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Bidirectional Associative Memory with Block Coding: A Comparison of Iterative Retrieval Methods

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Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation (ICANN 2019)

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Abstract

Recently, Gripon and Berrou (2011) have investigated a recurrently connected Willshaw-type auto-associative memory with block coding, a particular sparse coding method, reporting a significant increase in storage capacity compared to earlier approaches. In this study we verify and generalize their results by implementing bidirectional hetero-associative networks and comparing the performance of various retrieval methods both with block coding and without block coding. For iterative retrieval in networks of size \(n=4096\) our data confirms that block-coding with the so-called “sum-of-max” strategy performs best in terms of output noise (which is the normalized Hamming distance between stored and retrieved patterns), whereas the information storage capacity of the classical models cannot be exceeded because of the reduced Shannon information of block patterns. Our simulation experiments also provide accurate estimates of the maximum pattern number that can be stored at a tolerated noise level of 1%. It is revealed that block coding is most beneficial for sparse activity where each pattern has only \(k\sim \log n\) active units.

The authors acknowledge support by the state of Baden-Württemberg through bwHPC.

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Acknowledgments

The authors are grateful to Friedhelm Schwenker and Fritz Sommer for valuable discussions. The authors acknowledge support by the state of Baden-Württemberg through bwHPC.

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Authors and Affiliations

  1. KEIM Institute, Albstadt-Sigmaringen University, Albstadt, Germany

    Andreas Knoblauch

  2. Institute of Neural Information Processing, Ulm University, Ulm, Germany

    Günther Palm

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  1. Andreas Knoblauch
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  2. Günther Palm
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Correspondence to Andreas Knoblauch .

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Editors and Affiliations

  1. Helmholtz Zentrum München - Deutsches Forschungszentrum für Gesundheit und Umwelt (GmbH), Neuherberg, Germany

    Igor V. Tetko

  2. Institute of Computer Science, Czech Academy of Sciences, Prague 8, Czech Republic

    Věra Kůrková

  3. Helmholtz Zentrum München - Deutsches Forschungszentrum für Gesundheit und Umwelt (GmbH), Neuherberg, Germany

    Pavel Karpov

  4. Helmholtz Zentrum München - Deutsches Forschungszentrum für Gesundheit und Umwelt (GmbH), Neuherberg, Germany

    Fabian Theis

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Knoblauch, A., Palm, G. (2019). Bidirectional Associative Memory with Block Coding: A Comparison of Iterative Retrieval Methods. In: Tetko, I., Kůrková, V., Karpov, P., Theis, F. (eds) Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. ICANN 2019. Lecture Notes in Computer Science(), vol 11727. Springer, Cham. https://doi.org/10.1007/978-3-030-30487-4_1

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  • DOI: https://doi.org/10.1007/978-3-030-30487-4_1

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