🤖 AI Summary
研究通过Metric-Aware Deep Sets方法解决大型碰撞事件中几何结构学习问题，提高了粒子物理应用中能量转移距离计算的准确性和效率。
📝 Abstract
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.