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

• URL: http://arxiv.org/abs/2609.12024v1
• Date: Thu, 10 Sep 2026 13:22:01 GMT
• Title: Learning the Geometry of Collider Events with Metric-Aware Deep Sets
• Abstract summary: learned surrogates are faster, but need not preserve this metric structure.<n>We develop a Deep Sets surrogate for OT between variable-size weighted point clouds that enforces non-negativity, exchange symmetry, and zero self-distance.<n>These results demonstrate that targeted inductive biases can yield fast neural surrogates with substantially improved geometric fidelity.
• Score: 3.675517735057064
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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