利用拓扑感知自编码器增强异常检测
Enhancing anomaly detection with topology-aware autoencoders
AI总结：
提出将自编码器潜在空间设计为反映能量-动量守恒的球面、乘积和射影流形，并在强子顶夸克衰变模拟中证明其可提升异常事件检测的灵敏度与鲁棒性。
摘要：
高能物理中的异常检测对于识别超出标准模型的新物理至关重要。自编码器提供了一种与信号无关的方法，但受到其潜在空间拓扑的限制。本工作探索拓扑感知自编码器，将相空间分布嵌入到反映能量-动量守恒的紧致流形上。我们构建了具有球面（$S^n$）、乘积（$S^2 \otimes S^2$）和射影（$\mathbb{RP}^2$）潜在空间的自编码器，并将它们的异常检测性能与传统欧几里得嵌入进行比较。结果表明，具有拓扑先验的自编码器通过保持数据流形的全局结构并减少虚假重建误差，显著改善了异常分离。将该方法应用于模拟的强子顶夸克衰变，我们表明具有适当拓扑约束的潜在空间增强了检测异常事件的灵敏度和鲁棒性。本研究确立拓扑感知自编码器是在粒子碰撞数据中无监督搜索新物理的有力工具。
英文摘要：
Anomaly detection in high-energy physics is essential for identifying new physics beyond the Standard Model. Autoencoders provide a signal-agnostic approach but are limited by the topology of their latent space. This work explores topology-aware autoencoders, embedding phase-space distributions onto compact manifolds that reflect energy-momentum conservation. We construct autoencoders with spherical ($S^n$), product ($S^2 \otimes S^2$), and projective ($\mathbb{RP}^2$) latent spaces and compare their anomaly detection performance against conventional Euclidean embeddings. Our results show that autoencoders with topological priors significantly improve anomaly separation by preserving the global structure of the data manifold and reducing spurious reconstruction errors. Applying our approach to simulated hadronic top-quark decays, we show that latent spaces with appropriate topological constraints enhance sensitivity and robustness in detecting anomalous events. This study establishes topology-aware autoencoders as a powerful tool for unsupervised searches for new physics in particle-collision data.
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