# Machine Learning Toric Duality in Brane Tilings

arXiv: https://arxiv.org/abs/2409.15251 · HTML: https://mlsanity.com/paper/2409.15251/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 59 references that are in the map.
- First posted on arXiv 23 Sep 2024.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality](https://mlsanity.com/paper/2309.05702/) (2023)
- [Machine Learning Clifford invariants of ADE Coxeter elements](https://mlsanity.com/paper/2310.00041/) (2023)
- [Connecting Dualities and Machine Learning](https://mlsanity.com/paper/2002.05169/) (2020)
- [Breeding realistic D-brane models](https://mlsanity.com/paper/2112.08391/) (2021)
- [Constructing and Machine Learning Calabi-Yau Five-folds](https://mlsanity.com/paper/2310.15966/) (2023)

## Built on by (most cited first, 2 of 2)

- [Machine Learning Mutation-Acyclicity of Quivers](https://mlsanity.com/paper/2411.04209/) (2024)
- [Machine learning and optimization-based approaches to duality in statistical physics](https://mlsanity.com/paper/2411.04838/) (2024)

## Abstract (arXiv)

We apply a variety of machine learning methods to the study of Seiberg duality within 4d N=1 quantum field theories arising on the worldvolumes of D3-branes probing toric Calabi-Yau 3-folds. Such theories admit an elegant description in terms of bipartite tessellations of the torus known as brane tilings or dimer models. An intricate network of infrared dualities interconnects the space of such theories and partitions it into universality classes, the prediction and classification of which is a problem that naturally lends itself to a machine learning investigation. In this paper, we address a preliminary set of such enquiries. We begin by training a fully connected neural network to identify classes of Seiberg dual theories realised on mathbbZm×mathbbZn orbifolds of the conifold and achieve R2=0.988. Then, we evaluate various notions of robustness of our methods against perturbations of the space of theories under investigation, and discuss these results in terms of the nature of the neural network's learning. Finally, we employ a more sophisticated residual architecture to classify the toric phase space of the Y6,0 theories, and to predict the individual gauged linear σ-model multiplicities in toric diagrams thereof. In spite of the non-trivial nature of this task, we achieve remarkably accurate results; namely, upon fixing a choice of Kasteleyn matrix representative, the regressor achieves a mean absolute error of 0.021. We also discuss how the performance is affected by relaxing these assumptions.