Learning the Geometry of Collider Events with Metric-Aware Deep Sets

The paper introduces a Deep Sets surrogate for optimal transport (OT) that respects key metric properties—non-negativity, exchange symmetry, and zero self-distance—while leaving the triangle inequality unconstrained. Applied to the Energy Mover's Distance between collider events, the Metric-Aware Particle Flow Network achieves percent‑level mean absolute percentage error and markedly higher inference throughput compared to other exact and approximate methods. The architectural constraints also dramatically reduce triangle‑inequality violations, improving geometric fidelity across a large set of held‑out event triplets.

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