Abstract
In this paper we study some dynamical aspects of the synchronous update of Neural Networks. We exhibit Lyapunov Functional for discrete neural networks (binary states) and also for continuous local rules. By doing so we prove, in the context of binary networks, the convergence to cycles of period one or two for symmetric weights. Also we prove that “almost symmetric” Neural Networks admit large cycles (non-bounded in the size, n, of the array) and that the synchronous update with symmetric weights may have an exponential transient time in order to reach a fixed point. Finally, for continuous local rules we give the explicit expression of Lyapunov operators for synchronous and sequential iterations and we characterize the network dynamics for periodic trajectories.
Partially supported by FNC/89, DTI U. Chile, EHEI U. Paris-V and F. Andes-Chile/89
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© 1990 Springer-Verlag Berlin Heidelberg
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Goles, E. (1990). Neural Networks Dynamics. In: Soulié, F.F., Hérault, J. (eds) Neurocomputing. NATO ASI Series, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76153-9_11
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DOI: https://doi.org/10.1007/978-3-642-76153-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76155-3
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