mlsanityData to 14 Oct 2026

Learning to be Simple

arXiv 2312.05299 ↗First posted 8 Dec 2023cs.LG hep-th math-phcited by 0

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Abstract (arXiv)

In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated subgroups of the symmetric group on n-objects and conduct a classification of finite simple groups among them using shallow feed-forward neural networks. We show that this neural network classifier can decipher the property of simplicity with varying accuracies depending on the features. Our neural network model leads to a natural conjecture concerning the generators of a finite simple group. We subsequently prove this conjecture. This new toy theorem comments on the necessary properties of generators of finite simple groups. We show this explicitly for a class of sporadic groups for which the result holds. Our work further makes the case for a machine motivated study of algebraic structures in pure mathematics and highlights the possibility of generating new conjectures and theorems in mathematics with the aid of machine learning.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 17 of its 43 references that are in the map. First posted on arXiv 8 Dec 2023.

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References · 17

  1. 2016Group Equivariant Convolutional Networkscited by 1,165
  2. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  3. 2020Neural Network Approximations for Calabi-Yau Metricscited by 32
  4. 2021Learning Size and Shape of Calabi-Yau Spacescited by 28
  5. 2019Machine learning Calabi-Yau metricscited by 23
  6. 2018Machine Learning CICY Threefoldscited by 22
  7. 2020Learning selection strategies in Buchberger's algorithmcited by 20
  8. 2018The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learningcited by 19
  9. 2020Quiver Mutations, Seiberg Duality and Machine Learningcited by 19
  10. 2019Learning Algebraic Structures: Preliminary Investigationscited by 15
  11. 2020Machine-Learning the Sato--Tate Conjecturecited by 14
  12. 2020Machine Learning Lie Structures & Applications to Physicscited by 13
5 more
  1. 2020Disentangling a Deep Learned Volume Formulacited by 12
  2. 2020Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curvescited by 10
  3. 2019Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyercited by 8
  4. 2023Mathematical conjecture generation using machine intelligencecited by 8
  5. 2022A physics-informed search for metric solutions to Ricci flow, their embeddings, and visualisationcited by 3

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