6533b822fe1ef96bd127ce1c

RESEARCH PRODUCT

Exponential Transients in Continuous-Time Symmetric Hopfield Nets

Jirí SímaPekka Orponen

subject

Lyapunov functionHopfield netsstabilityneural networksExponential functionHopfield networksymbols.namesakeModels of neural computationRecurrent neural networkConvergence (routing)symbolsApplied mathematicsCombinatorial optimizationdynaamiset systeemitAlgorithmMathematicsNetwork model

description

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. peerReviewed

yearjournalcountryeditionlanguage
2001-01-01
https://doi.org/10.1007/3-540-44668-0_112