0000000000512411

AUTHOR

Jirí Síma

showing 2 related works from this author

Exponential Transients in Continuous-Time Symmetric Hopfield Nets

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. peerReviewed

Lyapunov functionHopfield netsstabilityneural networksExponential functionHopfield networksymbols.namesakeModels of neural computationRecurrent neural networkConvergence (routing)symbolsApplied mathematicsCombinatorial optimizationdynaamiset systeemitAlgorithmMathematicsNetwork model
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Some Afterthoughts on Hopfield Networks

1999

In the present paper we investigate four relatively independent issues, which complete our knowledge regarding the computational aspects of popular Hopfield nets. In Section 2 of the paper, the computational equivalence of convergent asymmetric and Hopfield nets is shown with respect to network size. In Section 3, the convergence time of Hopfield nets is analyzed in terms of bit representations. In Section 4, a polynomial time approximate algorithm for the minimum energy problem is shown. In Section 5, the Turing universality of analog Hopfield nets is studied. peerReviewed

TheoryofComputation_COMPUTATIONBYABSTRACTDEVICESQuantitative Biology::Neurons and CognitionComputer scienceParallel algorithmHopfield netsApproximation algorithmSection (fiber bundle)Hopfield networknetworksHopfieldAlgorithmTime complexityEquivalence (measure theory)Energy (signal processing)
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