论文概要
研究领域: ML 作者: Ali Rayat, Yaohang Li, Gia-Wei Chern 发布时间: 2026-04-22 arXiv: 2604.20797
中文摘要
局部规范对称性是基本相互作用和强关联量子物质的基础，但现有的机器学习方法缺乏一个通用的、有原则的框架来学习在位置依赖对称性下的系统，特别是对于本质上非局部的可观测量。在此，我们引入了一种规范等变图神经网络，通过矩阵值、规范协变特征和对称兼容更新，将非阿贝尔对称性直接嵌入消息传递中，将等变学习从全局对称性扩展到完全局部对称性。在这种形式化中，消息传递实现了晶格上的规范协变传输，允许非局部关联和环状结构从局部操作中自然涌现。我们在纯规范、规范-物质和动力学区域验证了该方法，确立了规范等变消息传递作为由局部对称性支配的系统中学习的通用范式。
原文摘要
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 dyn...
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