学习追踪塞伯格对偶性
Learning to Trace Seiberg Dualities
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中文总结 AI 辅助
本文针对超对称箭图规范理论的塞伯格对偶性问题，利用机器学习方法研究箭图突变，发现Transformer与多层感知器组成的网络在中等节点数箭图上优于确定性算法，补充路径查找器算法可提升性能，该类问题或可作为理论物理领域前沿AI模型的基准。
中文摘要 AI 辅助
对偶性在广泛的物理系统中对建立微观现象和涌现现象都起着重要作用。但在实践中，即使所有“规则”都已明确，确定两个系统何时对偶也常常在计算上具有挑战性。换句话说，当面对两个系统时，如何高效地确定它们确实是对偶的？在本文中，我们使用机器学习方法来解决超对称箭图规范理论的塞伯格对偶性问题。从数学上讲，这涉及到箭图的突变，而这又是“学习解结”主题的一种变体。一方面，这为我们提供了一个实用工具，用于确定不同对偶性的计算复杂性；另一方面，它也让我们能够研究不同网络架构如何学习追踪塞伯格对偶性。我们发现，对于具有中等数量箭图节点（约10个）的箭图，由Transformer和多层感知器组成的不同网络架构往往优于确定性算法。用成熟的路径查找器算法（本质上是“箭图的谷歌地图”）补充网络，可进一步提高搜索策略的效率和准确性。我们预计，这类问题可作为应用于理论物理学的前沿AI模型的有用基准。
英文摘要
Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known. Said differently, when confronted with two systems, how can one efficiently establish that they are in fact dual? In this paper we use machine learning methods to address this question for Seiberg dualities of supersymmetric quiver gauge theories. Mathematically, this involves establishing mutations of quivers, which is in turn a variation on the theme of "learning to unknot". On the one hand, this leads us to a practical tool for establishing the computational complexity of different dualities. On the other hand, it also allows us to study how different network architectures learn how to trace Seiberg dualities. We find that for quivers with a modest number of quiver nodes (of order $10$), different network architectures consisting of transformers and multi-layer perceptrons tend to outperform deterministic algorithms. Supplementing the network by well-established pathfinder algorithms (essentially "Google Maps for quivers") leads to an additional improvement in the efficiency and accuracy of the search strategy. We anticipate that this class of questions can serve as a useful benchmark for frontier AI models applied to theoretical physics.
发表机构
- University of Pennsylvania（宾夕法尼亚大学）
- University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。
