# Machine Learning Calabi-Yau Four-folds

arXiv: https://arxiv.org/abs/2009.02544 · HTML: https://mlsanity.com/paper/2009.02544/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2020.

## Built on by (most cited first, 17 of 17)

- [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)
- [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 Regularization for the Minimum Volume Formula of Toric Calabi-Yau 3-folds](https://mlsanity.com/paper/2310.19276/) (2023)
- [The R-mAtrIx Net](https://mlsanity.com/paper/2304.07247/) (2023)
- [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)
- [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)
- [Neural Network Learning and Quantum Gravity](https://mlsanity.com/paper/2403.03245/) (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)

Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we consider the data set of complete intersection Calabi-Yau four-folds, a set of about 900,000 topological types, and study supervised learning of the Hodge numbers h^1,1 and h^3,1 for these manifolds. We find that h^1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h^3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h^3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.