mlsanityData to 7 Oct 2026

Cluster Algebras: Network Science and Machine Learning

arXiv 2203.13847 ↗First posted 25 Mar 2022math.CO cs.LG hep-thcited by 9

Not on the map. Why?

Abstract (arXiv)

Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network analysis methods are applied to the exchange graphs for cluster algebras of varying mutation types. The analysis indicates that when the graphs are represented without identifying by permutation equivalence between clusters an elegant symmetry emerges in the quiver exchange graph embedding. The ratio between number of seeds and number of quivers associated to this symmetry is computed for finite Dynkin type algebras up to rank 5, and conjectured for higher ranks. Simple machine learning techniques successfully learn to classify cluster algebras using the data of seeds. The learning performance exceeds 0.9 accuracies between algebras of the same mutation type and between types, as well as relative to artificially generated data.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 20 of its 80 references that are in the map. First posted on arXiv 25 Mar 2022.

Builds on

20 of 80 references.

References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Learning to Unknotcited by 40
  3. 2020Detecting Symmetries with Neural Networkscited by 33
  4. 2020Neural Network Approximations for Calabi-Yau Metricscited by 32
  5. 2021Building Quantum Field Theories Out of Neuronscited by 27
  6. 2021Machine-Learning Mathematical Structurescited by 25
  7. 2018Machine Learning CICY Threefoldscited by 22
  8. 2017Deep-Learning the Landscapecited by 21
  9. 2020Learning selection strategies in Buchberger's algorithmcited by 20
  10. 2018The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learningcited by 19
  11. 2020Quiver Mutations, Seiberg Duality and Machine Learningcited by 19
  12. 2020Machine Learning Calabi-Yau Four-foldscited by 17
8 more
  1. 2019Learning Algebraic Structures: Preliminary Investigationscited by 15
  2. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  3. 2020Graph Laplacians, Riemannian Manifolds and their Machine-Learningcited by 12
  4. 2021Neurons on Amoebaecited by 11
  5. 2020Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curvescited by 10
  6. 2021Machine Learning Kreuzer--Skarke Calabi--Yau Threefoldscited by 8
  7. 2020Deep Learning Gauss-Manin Connectionscited by 4
  8. 2022Identifying equivalent Calabi--Yau topologies: A discrete challenge from math and physics for machine learningcited by 2

Built on by

Cited by year (2026 to 7 Oct)

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

9 papers.

  1. 2023Machine Learning Clifford invariants of ADE Coxeter elementscited by 6
  2. 2024A Triumvirate of AI Driven Theoretical Discoverycited by 5
  3. 2022Machine Learning Algebraic Geometry for Physicscited by 3
  4. 2024Machine Learning Toric Duality in Brane Tilingscited by 2
  5. 2024Machines and Mathematical Mutations: Using GNNs to Characterize Quiver Mutation Classescited by 2
  6. 2024Learning 3-Manifold Triangulationscited by 1
  7. 2024Machine Learning Mutation-Acyclicity of Quiverscited by 1
  8. 2023Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generationcited by 0
  9. 2026Learning the Graphical Nature of Symmetriescited by 0