用拓扑约束的自编码器提升高能物理异常检测能力
Enhancing anomaly detection with topology-aware autoencoders
- 在球面、乘积流形等拓扑空间构建隐变量表示
- 相比传统欧氏空间，异常分离性能显著提升
- 适合寻找粒子对撞中超越标准模型的新物理
高能物理中的异常检测对于发现标准模型之外的新物理至关重要。自编码器提供无信号依赖的方法，但受限于其隐空间的拓扑结构。本文探索了具有拓扑先验的自编码器，将相空间分布嵌入反映能量动量守恒的紧致流形中。我们构建了球面（S^n）、乘积流形（S^2 ⊗ S^2）和射影平面（RP^2）三种隐空间结构的自编码器，并与传统的欧氏嵌入进行异常检测性能对比。结果表明，带有拓扑先验的自编码器通过保留数据流形的全局结构，有效降低虚假重构误差，显著提升异常分离能力。在模拟的强子型顶夸克衰变数据上验证，合适的拓扑约束可增强对异常事件的敏感性和鲁棒性。本研究确立了拓扑感知自编码器在粒子碰撞数据无监督新物理搜索中的强大潜力。
原文摘要 · Abstract (English)
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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