Abstract
A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the dynamic system with the set of local minima of the energy functional, have been determined. The influence of the connection matrix diagonal elements on the structure of the fixed points set has been investigated.
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References
L.B.Litinsky. Neural network and factor analysis. Neural Network World 1996; 6: 325–330.
E.Domany, J.L. van Hemmen and K.Schulten (Eds.). Models of neural networks. Springer-Verlag, Berlin, 1991.
L.Personnaz, I.Guyon and G.Dreyfus. Collective computational properties of neural networks: new learning mechanisms. Phys. Rev. A 1986; 34: 4217–4228.
L.B.Litinsky. Direct calculation of the stable points of a neural network. Theor. and Math. Phys. 1994; 101: 1492–1501.
I.Kanter, H.Sompolinsky. Associative recall of memory without errors. Phys. Rev. A 1987; 35: 380–392.
A.A.Vedenov, A.A.Ezhov et al.. Structure of patterns in associative mem¬ory models. In: Neural Networks–Theory and Architecture, A.V. Holden and V.I. Kryukov (Eds.), Manch. Univ. Press, pp. 169–186, 1991.
P.Baldi. Symmetries and learning in neural network models. Phys. Rev. Lett. 1987; 59: 1976–1978.
P.Baldi, S.S.Venkatesh. Number of stable points for sipn-glass and neural networks of high orders. Phys. Rev. Lett. 1987; 58: 913–916.
P.Baldi. Neural networks, orientations of the hypercube, and algebraic threshold functions. IEEE Trans, on Inform. Theory 1988; 34: 523–530.
P.Kuhlman, J.K.Anlauf. The number of metastable states in the projection rule neural network. J. Phys. A: Math., Gen. 1994; 27: 5857–5870.
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© 1998 Springer-Verlag London Limited
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Litinsky, L.B. (1998). Energy Functional and Fixed Points of a Neural Network. In: Marinaro, M., Tagliaferri, R. (eds) Neural Nets WIRN VIETRI-97. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-1520-5_10
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DOI: https://doi.org/10.1007/978-1-4471-1520-5_10
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