# Exploring the flavor structure of quarks and leptons with reinforcement learning

arXiv: https://arxiv.org/abs/2304.14176 · HTML: https://mlsanity.com/paper/2304.14176/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 1 of 1)

- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)

## Built on by (most cited first, 12 of 12)

- [Reinforcement learning-based statistical search strategy for an axion model from flavor](https://mlsanity.com/paper/2409.10023/) (2024)
- [Truth, beauty, and goodness in grand unification: a machine learning approach](https://mlsanity.com/paper/2411.06718/) (2024)
- [Exploring the Truth and Beauty of Theory Landscapes with Machine Learning](https://mlsanity.com/paper/2401.11513/) (2024)
- [Exploring the flavor structure of leptons via diffusion models](https://mlsanity.com/paper/2503.21432/) (2025)
- [Towards AI-assisted Neutrino Flavor Theory Design](https://mlsanity.com/paper/2506.08080/) (2025)
- [Good flavor search in SU(5): a machine learning approach](https://mlsanity.com/paper/2511.08154/) (2025)
- [CDRL: Certification-Driven Reinforcement Learning for Neutrino Flavor Model Discovery](https://mlsanity.com/paper/2608.20686/) (2026)
- [Generating particle physics Lagrangians with transformers](https://mlsanity.com/paper/2501.09729/) (2025)
- [Unraveling particle dark matter with Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.17597/) (2025)
- [Diffusion-model approach to flavor models: A case study for S4^prime modular flavor model](https://mlsanity.com/paper/2504.00944/) (2025)
- [Revisiting One-Zero and Two-Zero Neutrino Mass Textures in Light of Recent Oscillation and Cosmological Data](https://mlsanity.com/paper/2607.08384/) (2026)
- [Uncovering Hidden Leptonic Correlations with Flow Matching and Autoencoders](https://mlsanity.com/paper/2608.15042/) (2026)

## Abstract (arXiv)

We propose a method to explore the flavor structure of quarks and leptons with reinforcement learning. As a concrete model, we utilize a basic value-based algorithm for models with U(1) flavor symmetry. By training neural networks on the U(1) charges of quarks and leptons, the agent finds 21 models to be consistent with experimentally measured masses and mixing angles of quarks and leptons. In particular, an intrinsic value of normal ordering tends to be larger than that of inverted ordering, and the normal ordering is well fitted with the current experimental data in contrast to the inverted ordering. A specific value of effective mass for the neutrinoless double beta decay and a sizable leptonic CP violation induced by an angular component of flavon field are predicted by autonomous behavior of the agent. Our finding results indicate that the reinforcement learning can be a new method for understanding the flavor structure.