Fixed points in a Hopfield model with random asymmetric interactions

Singh, Manoranjan P and Chengxiang, Zhang and Dasgupta, Chandan (1995) Fixed points in a Hopfield model with random asymmetric interactions. In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 52 (5). pp. 5261-5272.

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Abstract

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

Item Type:	Journal Article
Publication:	Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Publisher:	The American Physical Society
Additional Information:	Copyright of this article belongs to The American Physical Society.
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	18 May 2011 08:04
Last Modified:	18 May 2011 08:04
URI:	http://eprints.iisc.ac.in/id/eprint/37746

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