# Machine Learning CICY Threefolds

arXiv: https://arxiv.org/abs/1806.03121 · HTML: https://mlsanity.com/paper/1806.03121/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2018.

## Built on by (most cited first, 22 of 22)

- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Deep multi-task mining Calabi-Yau four-folds](https://mlsanity.com/paper/2108.02221/) (2021)
- [Group invariant machine learning by fundamental domain projections](https://mlsanity.com/paper/2202.02164/) (2022)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds](https://mlsanity.com/paper/2112.09117/) (2021)
- [Machine Learning Clifford invariants of ADE Coxeter elements](https://mlsanity.com/paper/2310.00041/) (2023)
- [Machine Learning Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [Breeding realistic D-brane models](https://mlsanity.com/paper/2112.08391/) (2021)
- [Constructing and Machine Learning Calabi-Yau Five-folds](https://mlsanity.com/paper/2310.15966/) (2023)
- [Machine Learning Algebraic Geometry for Physics](https://mlsanity.com/paper/2204.10334/) (2022)
- [From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook](https://mlsanity.com/paper/2202.06086/) (2022)
- [Identifying equivalent Calabi--Yau topologies: A discrete challenge from math and physics for machine learning](https://mlsanity.com/paper/2202.07590/) (2022)
- [Deep Learning Calabi-Yau four folds with hybrid and recurrent neural network architectures](https://mlsanity.com/paper/2405.17406/) (2024)
- [Generative AI for Brane Configurations and Coamoeba](https://mlsanity.com/paper/2411.16033/) (2024)
- [Machine Learning on generalized Complete Intersection Calabi-Yau Manifolds](https://mlsanity.com/paper/2209.10157/) (2022)
- [Deep learning complete intersection Calabi-Yau manifolds](https://mlsanity.com/paper/2311.11847/) (2023)
- [Black holes and the loss landscape in machine learning](https://mlsanity.com/paper/2306.14817/) (2023)
- [Calabi-Yau Four/Five/Six-folds as mathbbPnw Hypersurfaces: Machine Learning, Approximation, and Generation](https://mlsanity.com/paper/2311.17146/) (2023)
- [Learning to be Simple](https://mlsanity.com/paper/2312.05299/) (2023)
- [Machine Learning the 6d Supergravity Landscape](https://mlsanity.com/paper/2505.16131/) (2025)

## Abstract (arXiv)

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.