mlsanityData to 14 Oct 2026

Machine-Learning Mathematical Structures

arXiv 2101.06317 ↗First posted 15 Jan 2021cs.LG hep-th math.HOcited by 25

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Abstract (arXiv)

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, we present a comparative study of the accuracies on different problems. The paradigm should be useful for conjecture formulation, finding more efficient methods of computation, as well as probing into certain hierarchy of structures in mathematics.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). Builds on 27 of its 117 references that are in the map. First posted on arXiv 15 Jan 2021.

Builds on

27 of 117 references.

References · 27

  1. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  2. 2019Deep Learning for Symbolic Mathematicscited by 270
  3. 2019Universal Approximation with Deep Narrow Networkscited by 200
  4. 2017Approximating Continuous Functions by ReLU Nets of Minimal Widthcited by 122
  5. 2018Discovering physical concepts with neural networkscited by 117
  6. 2020Learning to Unknotcited by 40
  7. 2020Detecting Symmetries with Neural Networkscited by 34
  8. 2020Neural Network Approximations for Calabi-Yau Metricscited by 32
  9. 2019Machine learning Calabi-Yau metricscited by 23
  10. 2018Machine Learning CICY Threefoldscited by 22
  11. 2020Learning selection strategies in Buchberger's algorithmcited by 20
  12. 2018The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learningcited by 19
15 more
  1. 2020Quiver Mutations, Seiberg Duality and Machine Learningcited by 19
  2. 2020The world as a neural networkcited by 18
  3. 2020Machine learning for complete intersection Calabi-Yau manifolds: a methodological studycited by 17
  4. 2020Machine Learning Calabi-Yau Four-foldscited by 17
  5. 2019Learning Algebraic Structures: Preliminary Investigationscited by 15
  6. 2020Inception Neural Network for Complete Intersection Calabi-Yau 3-foldscited by 14
  7. 2020Machine-Learning the Sato--Tate Conjecturecited by 14
  8. 2020Machine Learning Lie Structures & Applications to Physicscited by 13
  9. 2020Graph Laplacians, Riemannian Manifolds and their Machine-Learningcited by 12
  10. 2020Disentangling a Deep Learned Volume Formulacited by 12
  11. 2020Explore and Exploit with Heterotic Line Bundle Modelscited by 11
  12. 2020Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curvescited by 10
  13. 2020Machine-Learning Number Fieldscited by 9
  14. 2019Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyercited by 8
  15. 2020Machine Learning String Standard Modelscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 9; 2024: 3; 2025: 1; 2026: 2.

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  1. 2022Towards Understanding Grokking: An Effective Theory of Representation Learningcited by 230
  2. 2023The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networkscited by 156
  3. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  4. 2021Neurons on Amoebaecited by 11
  5. 2022Cluster Algebras: Network Science and Machine Learningcited by 9
  6. 2023Machine learning detects terminal singularitiescited by 9
  7. 2023Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decompositioncited by 7
  8. 2023Machine learning the dimension of a Fano varietycited by 7
  9. 2024A Triumvirate of AI Driven Theoretical Discoverycited by 5
  10. 2023The R-mAtrIx Netcited by 4
  11. 2023Interpretable Graph Networks Formulate Universal Algebra Conjecturescited by 4
  12. 2024Symbolic Equation Solving via Reinforcement Learningcited by 4
13 more
  1. 2022Machine Learning Algebraic Geometry for Physicscited by 3
  2. 2021Abstraction, Reasoning and Deep Learning: A Study of the "Look and Say" Sequencecited by 2
  3. 2022From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlookcited by 2
  4. 2021Learning a performance metric of Buchberger's algorithmcited by 1
  5. 2022Machine-Learning the Classification of Spacetimescited by 1
  6. 2023Predicting the cardinality and maximum degree of a reduced Gr"obner basiscited by 1
  7. 2023Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formulacited by 1
  8. 2023Deep learning complete intersection Calabi-Yau manifoldscited by 1
  9. 2024Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systemscited by 1
  10. 2022SC-Square: Future Progress with Machine Learning?cited by 0
  11. 2025Testing Transformer Learnability on the Arithmetic Sequence of Rooted Treescited by 0
  12. 2026Murmurations: a case study in AI-assisted mathematicscited by 0
  13. 2026A penalised Saito functional for heuristic search of free line arrangementscited by 0