Holographic generative flows with AdS/CFT

TL;DR

This work introduces GenAdS, a holography‑inspired generative framework that uses AdS/CFT physics to guide data generation via flow matching. By encoding data as boundary sources and evolving bulk fields with Klein–Gordon dynamics, the model optimizes a velocity field in phase space on a spectral grid, enabling simulation‑free training and a physically interpretable flow. Experiments on a checkerboard distribution and MNIST show faster convergence and competitive or improved sample quality when leveraging AdS geometry, with the best MNIST results obtained when using a linear path and KG backbone. The results suggest that holographic encoding and AdS geometry provide a flexible, physics‑informed inductive bias for generative modeling, with future work exploring non‑AdS geometries, backreaction, and RG‑flow perspectives.

Abstract

We present a framework for generative machine learning that leverages the holographic principle of quantum gravity, or to be more precise its manifestation as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, with techniques for deep learning and transport theory. Our proposal is to represent the flow of data from a base distribution to some learned distribution using the bulk-to-boundary mapping of scalar fields in AdS. In the language of machine learning, we are representing and augmenting the flow-matching algorithm with AdS physics. Using a checkerboard toy dataset and MNIST, we find that our model achieves faster and higher quality convergence than comparable physics-free flow-matching models. Our method provides a physically interpretable version of flow matching. More broadly, it establishes the utility of AdS physics and geometry in the development of novel paradigms in generative modeling.

Figures (6)

• Figure 1: The Poincaré disk as depicted by M.C. Escher's Circle Limit IV print. The red circles represent constant radial slices. The angels and demons appear to shrink in size as we approach the edge of the disk, but in the hyperbolic metric their proper sizes remain constant.
• Figure 2: A schematic representation of the holographic encoding for a sample of the MNIST dataset. The image is treated as a source on the boundary for the corresponding bulk field, which flows to noise.
• Figure 3: We present the learned distributions of models trained on the checkerboard after 100 epochs. The AdS + KG (H) and AdS + KG (L) models are trained with the loss \ref{['residLoss']}, using Hermite and linear paths respectively, and the AdS model is trained with the loss \ref{['fullLoss']} and a linear path. The Baseline FCN uses no AdS information. We also show the final boundary-violation (BV) and within-cell-energy-distance (WED) metrics, the time per epoch $t_{\text{ep}}$, final inference time $t_{\text{inf}}$ for 10,000 samples, and estimated threshold time $t_{\text{thr}}$ when $\text{BV} < 0.1$ (assuming linearity of BV within each 10-epoch interval), all averaged over three seeds. Additionally, we plot the BV and WED metrics.
• Figure 4: The results from varying the scaling dimension $\Delta$, which corresponds to the bulk scalar's squared-mass $m^2 = \Delta(\Delta-2)$. These models are trained to 100 epochs. The models degrade when $\Delta \geq 2$, suggesting the optimal choice might generally be $\Delta < 2$, which corresponds to a relevant scalar operator on the boundary.
• Figure 5: The results from dialing the HSV parameter $p$. These models have $m^2 = 0$ and are trained to 100 epochs.