Linearized Optimal Transport for Collider Events

Abstract

We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which quantifies the "work" required to rearrange one event into another, while significantly reducing the computational cost. It also furnishes a Euclidean embedding amenable to simple machine learning algorithms and visualization techniques, which we demonstrate in a variety of jet tagging examples. The LOT approximation lowers the threshold for diverse applications of the theory of optimal transport to collider physics.

16 pages, 5 figures

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• SHAPER: Can You Hear the Shape of a Jet?
• Transport away your problems: Calibrating stochastic simulations with optimal transport
• Earth mover's distance as a measure of CP violation
• Differentiable Earth Mover's Distance for Data Compression at the High-Luminosity LHC
• Pileup and Infrared Radiation Annihilation (PIRANHA): A Paradigm for Continuous Jet Grooming
• Neural Conditional Reweighting
• The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification
• An Exploration of Learnt Representations of W Jets
• Using Kernel-Based Statistical Distance to Study the Dynamics of Charged Particle Beams in Particle-Based Simulation Codes
• The Linearized Hellinger--Kantorovich Distance
• Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distance
• A Linear Transportation ${\mathrm{L}}^p$ Distance for Pattern Recognition
• A Field Guide to Event-Shape Observables Using Optimal Transport