Exponential transients in continuous-time symmetric Hopfield nets
Sima, J., & Orponen, P. (2001). Exponential transients in continuous-time symmetric Hopfield nets. In G. Dorffner, H. Bischof, & K. Hornik (Eds.), ICANN 2001 : Artificial Neural Networks. Proceedings of the International Conference Vienna, Austria, August 21-25, 2001 (pp. 806-813). Lecture Notes in Computer Science, 2130. Berlin: Springer-Verlag. doi:10.1007/3-540-44668-0_112
Published inLecture Notes in Computer Science
© Springer-Verlag Berlin Heidelberg 2001
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.