将规范对称性融入图神经网络，实现局域对称下的量子系统学习。
Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
- 用矩阵值特征和对称更新实现规范协变的消息传递
- 在纯规范、规范-物质及动力学体系中均验证有效
- 适合研究具有局域对称性的强关联量子系统
局域规范对称性是基本相互作用和强关联量子物质的基础，但现有机器学习方法缺乏针对位点依赖对称性、特别是非局域可观测量的通用且有原则的框架。本文提出一种规范等变图神经网络，通过矩阵值的规范协变特征与对称相容的更新规则，将非阿贝尔对称性直接嵌入消息传递过程，实现了从全局对称到完全局域对称的等变学习拓展。在此框架下，消息传递相当于晶格上的规范协变传输，使非局域相关性和环状结构能由局部操作自然生成。我们在纯规范、规范-物质及动态体系中验证了该方法，确立了规范等变消息传递作为局域对称系统学习的一般范式。
原文摘要 · Abstract (English)
Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for intrinsically nonlocal observables. Here we introduce a gauge-equivariant graph neural network that embeds non-Abelian symmetry directly into message passing via matrix-valued, gauge-covariant features and symmetry-compatible updates, extending equivariant learning from global to fully local symmetries. In this formulation, message passing implements gauge-covariant transport across the lattice, allowing nonlocal correlations and loop-like structures to emerge naturally from local operations. We validate the approach across pure gauge, gauge-matter, and dynamical regimes, establishing gauge-equivariant message passing as a general paradigm for learning in systems governed by local symmetry.
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