Abstract
A neural network of Willshaw type is investigated under the crucial assumption of no overlap betweenp stored patterns covering the net completely. Taking the thermodynamic limit withp remaining finite a first order phase transition is found, indicating the transition from population of one stored pattern to equal population of all stored patterns. The approximation used to keep mathematics tractable is of Gaussian type.
Similar content being viewed by others
References
Willshaw, D.J., Buneman, O.P., Longuet-Higgins, H.C.: Nature (London)222, 960 (1969)
Palm, G.: Biol. Cybern.36, 19 (1980); Biol. Cybern.39, 125 (1981); In: Neural computers, Eckmiller, R., van der Malsburg, C. (eds.), p. 271. Berlin, Heidelberg, New York: Springer 1988
Amari, S.-I.: Neural Networks2, 451 (1989)
Buhmann, J., Divko, R., Schultern, K.: Phys. Rev. A39, 2689 (1989)
Golomb, D., Rubin, N., Sompolinsky, H.: Phys. Rev. A41, 1843 (1990)
Horner, H.: Z. Phys. B—Condensed Matter75, 133 (1989)
Tsodyks, M.V., Feigelman, M.V.: Europhys. Lett.6, 101 (1988)
Nadal, J.P.: J. Phys. A24, 1093 (1991)
Gardner, E.: J. Phys. A21, 257 (1988)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krisement, O. Phase transition in a Willshaw net. Z. Physik B - Condensed Matter 86, 145–149 (1992). https://doi.org/10.1007/BF01323559
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01323559