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

TL;DR

This paper introduces CYTransformer, a transformer-based deep learning model that automates the generation of fine, regular, and star triangulations of reflexive polytopes, facilitating the exploration of Calabi-Yau threefolds.

Contribution

The paper presents a novel transformer architecture for generating FRSTs, enabling efficient, unbiased sampling and self-improvement through retraining, advancing Calabi-Yau manifold research.

Findings

CYTransformer efficiently samples FRSTs across various polytope sizes.

The model can self-improve via retraining on its own outputs.

Results support the development of a community platform for Calabi-Yau exploration.

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.