Exponential Transients in Continuous-Time Symmetric Hopfield Nets

Reference:

Jiří Šíma and Pekka Orponen. Exponential transients in continuous-time 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. Springer-Verlag.

Abstract:

We establish a fundamental result in the theory of continuous-time neural computation, by showing that so called continuous-time 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 = {806--813},
    publisher = {Springer-Verlag},
    series = {Lecture Notes in Computer Science},
    title = {Exponential Transients in Continuous-Time Symmetric {H}opfield Nets},
    volume = {2130},
    year = {2001},
}