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Theoretical Foundations for the Alpha-Beta Associative Memories: 10 Years of Derived Extensions, Models, and Applications

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Abstract

The current paper contains the theoretical foundation for the off-the-mainstream model known as Alpha-Beta associative memories (\(\alpha \beta \) model). This is an unconventional computation model designed to operate as an associative memory, whose main application is the solution of pattern recognition tasks, particularly for pattern recall and pattern classification. Although this model was devised, proposed and created in 2002, it is worth noting that its theoretical support remains unpublished to this day. This is despite the fact that more than a hundred scientific articles have been published with applications, improvements, and new models derived from the \(\alpha \beta \) model. The present paper includes all the required definitions, and the rigorous mathematical demonstrations of the lemmas and theorems, explaining the operation of the \(\alpha \beta \) model, as well as the original models it has inspired or that have been derived from it. Also, brief descriptions of 60 selected articles related to the \(\alpha \beta \) model are presented. These latter works illustrate the competitiveness (and sometimes superiority) of several extensions and models derived from the original \(\alpha \beta \) model, when compared against some models and paradigms present in the mainstream current scientific literature.

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Acknowledgements

The authors would like to thank the Instituto Politécnico Nacional (Secretaría Académica, COFAA, SIP, CIDETEC, and CIC), the CONACyT, and SNI for their support to develop this work.

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  1. Unidad Profesional Adolfo López Mateos, Instituto Politécnico Nacional, Centro de Investigación en Computación, Juan de Dios Bátiz s/n esq. Miguel Othón de Mendizábal, Mexico, Mexico

    Cornelio Yáñez-Márquez & Amadeo José Argüelles-Cruz

  2. Unidad Profesional Adolfo López Mateos, Instituto Politécnico Nacional, Centro de Innovación y Desarrollo Tecnológico en Cómputo, Juan de Dios Bátiz s/n esq. Miguel Othón de Mendizábal, Mexico, Mexico

    Itzamá López-Yáñez, Mario Aldape-Pérez, Oscar Camacho-Nieto & Yenny Villuendas-Rey

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  1. Cornelio Yáñez-Márquez
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Yáñez-Márquez, C., López-Yáñez, I., Aldape-Pérez, M. et al. Theoretical Foundations for the Alpha-Beta Associative Memories: 10 Years of Derived Extensions, Models, and Applications. Neural Process Lett 48, 811–847 (2018). https://doi.org/10.1007/s11063-017-9768-2

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