Learning the Inverse Ryu--Takayanagi Formula with Transformers

TL;DR

This paper employs a Transformer model to learn the inverse Ryu--Takayanagi formula, enabling the reconstruction of black hole geometries from entanglement entropy data in AdS$_3$, demonstrating accurate results on various backgrounds.

Contribution

It introduces a data-driven Transformer approach to invert holographic entanglement entropy, a novel application in the context of AdS/CFT correspondence.

Findings

Transformer accurately reconstructs blackening functions from entanglement data

Model generalizes to horizonless geometries

Provides code and evaluation tools for further research

Abstract

We study the inverse problem of holographic entanglement entropy in AdS$_3$ 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 $S(\ell)$. Code and evaluation scripts are available at the provided repository.