mlsanityData to 14 Oct 2026

Learning Algebraic Structures: Preliminary Investigations

arXiv 1905.02263 ↗First posted 2 May 2019cs.LG hep-th math.GRcited by 15

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Abstract (arXiv)

We employ techniques of machine-learning, exemplified by support vector machines and neural classifiers, to initiate the study of whether AI can "learn" algebraic structures. Using finite groups and finite rings as a concrete playground, we find that questions such as identification of simple groups by "looking" at the Cayley table or correctly matching addition and multiplication tables for finite rings can, at least for structures of small size, be performed by the AI, even after having been trained only on small number of cases. These results are in tandem with recent investigations on whether AI can solve certain classes of problems in algebraic geometry.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). First posted on arXiv 2 May 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 5; 2023: 4; 2024: 2; 2025: 0; 2026: 1.

15 papers.

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  1. 2021Machine-Learning Mathematical Structurescited by 25
  2. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  3. 2023Is deep learning a useful tool for the pure mathematician?cited by 14
  4. 2021Neurons on Amoebaecited by 11
  5. 2022Group invariant machine learning by fundamental domain projectionscited by 11
  6. 2022Cluster Algebras: Network Science and Machine Learningcited by 9
  7. 2023Mathematical conjecture generation using machine intelligencecited by 8
  8. 2024A Triumvirate of AI Driven Theoretical Discoverycited by 5
  9. 2022Machine Learning Algebraic Geometry for Physicscited by 3
  10. 2022From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlookcited by 2
  11. 2024Transport of Algebraic Structure to Latent Embeddingscited by 2
  12. 2022Machine-Learning the Classification of Spacetimescited by 1
3 more
  1. 2023Machine-Learning Kronecker Coefficientscited by 1
  2. 2023Learning to be Simplecited by 0
  3. 2026Murmurations: a case study in AI-assisted mathematicscited by 0