pith. sign in

arxiv: 2606.24637 · v1 · pith:4I2XKJVUnew · submitted 2026-06-23 · ✦ hep-ph

Application of Deep Learning to Jet Charge Discrimination

Meisam Ghasemi Bostanabad , Mojtaba Mohammadi Najafabadi This is my paper

Pith reviewed 2026-06-25 23:24 UTC · model grok-4.3

classification ✦ hep-ph
keywords jet charge discriminationgraph neural networksdeep learningquark antiquark separationLHC jet taggingmachine learning in high energy physics
0
0 comments X

The pith

A graph neural network distinguishes up-quark jets from anti-up-quark jets with an AUC of 0.883 in QCD simulations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper benchmarks several machine learning models for jet charge discrimination, the task of telling whether a light-quark jet came from an up quark or an anti-up quark. This distinction matters for precision Standard Model tests and for searches that need to separate quarks from antiquarks. The authors run the comparison inside a controlled QCD simulation and report that a graph neural network reaches the highest score among the models examined. The study supplies a starting point for using these techniques in real LHC jet analyses.

Core claim

Among the machine learning models benchmarked for distinguishing up-quark from anti-up-quark jets in a controlled QCD environment, the graph neural network achieves the best performance with an AUC of 0.883.

What carries the argument

Graph neural network applied to jet constituents for electric charge discrimination.

If this is right

  • Charge asymmetry measurements in hadron collisions gain precision when quark versus antiquark jets can be separated.
  • Searches for new particles that rely on distinguishing quarks from antiquarks become more sensitive.
  • Modern machine-learning methods gain a documented path into jet-charge studies at the LHC experiments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If performance holds once detector effects are added, the network could be inserted into existing experimental pipelines without major redesign.
  • The same graph-based approach may transfer to discrimination among other parton types or to multi-class jet tagging.
  • Combining the network output with established jet taggers could produce a composite tagger whose performance exceeds either method alone.

Load-bearing premise

The controlled QCD environment used for the benchmark accurately represents real LHC detector conditions and jet charge discrimination performance.

What would settle it

Applying the same models to fully simulated collision events that include detector response and measuring whether the AUC remains near 0.883 would test the result.

Figures

Figures reproduced from arXiv: 2606.24637 by Meisam Ghasemi Bostanabad, Mojtaba Mohammadi Najafabadi.

Figure 1
Figure 1. Figure 1: Distributions of Qj for u, u¯ jets obtained from pp → ug or pp → ug¯ events with κ = 0.7, 1. 2 Physics Motivation and Scope The determination of the electric charge of jets, commonly referred to as jet-charge discrimination, is a powerful technique in collider physics. Although jets are extended objects formed through parton showering and hadronization, their overall charge encodes information about the in… view at source ↗
Figure 2
Figure 2. Figure 2: Left: the accuracy progression over 16 training epochs, showing both training (blue) and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: pixelated representation of a leading jet in the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: ROC curves for baseline and optimized CNN models. The optimized model (AUC = 0.717) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of a fully connected directed graph used to represent jet constituents in the GNN [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Left: Distribution of GCN output scores for up (signal) and anti-up (background) jets, showing [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The architecture of the Particle Transformer includes Embedding layer, Particle Attention Block [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: ROC curve for the plain Particle Transformer. The model achieves an AUC of 0.865, demon [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Vision Transformer architecture for jet charge discrimination, showing patch embedding, trans [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Left: Quantum feature map using ZZFeatureMap, with superposition from Hadamard gates [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Classification accuracy of VQC (left) and QSVM (right) models for up and anti-up quark jet [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: ROC curves comparing VQC and QSVM performance on jet classification. [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Left: Accuracy of various ML classifiers for discriminating up and anti-up quark jets. Right: [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Left: Distributions of Qj for d, ¯d jets obtained from pp → dg or pp → ¯dg events with κ = 0.7. Right: ROC curves comparing GCN and GraphSAGE performance on d ¯d jet classification. 5 Results and Discussion This study explored several machine learning models, both classical and deep learning-based for discrim￾inating between up and anti-up quark jets using jet charge information. Among the classical model… view at source ↗
Figure 15
Figure 15. Figure 15: ROC curves showing the performance of GCN models trained with different [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
read the original abstract

The Large Hadron Collider (LHC) produces an enormous volume of data in which the identification and characterization of hadronic jets is a central challenge. Determining the electric charge of the parton initiating a light-quark jet; a task known as jet-charge discrimination; is highly valuable for both precision tests of the Standard Model (SM) and searches for physics beyond it. In this work, we benchmark a range of classical and quantum machine-learning models for the task of distinguishing up-quark from anti-up-quark jets in a controlled QCD environment. Among the approaches tested, a Graph Neural Network achieved the best performance, with an AUC of 0.883. Jet-charge tagging of this kind has broad phenomenological applications, from improving measurements of charge asymmetries to enhancing sensitivity in searches for new particles from beyond the SM where quark versus antiquark discrimination is essential. Our study provides a methodological foundation for deploying modern machine-learning techniques in jet-charge analyses at the LHC experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript benchmarks a range of classical and quantum machine-learning models for distinguishing up-quark from anti-up-quark jets via jet charge in a controlled QCD environment. It reports that a Graph Neural Network achieves the best performance with an AUC of 0.883 and positions the study as a methodological foundation for jet-charge analyses at the LHC.

Significance. If the performance holds, the work supplies a benchmark comparison that includes quantum models and could serve as a starting point for ML-based jet charge tagging. The controlled-environment result itself is of limited direct phenomenological value given the absence of detector effects.

major comments (2)
  1. [Abstract] Abstract: The reported AUC of 0.883 is presented without any information on training data volume, feature definitions, baseline comparisons, cross-validation procedure, or statistical uncertainties. This absence prevents evaluation of whether the quoted performance supports the central claim.
  2. [Abstract] Abstract: The claim that the result provides a foundation for LHC analyses is undermined by the exclusive use of a controlled QCD environment that omits detector response, tracking efficiency, momentum smearing, and pile-up overlay, all of which directly alter the input features to any jet-charge tagger.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments. We agree that the abstract should be expanded to provide more context on the reported performance and to clarify the scope of the study. We address each point below and will make the corresponding revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The reported AUC of 0.883 is presented without any information on training data volume, feature definitions, baseline comparisons, cross-validation procedure, or statistical uncertainties. This absence prevents evaluation of whether the quoted performance supports the central claim.

    Authors: We concur that the abstract would benefit from additional details to allow proper evaluation. Although these aspects are described in the body of the manuscript, we will revise the abstract to briefly include the training data volume, the definitions of the input features, the baseline models used for comparison, the cross-validation procedure employed, and the method for estimating statistical uncertainties on the AUC. This revision will strengthen the presentation of our results. revision: yes

  2. Referee: [Abstract] Abstract: The claim that the result provides a foundation for LHC analyses is undermined by the exclusive use of a controlled QCD environment that omits detector response, tracking efficiency, momentum smearing, and pile-up overlay, all of which directly alter the input features to any jet-charge tagger.

    Authors: The referee correctly notes that our simulations are performed in a controlled QCD environment without detector effects. We position the work as providing a methodological foundation precisely because it isolates the performance of the machine learning models in an idealized setting. This controlled benchmark is a necessary first step before incorporating more realistic effects. We will revise the abstract to explicitly mention the controlled nature of the environment and to frame the result as an initial benchmark for future studies that include detector simulation. revision: yes

Circularity Check

0 steps flagged

Empirical ML benchmarking on simulated QCD data exhibits no circularity

full rationale

The paper reports results from training and evaluating classical and quantum ML models (including a GNN) on parton- or hadron-level QCD simulations to discriminate u vs ū jets, with the central output being an empirical AUC metric of 0.883. No derivation chain, first-principles prediction, or mathematical reduction is claimed; the AUC is obtained directly from hold-out evaluation on the same simulation framework used for training. No self-citations, fitted inputs renamed as predictions, ansatzes, or uniqueness theorems appear in the abstract or described content that would reduce the reported performance to its own inputs by construction. The simulation-to-reality gap noted by the skeptic is a validity concern, not a circularity issue.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No information available from abstract on free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5698 in / 941 out tokens · 19149 ms · 2026-06-25T23:24:10.504754+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

52 extracted references · 27 canonical work pages · 9 internal anchors

  1. [1]

    LHC Machine,

    L. Evans and P. Bryant, “LHC Machine,”JINST3(2008) S08001, doi:10.1088/1748- 0221/3/08/S08001

    work page doi:10.1088/1748- 2008

  2. [2]

    Jet Charge at the LHC

    D. Krohn, M. D. Schwartz, T. Lin and W. J. Waalewijn, “Jet Charge at the LHC,”Phys. Rev. Lett. 110, no.21, 212001 (2013) doi:10.1103/PhysRevLett.110.212001 [arXiv:1209.2421 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.110.212001 2013

  3. [3]

    Quark and Gluon Jet Substructure

    J. Gallicchio and M. D. Schwartz, “Quark and gluon jet substructure,”JHEP04(2013) 090, doi:10.1007/JHEP04(2013)090, arXiv:1211.7038 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep04(2013)090 2013

  4. [4]

    A parametrization of the properties of quark jets,

    R. D. Field and R. P. Feynman, “A parametrization of the properties of quark jets,”Nucl. Phys. B 136(1978) 1-76, doi:10.1016/0550-3213(78)90015-9

    work page doi:10.1016/0550-3213(78)90015-9 1978

  5. [5]

    Measurement of the top quark charge inppcollisions at √s= 7 TeV with the ATLAS detector,

    ATLAS Collaboration, “Measurement of the top quark charge inppcollisions at √s= 7 TeV with the ATLAS detector,”JHEP11(2013) 031, arXiv:1307.4568 [hep-ex]

    Pith/arXiv arXiv 2013

  6. [6]

    Measurement of jet charge in dijet events at √s= 8 TeV,

    CMS Collaboration, “Measurement of jet charge in dijet events at √s= 8 TeV,” CMS-PAS-JME- 13-002 (2013),https://cds.cern.ch/record/1599732

    arXiv 2013

  7. [7]

    Observation of charge asymmetry in hadron jets frome +e− annihilation at √s= 29 GeV,

    J. Bergeet al., “Observation of charge asymmetry in hadron jets frome +e− annihilation at √s= 29 GeV,”Nucl. Phys. B184(1981) 13-30, doi:10.1016/0550-3213(81)90163-X

    work page doi:10.1016/0550-3213(81)90163-x 1981

  8. [8]

    Jet Charge at the LHC

    W. J. Waalewijn, “Jet charge at the LHC,”Phys. Rev. D86(2012) 094030, doi:10.1103/PhysRevD.86.094030, arXiv:1209.2421 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.86.094030 2012

  9. [9]

    Measurement of charge asymmetry in hadronicZdecays,

    ALEPH Collaboration, D. Decampet al., “Measurement of charge asymmetry in hadronicZdecays,” Phys. Lett. B259(1991) 377-387, doi:10.1016/0370-2693(91)90844-G. 19

    work page doi:10.1016/0370-2693(91)90844-g 1991

  10. [10]

    Dynamic Jet Charge,

    Z. B. Kang, X. Liu, S. Mantry, M. C. Spraker and T. Wilson, “Dynamic Jet Charge,” Phys. Rev. D 103, no.7, 074028 (2021) doi:10.1103/PhysRevD.103.074028 [arXiv:2101.04304 [hep-ph]]

    work page doi:10.1103/physrevd.103.074028 2021

  11. [11]

    Measurement of the top quark charge usingt ¯tevents,

    CMS Collaboration, “Measurement of the top quark charge usingt ¯tevents,” CMS-PAS-TOP-13-013 (2014),https://cds.cern.ch/record/1728249

    arXiv 2014

  12. [12]

    Machine Learning Approaches to Top Quark Flavor-Changing Four-Fermion Interactions in Trilepton Signals at the LHC,

    M. Ghasemi Bostanabad and M. Mohammadi Najafabadi, “Machine Learning Approaches to Top Quark Flavor-Changing Four-Fermion Interactions in Trilepton Signals at the LHC,”Phys. Rev. D 111(2025) 112003,https://journals.aps.org/prd/abstract/10.1103/mk8x-nrpn

    work page doi:10.1103/mk8x-nrpn 2025

  13. [13]

    The CMS Particle Flow reconstruction and global event description with the Particle Flow algorithm,

    CMS Collaboration, “The CMS Particle Flow reconstruction and global event description with the Particle Flow algorithm,” CMS-PAS-PFT-09-001 (2009),https://cds.cern.ch/record/1194487

    arXiv 2009

  14. [14]

    Anomaly Detection for New Physics in LHC Events using Autoencoders,

    ATLAS Collaboration, “Anomaly Detection for New Physics in LHC Events using Autoencoders,” ATL-PHYS-PUB-2020-018 (2020),https://cds.cern.ch/record/2725620

    arXiv 2020

  15. [15]

    The CMS experiment at the CERN LHC

    CMS Collaboration, “The CMS Experiment at the CERN LHC,”JINST3(2008) S08004, doi:10.1088/1748-0221/3/08/S08004

    work page doi:10.1088/1748-0221/3/08/s08004 2008

  16. [17]

    Machine learning at the energy and intensity frontiers of particle physics,

    A. Radovic et al., “Machine learning at the energy and intensity frontiers of particle physics,” Nature 560 (2018) 41–48, arXiv:1806.11484 [hep-ex]

    Pith/arXiv arXiv 2018

  17. [18]

    Anomaly Detection for Resonant New Physics with Machine Learning,

    J. H. Collins, K. Howe and B. Nachman, “Anomaly Detection for Resonant New Physics with Machine Learning,” Phys. Rev. Lett. 121 (2018) 241803, arXiv:1805.02664 [hep-ph]

    Pith/arXiv arXiv 2018

  18. [19]

    A new method to distinguish hadronically decaying boosted $Z$ bosons from $W$ bosons using the ATLAS detector

    G. Aadet al.[ATLAS], “A new method to distinguish hadronically decaying boostedZbosons from Wbosons using the ATLAS detector,”Eur. Phys. J. C76, no.5, 238 (2016) doi:10.1140/epjc/s10052- 016-4065-1 [arXiv:1509.04939 [hep-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052- 2016

  19. [20]

    Identification techniques for highly boosted W bosons that decay into hadrons

    V. Khachatryanet al.[CMS], “Identification techniques for highly boosted W bosons that decay into hadrons,”JHEP12, 017 (2014) doi:10.1007/JHEP12(2014)017 [arXiv:1410.4227 [hep-ex]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep12(2014)017 2014

  20. [21]

    Theory and phenomenology of two-Higgs-doublet models

    G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher and J. P. Silva, “Theory and phenomenology of two-Higgs-doublet models,”Phys. Rept.516, 1-102 (2012) doi:10.1016/j.physrep.2012.02.002 [arXiv:1106.0034 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2012.02.002 2012

  21. [22]

    The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,

    J. Alwallet al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,”JHEP07(2014) 079, arXiv:1405.0301 [hep-ph]

    Pith/arXiv arXiv 2014

  22. [23]

    An introduction to PYTHIA 8.2,

    T. Sjostrandet al., “An introduction to PYTHIA 8.2,”Comput. Phys. Commun.191(2015) 159-177, arXiv:1410.3012 [hep-ph]

    Pith/arXiv arXiv 2015

  23. [24]

    The anti-k_t jet clustering algorithm

    M. Cacciari, G. P. Salam and G. Soyez, “The anti-k t jet clustering algorithm,”JHEP04(2008) 063, doi:10.1088/1126-6708/2008/04/063, arXiv:0802.1189 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2008/04/063 2008

  24. [25]

    FastJet user manual

    M. Cacciari, G. P. Salam and G. Soyez, “FastJet user manual,”Eur. Phys. J. C72(2012) 1896, doi:10.1140/epjc/s10052-012-1896-2, arXiv:1111.6097 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-012-1896-2 2012

  25. [26]

    Dispelling the N^3 myth for the Kt jet-finder

    M. Cacciari and G. P. Salam, “Dispelling theN 3 myth for thek t jet-finder,”Phys. Lett. B641 (2006) 57-61, doi:10.1016/j.physletb.2006.08.037, arXiv:hep-ph/0512210. 20

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2006.08.037 2006

  26. [27]

    Characterization of Jet Charge at the LHC,

    T. D. Rueter and K. Soni, “Characterization of Jet Charge at the LHC,” (2015),https://cs229. stanford.edu/proj2015/352_report.pdf

    2015

  27. [28]

    Searching for exotic particles in high-energy physics with deep learning,

    P. Baldi, P. Sadowski and D. Whiteson, “Searching for exotic particles in high-energy physics with deep learning,”Nature Communications5(2014) 4308, arXiv:1402.4735 [hep-ph]

    Pith/arXiv arXiv 2014

  28. [29]

    Scikit-learn: Machine Learning in Python,

    F. Pedregosaet al., “Scikit-learn: Machine Learning in Python,”J. Mach. Learn. Res.12(2011) 2825-2830,https://jmlr.org/papers/volume12/pedregosalia/pedregosalia.pdf

    2011

  29. [30]

    Keras: Deep Learning for humans,

    F. Chollet, “Keras: Deep Learning for humans,” (2015),https://keras.io

    2015

  30. [31]

    SciKeras: A Scikit-Learn API wrapper for Keras,

    A. Nicolaou and P. Andre, “SciKeras: A Scikit-Learn API wrapper for Keras,” (2021),https: //github.com/adriangb/scikeras

    2021

  31. [32]

    Gradient-based learning applied to document recognition.Proc

    Y. LeCun, L. Bottou, Y. Bengio and P. Haffner, “Gradient-based learning applied to document recognition,”Proc. IEEE86(1998) 2278-2324, doi:10.1109/5.726791

    work page doi:10.1109/5.726791 1998

  32. [33]

    Adam: A Method for Stochastic Optimization,

    D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” ICLR (2015), arXiv:1412.6980 [cs.LG]

    Pith/arXiv arXiv 2015

  33. [34]

    Keras Tuner,

    T. O’Malleyet al., “Keras Tuner,” (2019),https://github.com/keras-team/keras-tuner

    2019

  34. [35]

    Graph Neural Networks: A Review of Methods and Applications,

    J. Zhouet al., “Graph Neural Networks: A Review of Methods and Applications,”AI Open1(2020) 57-81, doi:10.1016/j.aiopen.2021.01.001

    work page doi:10.1016/j.aiopen.2021.01.001 2020

  35. [36]

    Semi-Supervised Classification with Graph Convolutional Networks,

    T. N. Kipf and M. Welling, “Semi-Supervised Classification with Graph Convolutional Networks,” ICLR (2017), arXiv:1609.02907 [cs.LG]

    Pith/arXiv arXiv 2017

  36. [37]

    Inductive Representation Learning on Large Graphs,

    W. L. Hamilton, R. Ying and J. Leskovec, “Inductive Representation Learning on Large Graphs,” NeurIPS (2017), arXiv:1706.02216 [cs.SI]

    Pith/arXiv arXiv 2017

  37. [38]

    Attention Is All You Need,

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser and I. Polosukhin, “Attention Is All You Need,” NeurIPS (2017), arXiv:1706.03762 [cs.CL]

    Pith/arXiv arXiv 2017

  38. [39]

    Particle Transformer for Jet Tagging,

    H. Qu, C. Li and S. Qian, “Particle Transformer for Jet Tagging,” PoS ICHEP2022 (2022) 1152, arXiv:2202.03772 [hep-ph]

    arXiv 2022

  39. [40]

    ParticleFormer: Learning Jet Structure with Transformers,

    V. Mikuni and F. Canelli, “ParticleFormer: Learning Jet Structure with Transformers,” JHEP 05 (2021) 221, arXiv:2102.05073 [hep-ph]

    arXiv 2021

  40. [41]

    An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale,

    A. Dosovitskiy et al., “An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale,” ICLR (2021), arXiv:2010.11929 [cs.CV]

    Pith/arXiv arXiv 2021

  41. [42]

    Supervised learning with quantum-enhanced feature spaces,

    V. Havlicek, A. D. Corcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow and J. M. Gam- betta, “Supervised learning with quantum-enhanced feature spaces,”Nature567(2019) 209-212, doi:10.1038/s41586-019-0980-2

    work page doi:10.1038/s41586-019-0980-2 2019

  42. [43]

    Qiskit: An Open-source Framework for Quantum Computing,

    H. Abrahamet al., “Qiskit: An Open-source Framework for Quantum Computing,” (2020),https: //qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html

    2020

  43. [44]

    I. T. Jolliffe,Principal Component Analysis, 2nd ed., Springer Series in Statistics (2002), doi:10.1007/b98835. 21

    work page doi:10.1007/b98835 2002

  44. [45]

    Barren plateaus in quantum neural network training landscapes,

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush and H. Neven, “Barren plateaus in quantum neural network training landscapes,”Nature Communications9(2018) 4812, doi:10.1038/s41467-018- 07090-4

    work page doi:10.1038/s41467-018- 2018

  45. [46]

    Qiskit Aer: High performance simulators for quantum circuits,

    H. Abrahamet al., “Qiskit Aer: High performance simulators for quantum circuits,” (2021),https: //qiskit.org/documentation/apidoc/aer.html

    2021

  46. [47]

    Multivariate stochastic approximation using a simultaneous perturbation gradient ap- proximation,

    J. C. Spall, “Multivariate stochastic approximation using a simultaneous perturbation gradient ap- proximation,”IEEE Trans. Automat. Control37(1992) 332-341,https://www.jhuapl.edu/spsa/ pdf-spsa/spall_tac92.pdf

    1992

  47. [48]

    Evaluating analytic gradients on quantum hardware

    M. Schuld, F. Petruccione, I. Sinayskiy and N. Killoran, “Evaluating analytic gradients on quantum hardware,”Phys. Rev. A99(2019) 032331, doi:10.1103/PhysRevA.99.032331

    work page doi:10.1103/physreva.99.032331 2019

  48. [49]

    , year =

    J. H. Friedman, “Greedy function approximation: A gradient boosting machine,”Annals of Statistics 29(2001) 1189-1232, doi:10.1214/aos/1013203451

    work page doi:10.1214/aos/1013203451 2001

  49. [50]

    Support-vector networks,

    C. Cortes and V. Vapnik, “Support-vector networks,”Machine Learning20(1995) 273-297, doi:10.1007/BF00994018

    work page doi:10.1007/bf00994018 1995

  50. [51]

    Machine Learning 45, 5–32

    L. Breiman, “Random forests,”Machine Learning45(2001) 5-32, doi:10.1023/A:1010933404324

    work page doi:10.1023/a:1010933404324 2001

  51. [52]

    A decision-theoretic generalization of on-line learning and an appli- cation to boosting,

    Y. Freund and R. E. Schapire, “A decision-theoretic generalization of on-line learning and an appli- cation to boosting,”J. Comput. Syst. Sci.55(1997) 119-139, doi:10.1006/jcss.1997.1504

    work page doi:10.1006/jcss.1997.1504 1997

  52. [53]

    Ghasemi Bostanabad, M. (2025). Light Flavor Jet Charge [Data set]. Zenodo. https://doi.org/10.5281/zenodo.15790634. 22

    work page doi:10.5281/zenodo.15790634 2025