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Neural addition and fibonacci numbers

  • Artificial Neural Nets Simulation and Implementation
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Engineering Applications of Bio-Inspired Artificial Neural Networks (IWANN 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1607))

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Abstract

This paper presents an intriguing relation between neural networks having as weights the Fibonacci numbers and the Addition of (two) binary numbers. The practical application of interest is that such ‘Fibonacci’ networks are VLSI-optimal with respect to the area of the circuit. We shortly present the state-of-the-art, and detail a class of multilayer solutions for Addition. For this class we will prove constructively that the weights of the threshold gates implementing the Boolean functions are the Fibonacci numbers. As the weights are the smallest integers (by construction), the area of the VLSI circuit—estimated as the sum of the digits needed to represent the weights—is minimised. Therefore this class of solutions is VLSI-optimal. Conclusions and open questions are ending the paper.

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Author information

Author notes

  1. Valeriu Beiu

    Present address: Computer Science Department, Politehnica University of Bucharest, Spl. Independentei 313, RO-77206, Bucharest, România

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  1. RN2R LLC, 14850 Montfort Drive, Suite 181, 75240, Dallas, Texas, USA

    Valeriu Beiu

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  1. Valeriu Beiu
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Correspondence to Valeriu Beiu .

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José Mira Juan V. Sánchez-Andrés

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© 1999 Springer-Verlag Berlin Heidelberg

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Beiu, V. (1999). Neural addition and fibonacci numbers. In: Mira, J., Sánchez-Andrés, J.V. (eds) Engineering Applications of Bio-Inspired Artificial Neural Networks. IWANN 1999. Lecture Notes in Computer Science, vol 1607. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0100486

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  • DOI: https://doi.org/10.1007/BFb0100486

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66068-2

  • Online ISBN: 978-3-540-48772-2

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