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Existence and Synthesis of Complex Hopfield Type Associative Memories

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Advances in Computational Intelligence (IWANN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9095))

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Abstract

In this research paper, a complex valued generalization of associative memory synthesized by Hopfield is considered and it is proved that it is impossible to synthesize such a neural network with desired unitary stable states when the dimension of the network (number of neurons) is odd. The linear algebraic structure of such a neural network is discussed. Using Sylvester construction of Hadamard matrix of suitable dimension, an algorithm to synthesize such a complex Hopfield neural network is discussed. Also, it is discussed how to synthesize real / complex valued associative memories with desired energy landscape (i.e. desired stable states and desired energy values of associated quadratic energy function).

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Author information

Authors and Affiliations

  1. International Institute of Information Technology, Hyderabad, India

    Garimella Rama Murthy

  2. Tampere University of Technology, Tampere, Finland

    Moncef Gabbouj

Authors
  1. Garimella Rama Murthy
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  2. Moncef Gabbouj
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Corresponding author

Correspondence to Garimella Rama Murthy .

Editor information

Editors and Affiliations

  1. University of Granada, Granada, Spain

    Ignacio Rojas

  2. Department of Electronics Technology, University of Malaga, Malaga, Spain

    Gonzalo Joya

  3. Polytechnic University of Catalonia, Vilanova i la Geltrú, Spain

    Andreu Catala

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Murthy, G.R., Gabbouj, M. (2015). Existence and Synthesis of Complex Hopfield Type Associative Memories. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2015. Lecture Notes in Computer Science(), vol 9095. Springer, Cham. https://doi.org/10.1007/978-3-319-19222-2_30

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  • DOI: https://doi.org/10.1007/978-3-319-19222-2_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19221-5

  • Online ISBN: 978-3-319-19222-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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