Holographic entanglement entropy, Wilson loops, and neural networks

Abstract

We apply artificial neural networks to the holographic inverse problem, reconstructing bulk geometry from boundary entanglement entropy by using the Ryu--Takayanagi area functional as a differentiable loss. Validated on the AdS-Schwarzschild background, this approach recovers the blackening factor with maximum absolute error below $3\times 10^{-3}$ across the entire bulk, reproducibly over independent training runs. For finite-density backgrounds like the Gubser--Rocha model, we demonstrate that equal-time strip entanglement entropy determines only the spatial metric. We resolve this exact one-function degeneracy by incorporating holographic Wilson loop data, which couples to the timelike metric. We present a semi-analytical inversion combining Bilson's and Hashimoto's formulas, alongside a general three-network variational method minimizing the combined area and Nambu--Goto actions. The neural network achieves maximum relative errors below $0.2\%$ for both metric functions without closed-form derivative relations, and accommodates additional holographic observables at the cost of one extra network and loss term.

36 pages, 18 figures, updated to match the published version

References in corpus (6)

• Extracting Spacetimes using the AdS/CFT Conjecture: Part II
• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
• Inability of linear axion holographic Gubser-Rocha model to capture all the transport anomalies of strange metals
• Dual Geometry of Entanglement Entropy via Deep Learning
• Inverse problem of correlation functions in holography
• Holographic flavour and neural networks