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Defining the Attractor of a Recurrent Neural Network by Boolean Expressions

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ICANN ’93 (ICANN 1993)

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Abstract

An autoassociator neural network can be operated to solve a computation problem with a high degree of parallelism. The set of stable states (solutions of the problem) that build up the attractor of such a recurrent network are determined by the feedback weights and biases. This set can be constructed by using the k-out-of-n design rule. It is shown how to convert arbitrary boolean expressions into a list of k-out-of-n constraints. Finally, a compiler for generating the network structure is described.

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References

  1. G. Tagliarmi, J. Christ, E. Page, Optimization Using Neural Networks, IEEE Tr. on Computers, Vol. 40, No. 12, Dec. 1991, 1347–1358

    Article  Google Scholar 

  2. E. Page, G. Tagliarini, Algorithm development for neural networks, Proc. IEEE SPIE, Vol. 880, High Speed Computing, 1988, 11–19

    Article  Google Scholar 

  3. T. Nakagawa, E. Page, G. Tagliarini, SDNN: A Computation Model for Strictly Digital Neural Networks and its Application, Proc. 5th AAAIC’89, ACM/SIGART Dayton, OH, 1989

    Google Scholar 

  4. T. Nakagawa, H. Kitagawa, E. Page, G. Tagliarini, SDNN-3: A Simple Processor Architecture for O(1) Parallel Processing in Combinatorial Optimization with Strictly Digital Neural Networks, IJCNN’91, Singapore Nov. 1991, 2444–2449

    Google Scholar 

  5. H. N. Schaller, On the Problem of Systematically Designing Energy Functions for Neural Expert Systems Based on Combinatorial Optimization Networks, Neuro-Nîmes’92, EC2, Nîmes, 1992, 648–653

    Google Scholar 

  6. D. Tank, J. Hopfield, Collective Computation in Neuronlike Circuits, Scientific American, Dec. 1987, 62–70

    Article  Google Scholar 

  7. D. Tank, J. Hopfield, Simple “Neural” Optimization Networks: An A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit, IEEE Tr. on CAS, Vol. CAS-33, No. 5, May 1986, 533–541

    Article  Google Scholar 

  8. J. Hopfield, D. Tank, “Neural” Computation of Decisions in Optimization Problems, Biol. Cybernetics, Springer, Vol. 52, 1985, 141–152

    MathSciNet  MATH  Google Scholar 

  9. H. N. Schaller, A collection of constraint design rules for neural optimization networks, in Artificial Neural Networks II: Proc. ICANN’92, Brighton, (Eds.: I. Aleksander, J. Taylor), Elsevier, 1992, 1039–1042

    Google Scholar 

  10. R. K. Brayton, G. D. Hachtel, et. al., Logic Minimization Algorithms for VLSI Synthesis, Kluwer Academic Publishers, 1984

    Google Scholar 

  11. K. Ehrenberger, Automatische Umsetzung von booleschen Funktionen in eine neuronale Struktur, Diplomarbeit, Lehrstuhl für Datenverarbeitung, Technische Universität München, 1992

    Google Scholar 

  12. M. Arai, T. Nakagawa, H. Kitagawa, An Approach to Automatic Test Pattern Generation Using Strictly Digital Neural Networks, IJCNN’92, Baltimore, June 1992, IV-474–479

    Google Scholar 

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© 1993 Springer-Verlag London Limited

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Schaller, H.N., Ehrenberger, K. (1993). Defining the Attractor of a Recurrent Neural Network by Boolean Expressions. In: Gielen, S., Kappen, B. (eds) ICANN ’93. ICANN 1993. Springer, London. https://doi.org/10.1007/978-1-4471-2063-6_199

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  • DOI: https://doi.org/10.1007/978-1-4471-2063-6_199

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  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19839-0

  • Online ISBN: 978-1-4471-2063-6

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