Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures
2024/07/12 by Mathilde Papillon, Sophia Sanborn, Papillon, Mathilde +20 · 13 voices · 2 citations
Computer Science · #Computational Physics and Python Applications
paper · pdf · doi:10.1088/2632-2153/adf375
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 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.
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Discussions
- Guide to Machine Learning with Geometric, Topological, and Algebraic Structures [hn, 176 points, 27 comments]
- December 5th our ML theory group at Cohere For AI is hosting @mathildepapillon.bsky.social to discuss their recent review arxiv.org/abs/2407.09468 on geometric/topological/algebraic ML. Join us onlin [bsky, 14 points, 0 comments]
- "Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures" arxiv.org/pdf/2407.09468 [bsky, 12 points, 0 comments]
- Enjoying and learning a lot from this piece! I don’t know if the best reading choice for a week of holiday 🤣🤯 but 100% recommended if you are like me still getting your head around TDL/GDL. @mathil [bsky, 12 points, 0 comments]
- The updated version is also available on arxiv at arxiv.org/pdf/2407.09468 [bsky, 8 points, 1 comments]
- Beyond Euclid: An Illustrated Guide to Modern Machine Learning [hn, 3 points, 0 comments]
- The world of visual explanations is on fire recently. Look at this illustrated guide to mathematical aspects of modern machine learning: arxiv.org/pdf/2407.09468 #mathSky #visualization #eduSky [bsky, 2 points, 0 comments]
- Guide to Machine Learning with Geometric, Topological, and Algebraic Structures https://www.arxiv.org/abs/2407.09468 [bsky, 0 points, 0 comments]
- Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures arxiv.org/abs/2407.09468 Machine learning is evolving to tackle complex, non-Euclid [bsky, 0 points, 0 comments]
- Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures arxiv.org/abs/2407.094... [bsky, 0 points, 0 comments]
- I don't know how significant Geometry, Topology, or Algebra, will be on machine learning. Nonetheless, It's great to see a paper surveying and introducing such emerging fields. #AI #MathSky #TCSsky ar [bsky, 0 points, 0 comments]
- Guide to Machine Learning with Geometric, Topological, and Algebraic Structures (arxiv.org) Main Link | Discussion [bsky, 0 points, 0 comments]
- An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures arxiv.org/pdf/2407.09468 [bsky, 0 points, 0 comments]
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