# Machine Learning Calabi-Yau Hypersurfaces

arXiv: https://arxiv.org/abs/2112.06350 · HTML: https://mlsanity.com/paper/2112.06350/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 12 Dec 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Detecting Symmetries with Neural Networks](https://mlsanity.com/paper/2003.13679/) (2020)
- [Neural Network Approximations for Calabi-Yau Metrics](https://mlsanity.com/paper/2012.15821/) (2020)
- [Learning Size and Shape of Calabi-Yau Spaces](https://mlsanity.com/paper/2111.01436/) (2021)
- [Building Quantum Field Theories Out of Neurons](https://mlsanity.com/paper/2112.04527/) (2021)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Machine Learning CICY Threefolds](https://mlsanity.com/paper/1806.03121/) (2018)
- [Deep-Learning the Landscape](https://mlsanity.com/paper/1706.02714/) (2017)
- [The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning](https://mlsanity.com/paper/1812.02893/) (2018)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Machine learning for complete intersection Calabi-Yau manifolds: a methodological study](https://mlsanity.com/paper/2007.15706/) (2020)
- [Machine Learning Calabi-Yau Four-folds](https://mlsanity.com/paper/2009.02544/) (2020)
- [Learning Algebraic Structures: Preliminary Investigations](https://mlsanity.com/paper/1905.02263/) (2019)
- [Inception Neural Network for Complete Intersection Calabi-Yau 3-folds](https://mlsanity.com/paper/2007.13379/) (2020)
- [Graph Laplacians, Riemannian Manifolds and their Machine-Learning](https://mlsanity.com/paper/2006.16619/) (2020)
- [Neurons on Amoebae](https://mlsanity.com/paper/2106.03695/) (2021)
- [Deep multi-task mining Calabi-Yau four-folds](https://mlsanity.com/paper/2108.02221/) (2021)
- [Searching the Landscape of Flux Vacua with Genetic Algorithms](https://mlsanity.com/paper/1907.10072/) (2019)
- [Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves](https://mlsanity.com/paper/2004.05218/) (2020)
- [Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer](https://mlsanity.com/paper/1911.02008/) (2019)
- [hep-th](https://mlsanity.com/paper/1807.00735/) (2018)
- [SO(8) Supergravity and the Magic of Machine Learning](https://mlsanity.com/paper/1906.00207/) (2019)

## Built on by (most cited first, 15 of 15)

- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [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)
- [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)
- [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)
- [Intelligent Explorations of the String Theory Landscape](https://mlsanity.com/paper/2204.08073/) (2022)
- [Learning 3-Manifold Triangulations](https://mlsanity.com/paper/2405.09610/) (2024)
- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)
- [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)

## Abstract (arXiv)

We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. This then allows us to identify a previously unnoticed clustering in the Calabi-Yau data. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weights with an accuracy of R^2 > 95%. Supervised learning also allows us to identify weighted-P4s which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behaviour.