Reference:
Jiří Šíma and Pekka Orponen. Exponential transients in continuoustime symmetric Hopfield nets. In G. Dorffner, H. Bischof, and K. Hornik, editors, Proceedings of Artificial Neural Networks – ICANN 2001 (Vienna, August 2001), volume 2130 of Lecture Notes in Computer Science, pages 806–813, Berlin Heidelberg, 2001. SpringerVerlag.
Abstract:
We establish a fundamental result in the theory of continuoustime neural computation, by showing that so called continuoustime symmetric Hopfield nets, whose asymptotic convergence is always guaranteed by the existence of a Liapunov function may, in the worst case, possess a transient period that is exponential in the network size. The result stands in contrast to e.g. the use of such network models in combinatorial optimization applications.
Keywords:
dynamical systems, continuous time, neural networks, Hopfield model, convergence time
Suggested BibTeX entry:
@inproceedings{SiOr01b,
address = {Berlin Heidelberg},
author = {Ji{\v{r}}{\'{\i}} {\v{S}}{\'{\i}}ma and Pekka Orponen},
booktitle = {Proceedings of Artificial Neural Networks  ICANN 2001 (Vienna, August 2001)},
editor = {G. Dorffner and H. Bischof and K. Hornik},
pages = {806813},
publisher = {SpringerVerlag},
series = {Lecture Notes in Computer Science},
title = {Exponential Transients in ContinuousTime Symmetric {H}opfield Nets},
volume = {2130},
year = {2001},
}
