Functional anatomy of Pythia-Herwig differences with Kolmogorov-Arnold networks

Abstract

Differences between high-energy event generators can arise at several stages of the collision simulation, from the hard scattering through parton showering and hadronization to the final event. These differences are usually summarized using observable distributions or global classifier scores. While these quantify the disagreement, they do not reveal which observable-level structures carry it or whether those structures persist through different stages of event generation. In this work, we formulate this problem as a staged functional analysis of generator-model differences. Following the same hard dijet events through Pythia and Herwig at shower-only, hadronized, and full-generator levels, we use an additive Kolmogorov-Arnold network (KAN) representation of the classifier-derived log density ratio to decompose the learned discrepancy into explicit one-dimensional observable responses that can be isolated, recomposed, and transported between generator stages. Within the same eight-observable jet representation, the Pythia-Herwig difference is driven mainly by multiplicity at shower level, shifts toward jet mass and shape after hadronization, and develops a mixed shape-multiplicity driven structure in the full-generator configuration. Transporting the individual shower-level functional components downstream shows that shower-level multiplicity information can retain its reweighting power, whereas the corresponding shape responses need not do so even though shape becomes important again at later stages. The jet-mass factors, meanwhile, are limited by poor statistical support. This KAN-based framework therefore provides a functional anatomy of generator-model dependence, exposing both persistent structures and support failures that are hidden inside a single global classifier-derived reweighting function.