Reference:
Jiří Šíma and Pekka Orponen. Continuoustime symmetric Hopfield nets are computationally universal. Neural Computation, 15(3):693–733, March 2003.
Abstract:
We establish a fundamental result in the theory of computation by continuoustime dynamical systems, by showing that systems corresponding to so called continuoustime symmetric Hopfield nets are capable of general computation. As is well known, such networks have very constrained, Liapunovfunction controlled dynamics. Nevertheless, we show that they are universal and efficient computational devices, in the sense that any convergent synchronous fully parallel computation by a recurrent network of discretetime binary neurons, with in general asymmetric coupling weights, can be simulated by a symmetric continuoustime Hopfield net containing only units employing the saturatedlinear activation function. Moreover, if the asymmetric network has maximum integer weight size and converges in discrete time , then the corresponding Hopfield net can be designed to operate in continuous time , for any such that . In terms of standard discrete computation models, our result implies that any polynomially spacebounded Turing machine can be simulated by a family of polynomialsize continuoustime symmetric Hopfield nets.
Keywords:
dynamical systems, continuous time, neural networks, Hopfield model, computational power
Suggested BibTeX entry:
@article{SiOr03a,
author = {Ji{\v{r}}{\'{\i}} {\v{S}}{\'{\i}}ma and Pekka Orponen},
journal = {Neural Computation},
month = {March},
number = {3},
pages = {693733},
title = {ContinuousTime Symmetric {H}opfield Nets are Computationally Universal},
volume = {15},
year = {2003},
}
