Holographic generative flows with AdS/CFT

TL;DR

This paper introduces a novel generative modeling framework that integrates the holographic principle from quantum gravity, specifically AdS/CFT correspondence, with deep learning techniques, resulting in faster convergence and higher quality results.

Contribution

It presents a new approach combining AdS/CFT physics with flow-based generative models, enhancing interpretability and performance in machine learning.

Findings

Faster convergence on MNIST compared to existing models

Higher quality generated data with the proposed method

Provides a physically interpretable flow-matching framework

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.