[论文解读] Reconstruction of overlapping electromagnetic showers in calorimeters using Transformers

Yuliia Maidannyk, Fabrice Couderc+2 more|arXiv (Cornell University)|Mar 18, 2026

Particle physics theoretical and experimental studies被引用 0

一句话总结

论文提出基于深度学习的聚类方法，包括两步架构和单步图变换器（ClusTEX），用于在卡路里计中重建重叠电磁 showers 的能量和位置，具有新颖的定位编码策略，在 toy 场景和受 ECAL 启发的拓扑中表现鲁棒。

ABSTRACT

Accurate clustering of electromagnetic energy deposits is essential for reconstructing photons and electrons in modern hadron collider experiments, where boosted topologies and pileup cause overlapping showers and ambiguous energy assignment. We present deep learning-based clustering approaches that reconstruct particle energy and position directly from calorimeter readout. The study includes a two-step strategy in which candidate seed windows are identified and then jointly processed via distance-weighted message passing or attention mechanism and a single-step graph transformer, ClusTEX, which performs candidate selection and reconstruction in one inference stage. ClusTEX uses a novel positional encoding scheme that separates local coordinates within the graph from global detector coordinates, enabling efficient, geometry-aware inference. Models are trained on GEANT4 simulations of a simplified (toy) and an ECAL-inspired topology with an explicit $η-ϕ$ dependence. Performance is evaluated using efficiency, energy and position resolutions and splitting rate - reconstruction of two objects for a single photon. In the toy calorimeter, attention-based interactions improve the reconstruction of overlapping showers relative to both the standard algorithm and distance-driven message passing, while maintaining performance on isolated photons and reducing splitting without multi-pass inference. For boosted $π^0 oγγ$, the attention-based model retains di-photon mass reconstruction capability, where the standard algorithm becomes inefficient. In the ECAL-inspired topology, ClusTEX provides the best overall performance, yielding improved energy resolution and reduced splitting compared to two-step approaches and the standard algorithm. It also remains robust under localized detector failures, showing improved stability and partial recovery of energy in non-responsive channels.

研究动机与目标

• 在 HL-LHC 环境下高占用和淋洗重叠的条件下，推动对卡路里计中电磁能量沉积的聚类改进。
• 开发基于 ML 的聚类方法，直接从卡路里计读出重建能量和冲击位置。
• 将两步和单步变换器架构与 CMS PFClustering 基线及 GNN 方法进行对比。
• 利用 toy 场景和受 ECAL 启发的仿真，评估几何效应与探测器非均匀性对鲁棒性的影响。

提出的方法

• 引入 SeedFinder 以识别候选种子窗口并筛选子集用于回归。
• 开发两步 PoEN 网络：距离加权消息传递 PoEN（DW-PoEN）和基于注意力的 PoEN（GAT-PoEN），以联合从多个候选中重建能量与位置。
• 实现单步图变换器（ClusTEX），在一个推断阶段执行候选选择和重建，采用新颖的局部/全局定位编码策略。
• 使用在图窗口内连接的局部位置信息与全局探测器中心定位嵌入相结合，以实现几何感知推理。
• 在 Geant4 模拟的 toy 卡路里计和受 ECAL 启发的拓扑上进行训练和验证，包括重叠 shower 和潜在通道失效的情景。
• 使用 SeedFinder 过滤 P_SF 的种子，并将前若干候选输入 PoEN 或 ClusTEX 进行最终重建。

Figure 1 : Left: realistic CMS ECAL simulation geometry, where each PbWO 4 crystal is quasi-projective and aligned toward the interaction point with a 3 ∘ tilt in both the $z$ and $\phi$ directions. Right (top): example calorimeter window for a single-photon event showing the energy deposits in the

实验结果

研究问题

• RQ1 基于 Transformer 的架构是否能在重叠 EM shower 的能量与位置重建上优于 PFClustering 和以往的 GNN 方法？
• RQ2 注意力基模型与单步 Transformer 是否对探测器几何效应和非均匀性（包括 η、φ 依赖和通道失效）具有鲁棒性？
• RQ3 提出的定位编码方案在几何丰富的卡路里计拓扑中对性能的影响如何？
• RQ4 在提升 π0 → γγ 的情景中，分裂率与二光子质心重建的影响如何？
• RQ5 方法是否能够从 toy 场景扩展到受 ECAL 启发的现实探测器拓扑？

主要发现

• 基于注意力的相互作用（GAT-PoEN）在重构重叠 shower 方面优于标准算法和基于距离的消息传递，同时保持孤立光子性能并减少多次推断导致的分裂。
• 在提升的 π0 → γγ 事件中，基于注意力的模型能够保留二光子质量重建能力，而标准算法在此变得低效。
• ClusTEX（单步变换器）在受 ECAL 启发的拓扑中表现最佳，能量分辨率提升、相比两步方法和标准算法的分裂减少。
• ClusTEX 对局部探测器故障仍然鲁棒，显示出稳定性提升和对无响应通道的能量部分恢复。
• SeedFinder 能有效减少候选窗口，保持高效率，同时实现 PoEN/ClusTEX 的联合重建。
• 模型在具有显式 η、φ 依赖和探测器非均匀性的 Geant4 仿真上进行训练和评估，展示几何感知推理的优势。

Figure 2 : The optimized CNN based SeedFinder (SF) model architecture. The seed window candidates passing the threshold on deposited energy are taken as inputs to the SF model. The model assigns a probability whether the window is centred around the true seed crystal of a generated photon. The netwo