Learning the Geometry of Collider Events with Metric-Aware Deep Sets
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 106 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.
Related
- Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion
- The Intrinsic Dimension of Collider Events and Model-Independent Searches in 100 Dimensions
- Probabilistic Energy-Based Neural Networks for Uncertainty-Aware Collider Data Analyses
- Particle track reconstruction in high-density collider environments with an Evolving-Geometry Transformer
- From Geometry to Gravity: A Friendly Introduction to the Schwarzschild Metric
BibTeX
@misc{hay2026learning,
title = {{Learning the Geometry of Collider Events with Metric-Aware Deep Sets}},
author = {Lauren Hay and Rishabh Jain and Matt LeBlanc and Jennifer Roloff},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12024},
eprint = {2609.12024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12024},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning the Geometry of Collider Events with Metric-Aware Deep Sets
AU - Lauren Hay
AU - Rishabh Jain
AU - Matt LeBlanc
AU - Jennifer Roloff
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12024
UR - https://arxiv.org/abs/2609.12024
AB - 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.
ER -