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

arXiv: https://arxiv.org/abs/2507.03732 · HTML: https://mlsanity.com/paper/2507.03732/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)
- [Iteration Head: A Mechanistic Study of Chain-of-Thought](https://mlsanity.com/paper/2406.02128/) (2024)
- [Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers](https://mlsanity.com/paper/2410.08304/) (2024)
- [Asymmetric REINFORCE for off-Policy Reinforcement Learning: Balancing positive and negative rewards](https://mlsanity.com/paper/2506.20520/) (2025)
- [Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory](https://mlsanity.com/paper/2405.06107/) (2024)
- [Searching the Landscape of Flux Vacua with Genetic Algorithms](https://mlsanity.com/paper/1907.10072/) (2019)
- [Breeding realistic D-brane models](https://mlsanity.com/paper/2112.08391/) (2021)
- [Reconstructing S-matrix Phases with Machine Learning](https://mlsanity.com/paper/2308.09451/) (2023)

## Built on by (most cited first, 5 of 5)

- [Can Neural Networks Learn Small Algebraic Worlds? An Investigation Into the Group-theoretic Structures Learned By Narrow Models Trained To Predict Group Operations](https://mlsanity.com/paper/2601.21150/) (2026)
- [Reconstructing conformal field theoretical compositions with Transformers](https://mlsanity.com/paper/2605.01072/) (2026)
- [Sampling Triangulations and Calabi-Yau Threefolds with Autoregressive GNNs](https://mlsanity.com/paper/2605.27770/) (2026)
- [TriSearch: Learning to Optimize Triangulations via Bistellar Flips](https://mlsanity.com/paper/2605.30220/) (2026)
- [Generating Special Triangulations with Transformers](https://mlsanity.com/paper/2606.26660/) (2026)

## Abstract (arXiv)

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.