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Proceedings Paper

Global dynamics of winner-take-all networks
Author(s): Ibrahim M. Elfadel
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Paper Abstract

In this paper, we study the global dynamics of winner-take-all (WTA) networks. These networks generalize Hopfield's networks to the case where competitive behavior is enforced within clusters of neurons while the interaction between clusters is modeled by cluster-to- cluster connectivity matrices. Under the assumption of intracluster and intercluster symmetric connectivity, we show the existence of Lyapunov functions that allow us to draw rigorous results about the long-term behavior for both the iterated-map and continuous-time dynamics of the WTA network. Specifically, we show that the attractors of the synchronous, iterated- map dynamics are either fixed points or limit cycles of period 2. Moreover, if the network connectivity matrix satisfies a weakened form of positive definiteness, limit cycles can be ruled out. Furthermore, we show that the attractors of the continuous-time dynamics are only fixed points for any connectivity matrix. Finally, we generalize the WTA dynamics to distributed networks of clustered neurons where the only requirement is that the input-output mapping of each cluster be the gradient map of a convex potential.

Paper Details

Date Published: 29 October 1993
PDF: 11 pages
Proc. SPIE 2032, Neural and Stochastic Methods in Image and Signal Processing II, (29 October 1993); doi: 10.1117/12.162029
Show Author Affiliations
Ibrahim M. Elfadel, Massachusetts Institute of Technology (United States)

Published in SPIE Proceedings Vol. 2032:
Neural and Stochastic Methods in Image and Signal Processing II
Su-Shing Chen, Editor(s)

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