Tensor networks for dimensionality reduction, big data and deep learning

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    11 Citations (Scopus)

    Abstract

    Large scale multidimensional data are often available as multiway arrays or higher-order tensors which can be approximately represented in distributed forms via low-rank tensor decompositions and tensor networks. Our particular emphasis is on elucidating that, by virtue of the underlying low-rank approximations, tensor networks have the ability to reduce the dimensionality and alleviate the curse of dimensionality in a number of applied areas, especially in large scale optimization problems and deep learning. We briefly review and provide tensor links between low-rank tensor network decompositions and deep neural networks. We elucidating, through graphical illustrations, that low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volume of data/parameters. Our focus is on the Hierarchical Tucker, tensor train (TT) decompositions and MERA tensor networks in specific applications.

    Original languageEnglish
    Title of host publicationStudies in Computational Intelligence
    PublisherSpringer Verlag
    Pages3-49
    Number of pages47
    DOIs
    Publication statusPublished - 2018

    Publication series

    NameStudies in Computational Intelligence
    Volume738
    ISSN (Print)1860-949X

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