, M.R. and J.Y. Han.1987. "Pattern Recognition Using Neural Networks", Proceedings of SPIE, 848:281-285.
10.
Sayeh, M.R., A. Ragu and H.H. Szu.1991. "Design of Unsupervised Classifier", IJCNN, Seattle, WA, pp. 11417-11422.
