Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914155334729728 |
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| author | Yip, Jacky H. T. Arnal, Charles Charton, François Shiu, Gary |
| author_facet | Yip, Jacky H. T. Arnal, Charles Charton, François Shiu, Gary |
| contents | Fine, regular, and star triangulations (FRSTs) of four-dimensional reflexive polytopes give rise to toric varieties, within which generic anticanonical hypersurfaces yield smooth Calabi-Yau threefolds. We introduce CYTransformer, a deep learning model based on the transformer architecture, to automate the generation of FRSTs. We demonstrate that CYTransformer efficiently and unbiasedly samples FRSTs for polytopes across a range of sizes, and can self-improve through retraining on its own output. These results lay the foundation for AICY: a community-driven platform designed to combine self-improving machine learning models with a continuously expanding database to explore and catalog the Calabi-Yau landscape. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_03732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers Yip, Jacky H. T. Arnal, Charles Charton, François Shiu, Gary High Energy Physics - Theory Machine Learning Algebraic Geometry Fine, regular, and star triangulations (FRSTs) of four-dimensional reflexive polytopes give rise to toric varieties, within which generic anticanonical hypersurfaces yield smooth Calabi-Yau threefolds. We introduce CYTransformer, a deep learning model based on the transformer architecture, to automate the generation of FRSTs. We demonstrate that CYTransformer efficiently and unbiasedly samples FRSTs for polytopes across a range of sizes, and can self-improve through retraining on its own output. These results lay the foundation for AICY: a community-driven platform designed to combine self-improving machine learning models with a continuously expanding database to explore and catalog the Calabi-Yau landscape. |
| title | Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers |
| topic | High Energy Physics - Theory Machine Learning Algebraic Geometry |
| url | https://arxiv.org/abs/2507.03732 |