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.

翻译：我们提出了一种生成式机器学习框架，该框架结合了量子引力的全息原理（更精确地说是其表现形式——反德西特/共形场论对应关系）与深度学习和输运理论技术。我们的核心方案是利用AdS中标量场的体-边界映射，表征数据从基础分布到学习分布的流动过程。用机器学习的术语来说，我们通过AdS物理机制实现并增强了流匹配算法。基于棋盘格玩具数据集和MNIST的实验表明，相较于无物理约束的流匹配模型，我们的模型实现了更快且更高质量的收敛。本方法提供了具有物理解释性的流匹配实现方案。更广泛而言，该研究确立了AdS物理与几何在开发新型生成建模范式中的实用价值。