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Limitations and Future Trends in Neural Computation
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SYSNO ASEP 0404167 Document Type M - Monograph Chapter R&D Document Type Monograph Chapter Title Energy-Based Computation with Symmetric Hopfield Nets Author(s) Šíma, Jiří (UIVT-O) RID, SAI, ORCID Source Title Limitations and Future Trends in Neural Computation / Ablameyko S. ; Gori M. ; Goras L. ; Piuri V.. - Amsterdam : IOS Press, 2003 - ISBN 1-58603-324-7 Pages s. 45-70 Number of pages 26 s. Language eng - English Country NL - Netherlands Keywords Hopfield network ; energy function ; computational power ; analog state ; continuous time Subject RIV BA - General Mathematics R&D Projects IAB2030007 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) GA201/01/1192 GA ČR - Czech Science Foundation (CSF) CEZ 1030915 UT WOS 000189476100003 Annotation We propose a unifying approach to the analysis of computational aspects of symmetric Hopfield nets which is based on the concept of "energy source". Within this framework we present different results concerning the computational power of various Hopfield model classes. It is shown that polynomial-time computations by nondeterministic Turing machines can be reduced to the process of minimizing the energy in Hopfield nets (the MIN ENERGY problem). Furthermore, external and internal sources of energy are distinguished. The external sources include e.g. energizing inputs from so-called Hopfield languages, and also certain external oscillators that prove finite analog Hopfield nets to be computationally Turing universal. On the other hand, the internal source of energy can be implemented by a symmetric clock subnetwork producing an exponential number of oscillations which are used to energize the simulation of convergent asymmetric networks by Hopfield nets. This shows that infinite... Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2004
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