J. Phys. I France
Volume 3, Numéro 3, March 1993
Page(s) 777 - 786
DOI: 10.1051/jp1:1993162
J. Phys. I France 3 (1993) 777-786

Attraction domains in neural networks

L. Viana and A. C. C. Coolen

Lab. de Ensenada, Instituto de Física, UNAM, A. Postal 2681, 22800 Ensenada, B.C. México, Department of Theoretical Physics, University of Oxford, 1 Keble Road, Oxford 0X1 3NP, U.K.

(Received 28 April 1992, accepted in revised form 8 October 1992)

We performed a systematic study of the sizes of the basins of attraction in a Hebbian-type neural network in which small numbers of patterns were stored with non-uniform embedding strengths $w_\mu$. This was done by iterating numerically the flux equations for the " overlaps " between the stored patterns and the dynamical state of the system for zero noise level T. We found that the existence of attractors related to mixtures of three or more pure memories depends on the specific values of the embedding strengths involved. With the same method we also obtained the domain sizes for the standard Hopfield model for $p \le 18$.

87.30 - 75.10H - 64.60I

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