# Machine learning assisted exploration for affine Deligne-Lusztig varieties

arXiv: https://arxiv.org/abs/2308.11355 · HTML: https://mlsanity.com/paper/2308.11355/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 75 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Is deep learning a useful tool for the pure mathematician?](https://mlsanity.com/paper/2304.12602/) (2023)
- [Machine Learning Kreuzer--Skarke Calabi--Yau Threefolds](https://mlsanity.com/paper/2112.09117/) (2021)

## Built on by (most cited first, 3 of 3)

- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimization](https://mlsanity.com/paper/2512.09443/) (2025)
- [Flow-based Extremal Mathematical Structure Discovery](https://mlsanity.com/paper/2601.18005/) (2026)

## Abstract (arXiv)

This paper presents a novel, interdisciplinary study that leverages a Machine Learning (ML) assisted framework to explore the geometry of affine Deligne-Lusztig varieties (ADLV). The primary objective is to investigate the nonemptiness pattern, dimension and enumeration of irreducible components of ADLV. Our proposed framework demonstrates a recursive pipeline of data generation, model training, pattern analysis, and human examination, presenting an intricate interplay between ML and pure mathematical research. Notably, our data-generation process is nuanced, emphasizing the selection of meaningful subsets and appropriate feature sets. We demonstrate that this framework has a potential to accelerate pure mathematical research, leading to the discovery of new conjectures and promising research directions that could otherwise take significant time to uncover. We rediscover the virtual dimension formula and provide a full mathematical proof of a newly identified problem concerning a certain lower bound of dimension. Furthermore, we extend an open invitation to the readers by providing the source code for computing ADLV and the ML models, promoting further explorations. This paper concludes by sharing valuable experiences and highlighting lessons learned from this collaboration.