mlsanityData to 14 Oct 2026

Neurons on Amoebae

arXiv 2106.03695 ↗First posted 7 Jun 2021math.AG cs.LG hep-thcited by 11

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Abstract (arXiv)

We apply methods of machine-learning, such as neural networks, manifold learning and image processing, in order to study 2-dimensional amoebae in algebraic geometry and string theory. With the help of embedding manifold projection, we recover complicated conditions obtained from so-called lopsidedness. For certain cases it could even reach ~99% accuracy, in particular for the lopsided amoeba of F0 with positive coefficients which we place primary focus. Using weights and biases, we also find good approximations to determine the genus for an amoeba at lower computational cost. In general, the models could easily predict the genus with over 90% accuracies. With similar techniques, we also investigate the membership problem, and image processing of the amoebae directly.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 10 of its 55 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

10 of 55 references.

References · 10

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2018Tropical Geometry of Deep Neural Networkscited by 95
  3. 2018A Tropical Approach to Neural Networks with Piecewise Linear Activationscited by 26
  4. 2021Machine-Learning Mathematical Structurescited by 25
  5. 2017Deep-Learning the Landscapecited by 21
  6. 2018The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learningcited by 19
  7. 2020Quiver Mutations, Seiberg Duality and Machine Learningcited by 19
  8. 2019Learning Algebraic Structures: Preliminary Investigationscited by 15
  9. 2020Graph Laplacians, Riemannian Manifolds and their Machine-Learningcited by 12
  10. 2020Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curvescited by 10

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 2; 2023: 4; 2024: 4.

11 papers.

  1. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  2. 2022Cluster Algebras: Network Science and Machine Learningcited by 9
  3. 2023Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Dualitycited by 8
  4. 2023Machine Learning Clifford invariants of ADE Coxeter elementscited by 6
  5. 2023Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-foldscited by 5
  6. 2022Machine Learning Algebraic Geometry for Physicscited by 3
  7. 2024Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CADcited by 2
  8. 2024Learning 3-Manifold Triangulationscited by 1
  9. 2024Algebraic Representations for Faster Predictions in Convolutional Neural Networkscited by 1
  10. 2024Machine Learning Mutation-Acyclicity of Quiverscited by 1
  11. 2023Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generationcited by 0