Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory

2026-01-27

AI Summary

This work proposes the first gauge-equivariant diffusion generative model to address the challenges of efficient modeling and generalization in non-Abelian lattice gauge theories. By integrating lattice gauge-equivariant convolutional neural networks (L-CNNs)—which respect both local and global gauge symmetries—with a Metropolis-adjusted annealed Langevin algorithm (MAALA), the method achieves high-fidelity generalization to larger lattice volumes and weaker coupling regimes from a single training dataset. Evaluated on two-dimensional U(2) and SU(2) gauge theories, the model accurately predicts various Wilson loops and topological susceptibilities while maintaining high sampling acceptance rates and low estimation errors across both strong and weak coupling regimes, as well as under lattice-size extrapolation, significantly outperforming conventional Monte Carlo approaches.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Natural Language Processing: (Large) Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.

Problem

• non-Abelian lattice gauge theory
• gauge equivariant diffusion models
• generalization
• Wilson loops
• topological susceptibility

Innovation

• gauge equivariant diffusion
• non-Abelian lattice gauge theory
• L-CNNs
• MAALA
• generalization