Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers
Jacky H. T. Yip, Charles Arnal, Francois Charton, Gary Shiu
2025-07-04Language Modelling
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 employ transformers -- deep learning models originally developed for language modeling -- to generate FRSTs across a range of polytope sizes. Our models exhibit efficient and unbiased sampling, and can self-improve through retraining on their own output. These results lay the foundation for AICY: a community-driven platform that combines self-improving machine learning models with a continuously expanding FRST database to explore and catalog the Calabi-Yau landscape.
Related Papers
Visual-Language Model Knowledge Distillation Method for Image Quality Assessment2025-07-21Making Language Model a Hierarchical Classifier and Generator2025-07-17VisionThink: Smart and Efficient Vision Language Model via Reinforcement Learning2025-07-17The Generative Energy Arena (GEA): Incorporating Energy Awareness in Large Language Model (LLM) Human Evaluations2025-07-17Inverse Reinforcement Learning Meets Large Language Model Post-Training: Basics, Advances, and Opportunities2025-07-17Assay2Mol: large language model-based drug design using BioAssay context2025-07-16Describe Anything Model for Visual Question Answering on Text-rich Images2025-07-16InstructFLIP: Exploring Unified Vision-Language Model for Face Anti-spoofing2025-07-16