6 April 1995 Dynamical Boolean systems: stability analysis and applications
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In this paper, recurrent neural networks are analyzed from the point of view of sequential machines. Their dynamical behavior is described by a system of coupled Boolean equations, and stability results are presented. The typical stability analysis for recurrent Hopfield-type neural nets is to define an energy function and demonstrate that it is a Liaponov function for the system. This analysis works well for single layer networks, but has not been successfully applied to multilayer networks; although, in theory, an energy function for multi-layered nets may be possible to derive. Alteratively, the stability results presented in this paper are applicable to single layer as well as multilayer recurrent networks. Furthermore, our approach is potentially more systematic and easier to apply than the ad-hoc energy function synthesis methods. As an application of this approach, we show how to design recurrent neural nets to design high performance associative neural memories.
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Paul B. Watta, Paul B. Watta, Kaining Wang, Kaining Wang, Rahul Shringarpure, Rahul Shringarpure, Mohamad H. Hassoun, Mohamad H. Hassoun, } "Dynamical Boolean systems: stability analysis and applications", Proc. SPIE 2492, Applications and Science of Artificial Neural Networks, (6 April 1995); doi: 10.1117/12.205156; https://doi.org/10.1117/12.205156

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