Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures
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| Yayımlandı: | Machine Learning : Science and Technology vol. 6, no. 3 (Sep 2025), p. 031002 |
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| Diğer Yazarlar: | , , , , , , , , , |
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IOP Publishing
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| Online Erişim: | Citation/Abstract Full Text - PDF |
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| 001 | 3235721227 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2632-2153 | ||
| 024 | 7 | |a 10.1088/2632-2153/adf375 |2 doi | |
| 035 | |a 3235721227 | ||
| 045 | 2 | |b d20250901 |b d20250930 | |
| 100 | 1 | |a Papillon, Mathilde |u UC Santa Barbara , Santa Barbara, United States of America; Equal contribution | |
| 245 | 1 | |a Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures | |
| 260 | |b IOP Publishing |c Sep 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a 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 non-Euclidean. 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. | |
| 653 | |a Structured data | ||
| 653 | |a Taxonomy | ||
| 653 | |a Machine learning | ||
| 653 | |a Algebra | ||
| 653 | |a Euclidean space | ||
| 653 | |a Geometry | ||
| 653 | |a Euclidean geometry | ||
| 653 | |a Topology | ||
| 700 | 1 | |a Sanborn, Sophia |u Stanford University , Palo Alto, United States of America; Equal contribution | |
| 700 | 1 | |a Mathe, Johan |u Atmo, Inc., San Francisco , United States of America; Equal contribution | |
| 700 | 1 | |a Cornelis, Louisa |u UC Santa Barbara , Santa Barbara, United States of America; Equal contribution | |
| 700 | 1 | |a Bertics, Abby |u UC Santa Barbara , Santa Barbara, United States of America | |
| 700 | 1 | |a Domas Buracas |u New Theory AI , San Francisco, United States of America | |
| 700 | 1 | |a Lillemark, Hansen J |u New Theory AI , San Francisco, United States of America; UC Berkeley , Berkeley, United States of America | |
| 700 | 1 | |a Shewmake, Christian |u New Theory AI , San Francisco, United States of America | |
| 700 | 1 | |a Dinc, Fatih |u UC Santa Barbara , Santa Barbara, United States of America | |
| 700 | 1 | |a Pennec, Xavier |u Université Côte d’Azur & Inria , Nice, France | |
| 700 | 1 | |a Miolane, Nina |u UC Santa Barbara , Santa Barbara, United States of America; Stanford University , Palo Alto, United States of America; Atmo, Inc., San Francisco , United States of America; New Theory AI , San Francisco, United States of America | |
| 773 | 0 | |t Machine Learning : Science and Technology |g vol. 6, no. 3 (Sep 2025), p. 031002 | |
| 786 | 0 | |d ProQuest |t Science Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3235721227/abstract/embedded/J7RWLIQ9I3C9JK51?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3235721227/fulltextPDF/embedded/J7RWLIQ9I3C9JK51?source=fedsrch |