用机器学习追踪超对称量子图模型的对偶关系，提升计算效率。
Learning to Trace Seiberg Dualities
- 基于Transformer和多层感知机的神经网络学习量子图突变
- 节点数约10时，模型性能优于传统确定性算法
- 结合路径查找算法可进一步提升搜索效率与准确率
对偶性在众多物理系统中连接微观与涌现现象。然而，即使规则明确，判断两个系统是否对偶仍常面临计算挑战。本文针对超对称量子图规范理论的Seiberg对偶，利用机器学习方法解决该问题。数学上，这等价于识别量子图的突变，可视为“学会解结”的变体。我们发现，对于节点数约为10的量子图，基于Transformer和多层感知机的网络架构普遍优于确定性算法。若将网络与成熟的路径查找算法（类比“量子图版谷歌地图”）结合，搜索策略的效率与准确性进一步提升。此类问题有望成为前沿人工智能模型应用于理论物理的重要基准。
原文摘要 · Abstract (English)
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.
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