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Computer Science > Machine Learning

arXiv:2407.09468 (cs)
[Submitted on 12 Jul 2024]

Title:Beyond Euclid: An Illustrated Guide to Modern Machine Learning
with Geometric, Topological, and Algebraic Structures

Authors:Sophia Sanborn, Johan Mathe, Mathilde Papillon, Domas Buracas
, Hansen J Lillemark, Christian Shewmake, Abby Bertics, Xavier Pennec
, Nina Miolane
View a PDF of the paper titled Beyond Euclid: An Illustrated Guide to
Modern Machine Learning with Geometric, Topological, and Algebraic
Structures, by Sophia Sanborn and 8 other authors
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    Abstract:The enduring legacy of Euclidean geometry underpins
    classical machine learning, which, for decades, has been
    primarily developed for data lying in Euclidean space. Yet,
    modern machine learning increasingly encounters richly structured
    data that is inherently nonEuclidean. This data can exhibit
    intricate geometric, topological and algebraic structure: from
    the geometry of the curvature of space-time, to topologically
    complex interactions between neurons in the brain, to the
    algebraic transformations describing symmetries of physical
    systems. Extracting knowledge from such non-Euclidean data
    necessitates a broader mathematical perspective. Echoing the
    19th-century revolutions that gave rise to non-Euclidean
    geometry, an emerging line of research is redefining modern
    machine learning with non-Euclidean structures. Its goal:
    generalizing classical methods to unconventional data types with
    geometry, topology, and algebra. In this review, we provide an
    accessible gateway to this fast-growing field and propose a
    graphical taxonomy that integrates recent advances into an
    intuitive unified framework. We subsequently extract insights
    into current challenges and highlight exciting opportunities for
    future development in this field.

Subjects: Machine Learning (cs.LG)
Cite as:  arXiv:2407.09468 [cs.LG]
          (or arXiv:2407.09468v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2407.09468
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Johan Mathe [view email]
[v1] Fri, 12 Jul 2024 17:48:36 UTC (39,168 KB)
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