Abstract
The standard Hopfield model is generalized to the case when input patterns are provided with weights that are proportional to the frequencies of patterns occurrence at the learning process. The main equation is derived by methods of statistical physics, and is solved for an arbitrary distribution of weights. An infinitely large number of input patterns can be written down in connection matrix however the memory of the network will consist of patterns whose weights exceed a critical value. The approach eliminates the catastrophic destruction of the memory characteristic to the standard Hopfield model.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amit, D., Gutfreund, H., Sompolinsky, H.: Storing Infinite Numbers of Patterns in a Spin-Glass Model of Neural Networks. Phys. Rev. Lett. 55, 1530–1533 (1985)
Amit, D., Gutfreund, H., Sompolinsky, H.: Statistical mechanics of neural networks near saturation. Annals of Physics 173, 30–67 (1987)
Hertz, J., Krogh, A., Palmer, R.: Introduction to the Theory of Neural Computation. Addison-Wesley, Massachusetts (1991)
Parisi, G.: A memory which forgets. J. of Phys. A19, L617–L620 (1986)
Nadal, J.P., Toulouse, G., Changeux, J.P., Dehaene, S.: Networks of Formal Neurons and Memory Palimpsest. Europhys. Lett. 1, 535–542 (1986)
van Hemmen, J.L., Keller, G., Kuhn, R.: Forgetful Memories. Europhys. Lett. 5, 663–668 (1988)
van Hemmen, J.L., Kuhn, R.: Collective Phenomena in Neural Networks. In: Domany, E., van Hemmen, J.L., Schulten, K. (eds.) Models of Neural Networks, pp. 1–105. Springer, Berlin (1992)
Karandashev, Y., Kryzhanovsky, B., Litinskii, L.: Local Minima of a Quadratic Binary Functional with a Quasi-Hebbian Connection Matrix. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds.) ICANN 2010, Part III. LNCS, vol. 6354, pp. 41–51. Springer, Heidelberg (2010)
Karandashev, Y., Kryzhanovsky, B., Litinskii, L.: Weighted Patterns as a Tool for Improving the Hopfield Model. Phys. Rev. E85, 041925 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Karandashev, I., Kryzhanovsky, B., Litinskii, L. (2012). Properties of the Hopfield Model with Weighted Patterns. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33269-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-33269-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33268-5
Online ISBN: 978-3-642-33269-2
eBook Packages: Computer ScienceComputer Science (R0)