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

Arghya Chattopadhyay

hep-phAug 16, 2026

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

Authors: Arghya Chattopadhyay

Organizations: Department of Physics, University of Puerto Rico at Mayagüez Mayagüez, Puerto Rico 00681, USA

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.

Figures & tables

Figure 1: Out-of-fold Pythia - Herwig separation on the common eight-observable representation. The dotted reference corresponds to chance-level separation.

Generator configuration	additive KAN	deep KAN	$\Delta\mathrm{AUC}$
A: shower only	0.9787	0.9924	+0.0137
B: shower + hadronization	0.5933	0.5941	+0.0008
C: full generator	0.6061	0.6062	+0.0001

Table 1: OOF generator separation on the development sample. The final column diagnoses additional non-additive discriminating information.

Figure 2: Representative additive-KAN response functions at stage A.

Figure 3: Representative additive-KAN response functions at stage B.

Figure 4: Representative additive-KAN response functions at stage C.

Panel of Figure 5 — Figure 5: Grouped Shapley allocations for the multiplicity, mass, and shape sectors at the three generator stages. Error bars show hard-event-clustered bootstrap intervals.

Panel of Figure 6 — Figure 6: Transport of the individual stage A factors to the later generator stages. The dashed line shows the unweighted generator separation and the dotted line corresponds to an AUC of $0.5$ . The mass factors are omitted because their effective sample sizes are too small for a reliable weighted comparison.

Figure 7: Development and final-test results for the transported stage A leading-multiplicity factor.

Panel of Figure 8 — Figure 8: Statistical support of the stage A component weights. Left: number of development events required to accumulate $50\%$ of the normalized component weight. Right: leading-jet mass associated with the same influential hard event in the paired Pythia and Herwig configurations at stages A, B, and C.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Stage	value function	multiplicity	mass	shape
A	separation	$0.4050\,[0.4021,0.4078]$	$-0.0005\,[-0.0034,0.0022]$	$0.0751\,[0.0720,0.0789]$
A	closure	$0.1796\,[0.1403,0.2186]$	$0.0286\,[0.0072,0.0538]$	$-0.0001\,[-0.0048,0.0044]$
B	separation	$0.0039\,[0.0024,0.0056]$	$0.0498\,[0.0442,0.0554]$	$0.0478\,[0.0415,0.0544]$
B	closure	$-0.0024\,[-0.0031,-0.0013]$	$0.0537\,[0.0514,0.0553]$	$0.0378\,[0.0341,0.0392]$
C	separation	$0.0365\,[0.0308,0.0420]$	$0.0205\,[0.0148,0.0257]$	$0.0554\,[0.0488,0.0625]$
C	closure	$0.0352\,[0.0304,0.0390]$	$0.0133\,[0.0104,0.0153]$	$0.0519\,[0.0480,0.0561]$

Appendix

Table 2: Grouped Shapley allocations used in Analysis I. Brackets denote

95\%

hard-event-clustered bootstrap intervals.

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