学习对撞机事件的几何结构：度量感知深度集合
Learning the Geometry of Collider Events with Metric-Aware Deep Sets
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中文总结 AI 辅助
本研究提出度量感知深度集合网络，作为最优传输的快速替代模型，应用于对撞机事件的能量移动距离，在保持高精度和推理速度的同时，显著减少三角形不等式违反，提升几何保真度。
中文摘要 AI 辅助
最优传输为结构化数据赋予了几何结构，但在利用距离间关系的大规模成对分析中，精确评估代价高昂。学习型替代模型速度更快，但可能不保持这种度量结构。我们开发了一种用于变大小加权点云之间最优传输的深度集合替代模型，该模型强制满足非负性、交换对称性和零自距离，而三角形不等式则不加约束。在粒子物理应用中，将其应用于对撞机事件之间的能量移动距离，度量感知粒子流网络实现了百分级别的平均绝对百分比误差，同时显著提高了推理吞吐量，优于所调查的其他精确和近似方法。研究发现，架构约束改善了未显式强制的性质：在10^6个保留事件三元组中，三角形不等式违反次数从匹配的无约束网络的199次降至2次，最大值从149.5 GeV降至5.8 GeV。这些结果表明，有针对性的归纳偏置可以产生具有显著改善几何保真度的快速神经替代模型。
英文摘要
Optimal transport gives structured data a geometry, but exact evaluation is costly in large pairwise analyses that exploit relationships among distances. Learned surrogates are faster, but need not preserve this metric structure. We develop a Deep Sets surrogate for OT between variable-size weighted point clouds that enforces non-negativity, exchange symmetry, and zero self-distance, leaving the triangle inequality unconstrained. Applied to the Energy Mover's Distance between collider events in a particle physics application, the Metric-Aware Particle Flow Network achieves percent-level mean absolute percentage error while significantly improving inference throughput over other exact and approximate methods surveyed. The architectural constraints are found to improve properties that are not explicitly enforced: across $10^6$ held-out event triplets, triangle-inequality violations fall from 199 for a matched unconstrained network to 2, and the maximum from 149.5 to 5.8 GeV. These results demonstrate that targeted inductive biases can yield fast neural surrogates with substantially improved geometric fidelity.
发表机构
- Brown University（布朗大学）
- IAIFI（人工智能与基础相互作用研究所）
机构由 AI 辅助整理，请以论文原文为准。
