Abstract
The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according the Hebb rule from the set of memorized patterns which are treated as distorted copies of the standard-vector. It is found that the dependence of the set of the fixed points on the value of the distortion parameter can be described analytically. The obtained results are interpreted in the terms of neural networks and the Ising model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.J. Hopfield. Proc. Natl. Acad. Sci. USA, 1982, 79, p.2554.
E. Domany, J.L. van Hemmen and K. Schulten (Eds.). Models of neural networks. Berlin, Springer-Verlag, 1991.
H. Rieger, U. Blasum. Ground state properties of solid-on-solid models with disordered substrates. Cond-mat/9608136, 1996.
N. Sourlas. Europhys. Letters, 1994, 25, p.159.
G. Parisi. Attractor Neural Networks. Cond-mat/9412030, 1994.
E.M. Braverman, I.B. Muchnik. The structural methods of the empirical date processing (in russian). Nauka, Moscow, 1983.
L.B. Litinsky. Neural Network World, 1996, 6, p.325.
L.B. Litinsky. Energy functional and fixed points of neural network. Condmat/9706280, 1997. Also in: “Neural Nets. WIRN VIETRI-97. Proceedings...”, M. Marinaro and R. Tagliaferri (Eds.), Springer-Verlag, 1998.
L.B. Litinskii. Theor. and Math. Phys., 1999 (in press).
L.B. Litinskii. Theor. and Math. Phys., 1994, 101, p.1492.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Litinskii, L.B. (1999). Neural networks of the hopfield type. In: Mira, J., Sánchez-Andrés, J.V. (eds) Foundations and Tools for Neural Modeling. IWANN 1999. Lecture Notes in Computer Science, vol 1606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098184
Download citation
DOI: https://doi.org/10.1007/BFb0098184
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66069-9
Online ISBN: 978-3-540-48771-5
eBook Packages: Springer Book Archive