SPECTER: Efficient Evaluation of the Spectral EMD

TL;DR

The paper introduces SPECTER, a fast, closed-form method for evaluating the Spectral Energy Mover's Distance (SEMD), enabling efficient event and jet shape analysis in collider physics, significantly outperforming traditional EMD computations.

Contribution

It provides a closed-form expression for SEMD, enabling rapid computation and new shape observables, along with a highly parallelized implementation called SPECTER.

Findings

SPECTER is up to 1000 times faster than traditional EMD methods.

Closed-form expressions for SEMD-based observables are derived.

SPECTER enables efficient, parallelized computation of spectral distances.

Abstract

The Energy Mover's Distance (EMD) has seen use in collider physics as a metric between events and as a geometric method of defining infrared and collinear safe observables. Recently, the Spectral Energy Mover's Distance (SEMD) has been proposed as a more analytically tractable alternative to the EMD. In this work, we obtain a closed-form expression for the Riemannian-like p = 2 SEMD metric between events, eliminating the need to numerically solve an optimal transport problem. Additionally, we show how the SEMD can be used to define event and jet shape observables by minimizing the distance between events and parameterized energy flows (similar to the EMD), and we obtain closed-form expressions for several of these observables. We also present the SPECTER framework, an efficient and highly parallelized implementation of the SEMD metric and SEMD-derived shape observables as an analogue of the previously-introduced SHAPER for EMD-based computations. We demonstrate that computing the SEMD with SPECTER can be up to a thousand times faster than computing the EMD with standard optimal transport libraries.