事件图的量子框架
Quantum framework for event graphs
AI总结：
该研究构建了基于参与者图的量子框架，通过线图变换生成事件图并建立U(1)格点规范理论，为量子启发的图异常检测提供了数学基础，搭建了图学习、格点规范理论与量子信息的桥梁。
AI中文摘要：
离散事件的图表示为异常检测的机器学习模型提供了自然基础，同时也暗示了更深层次的量子描述，其中图结构会产生相互作用的量子自由度。我们开发了一种基于有向参与者图的量子框架，该图的边表示连接源顶点和目标顶点对的事件。线图变换将每个事件映射为双向事件图的节点，其边从参与者图继承关系信息。由于事件数据集自然组织为事件记录的集合，其原始属性直接与事件图的节点对齐。我们为参与者图的每个节点分配一个量子谐振子（QHO），这些QHO的集体希尔伯特空间为表示量子态提供了完整基。由此，参与者图的每条有向边都会因两个端点振荡器而获得施温格同位旋。在线图变换下，事件图的节点对应于可观测的同位旋，其通过双向边的相互作用为从事件数据集学习提供了天然基底，而底层参与者节点相关的量子态保持潜在状态，无法直接观测。在该框架内，我们在事件图上构建了一个紧凑的U(1)格点规范理论（LGT），其会产生一个Kogut-Susskind哈密顿量（KSH），形式为XY型自旋模型，用于控制浸没在大量标称事件的浴中的稀疏异常事件同位旋的动力学。该框架为基于量子启发图的异常检测建立了数学基础，并在图学习、LGT与量子信息之间提供了原则性桥梁。
英文摘要：
Graph representations of discrete events provide a natural foundation for machine-learning models of anomaly detection, yet they also suggest a deeper quantum description in which graph structure gives rise to interacting quantum degrees of freedom. We develop a quantum framework based on a directed participant graph whose edges represent events connecting pairs of source and destination vertices. A line-graph transformation maps each event to a node of a bidirectional event graph, whose edges inherit relational information from the participant graph. Since event datasets are naturally organized as collections of event records, their raw attributes align directly with the nodes of the event graph. A quantum harmonic oscillator (QHO) is assigned to every node of the participant graph, with the collective Hilbert space of these QHOs providing a complete basis for representing quantum states. Every directed edge of the participant graph thereby acquires a Schwinger isospin arising from the two endpoint oscillators. Under the line-graph transformation, event-graph nodes correspond to observable isospins whose interactions through bidirectional edges provide a natural substrate for learning from event datasets, while the quantum states associated with the underlying participant nodes remain latent and inaccessible to direct observation. Within this framework we formulate a compact U(1) lattice gauge theory (LGT) on the event graph that leads to a Kogut-Susskind Hamiltonian (KSH) in the form of an XY-type spin model governing the dynamics of sparse anomalous-event isospins immersed in a bath of many nominal events. The proposed framework establishes a mathematical foundation for quantum-inspired graph-based anomaly detection and provides a principled bridge between graph learning, LGT, and quantum information.
