用Transformer自动生成卡拉比-丘流形的三角剖分，加速新几何结构发现。
Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers
- 基于Transformer架构，自动生成四维正则反射多面体的精细星三角剖分。
- 模型高效无偏采样多种尺寸多面体的三角剖分，且可自我优化重训练。
- 为构建持续扩展的卡拉比-丘几何数据库提供智能引擎，适合理论物理与数学研究者。
四维反射多面体的精细、规则、星三角剖分（FRST）生成塔里克流形，其一般反典型超曲面构成光滑的卡拉比-丘三流形。本文提出CYTransformer，一种基于Transformer架构的深度学习模型，用于自动化生成FRST。实验表明，该模型能高效且无偏地采样不同规模多面体的FRST，并可通过自身输出数据进行重训练实现自我改进。这些成果为AICY——一个融合自进化机器学习模型与不断增长数据库的社区驱动平台——奠定了基础，旨在探索与编目卡拉比-丘景观。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。