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arXiv · 2507.03732

Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers

Jacky H. T. Yip·Charles Arnal·François Charton·Gary Shiu
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Abstract

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.

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Jacky H. T. Yip, Charles Arnal, François Charton, Gary Shiu. 2025-07-04. Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers. https://arxiv.org/abs/2507.03732

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