# Learning the Inverse Ryu--Takayanagi Formula with Transformers

arXiv: https://arxiv.org/abs/2511.06387 · HTML: https://mlsanity.com/paper/2511.06387/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [Gravitational Duals from Equations of State](https://mlsanity.com/paper/2403.14763/) (2024)
- [AdS/Deep-Learning made easy: simple examples](https://mlsanity.com/paper/2011.13726/) (2020)
- [Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experiments](https://mlsanity.com/paper/2411.16052/) (2024)
- [Aspects of holographic entanglement using physics-informed-neural-networks](https://mlsanity.com/paper/2509.25311/) (2025)
- [Phase Diagram from Nonlinear Interaction between Superconducting Order and Density: Toward Data-Based Holographic Superconductor](https://mlsanity.com/paper/2410.06523/) (2024)

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

- [AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems](https://mlsanity.com/paper/2511.22522/) (2025)
- [Machine learning modularity](https://mlsanity.com/paper/2601.01779/) (2026)

## Abstract (arXiv)

We study the inverse problem of holographic entanglement entropy in AdS3 using a data-driven generative model. Training data consist of randomly generated geometries and their holographic entanglement entropies using the Ryu--Takayanagi formula. After training, the Transformer reconstructs the blackening function within our metric ansatz from previously unseen inputs. The Transformer achieves accurate reconstructions on smooth black hole geometries and extrapolates to horizonless backgrounds. We describe the architecture and data generation process, and we quantify accuracy on both f(z) and the reconstructed S(ℓ). Code and evaluation scripts are available at the provided repository.