High-Dimensional Unfolding in Large Backgrounds

Adam Takacs; Alexandre Falc\~ao

REVIEW 4 major objections 5 minor 1 cited by

High-Dimensional Unfolding in Large Backgrounds

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Including auxiliary observables in the unfolding input, up to 18 dimensions, improves unfolded jet transverse momentum and substructure observables from 10–20% agreement with truth to percent-level agreement in a heavy-ion-like environment.

desk verdict Solid extension of OmniFold to dense backgrounds with a useful auxiliary-observable strategy; the central result holds at fixed iterations, but the 1D baseline comparison is not iteration-controlled. read the letter →

arxiv 2507.06291 v2 pith:ZGFOX6IJ submitted 2025-07-08 hep-ph hep-exnucl-exnucl-th

Alexandre Falcão , Adam Takacs This is my paper

classification hep-phhep-exnucl-exnucl-th

keywords jetunfoldingheavy-ioncollisionsmachinelearningOmniFoldauxiliaryobservablessubstructureiterativeBayesiancalibration

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that unfolding jet observables in dense, high-background environments improves dramatically when the unfolding input includes many auxiliary observables alongside the target: in a realistic heavy-ion-like setup with full detector simulation, going from 1D to 18-dimensional unfolding moves agreement with truth from the 10–20% level down to percent level. To do this it introduces OmniFold-HI, an unbinned, machine-learning unfolding algorithm that extends OmniFold to handle background, fake jets, detector acceptance, efficiency, and uncertainties, and proves the method is mathematically equivalent to iterative Bayesian unfolding and to expectation-maximization. The paper further argues that calibration and unfolding should be merged into one high-dimensional step, because standard jet-energy-resolution smearing decorrelates observables and degrades unfolding. If these results hold, the dominant systematic uncertainties in heavy-ion and high-luminosity jet analyses could be substantially reduced, and observables not explicitly unfolded can still be recovered through correlations.

What carries the argument

The machine at the center is OmniFold-HI, an extension of the unbinned OmniFold algorithm. Two neural-network classifiers are trained with weighted binary-cross-entropy losses to estimate the likelihood ratios $\omega_n(m)=x(m)/x_{n-1}(m)$ and $\nu_n(t)=x_n(t)/x_0(t)$; iterating these ratios reweights simulated events toward the measured distribution, and the paper proves this recursion is exactly the EM algorithm / IBU in unbinned form. Efficiency and fake events are handled through an $\epsilon(t)$ factor and delta-function assignments, and statistical uncertainties are unfolded by a second pass with squared weights. The auxiliary-observable strategy selects inputs by clustering observables using correlation distances $d_{ij}=1-|\mathrm{LC}(i,j)|$, so each cluster contributes one informative variable.

What would settle it

Use a known-truth dataset and deliberately corrupt the detector response of a single auxiliary observable in one phase-space region; if adding that observable to the unfolding input still improves agreement with truth, the paper's assumption that response fidelity limits high-dimensional unfolding is wrong.

Watch

Extended reading notes

Core claim

The central discovery, as the authors state it, is that the dimensionality of the unfolding space itself is a precision handle: including auxiliary observables in the unfolding input lets the algorithm capture correlations among jet quantities that 1D unfolding ignores, and this is what drives the improvement. In the paper's testbed — dijets at 5.02 TeV with a heavy-ion-like underlying event, detector effects from a fast simulation, one generator serving as the simulated/generated sample and another as the truth/measured sample — unfolding $p_T$, $k_{t,g}$, and $\tau_2$ improves from about 10–20% agreement to percent level as the input grows to 18 observables. OmniFold-HI is shown to be the unbinned equivalent of IBU, with fake/trash handling and direct uncertainty unfolding, and the authors show that unfolding reconstructed-level quantities directly (skipping standard calibration) outperforms calibrate-then-unfold because calibration smearing destroys inter-observable correlations.

Load-bearing premise

The method's accuracy rests on Monte Carlo simulation covering the full joint space of all included observables; if the simulation mis-models any auxiliary observable, extra dimensions can add bias instead of removing it.

Editorial extensions

If this is right

18-dimensional unfolding reaches percent-level accuracy on $p_T$, $k_{t,g}$, and $\tau_2$ in a heavy-ion-like environment, versus 10–20% for 1D; this would shrink a dominant source of systematic uncertainty in jet measurements.
Observables left out of the training set, such as the recursive Soft Drop multiplicity $n_{\mathrm{rsd}}$, are unfolded correctly through correlations, suggesting full-event unfolding is feasible with a modest input set.
Since OmniFold-HI equals IBU/EM, standard unfolding theory applies to the machine-learning implementation, giving a principled basis for choosing iteration counts and regularizing.
Merging calibration and unfolding avoids jet-energy-resolution decorrelation and outperforms the calibrate-then-unfold workflow in high dimensions.
Particle-level background subtraction preserves inter-observable correlations and maintains the high-dimensional unfolding performance, unlike momentum-only calibration.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the correlation-clustering selection recipe suggests a general rule — choose auxiliary observables to cover the response matrix's phase-space dimensions rather than to maximize correlation with the target; a testable prediction is that adding observables whose detector response is mis-modeled will degrade performance, so the optimal dimension is environment-dependent.
Beyond the paper: the direct-uncertainty-unfolding trick could be extended to model (generator) uncertainties by unfolding the difference between two response matrices, yielding systematic uncertainties without repeated bootstrap training.
Beyond the paper: if calibration folds into unfolding, existing jet calibration constants become unnecessary for final cross-sections, which would change how collider experiments publish jet measurements; this could be tested by re-analyzing a public jet measurement with and without prior calibration.
Beyond the paper: the method's reliance on simulation coverage implies that high-dimensional unfolding in real heavy-ion data requires careful validation of auxiliary observables against control samples, otherwise the extra dimensions may inject rather than remove bias.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my read on 2507.06291. The paper extends OmniFold to dense environments — backgrounds, fakes, trash, efficiency, and uncertainties — gives a clean derivation showing equivalence to IBU and EM, and demonstrates that including up to 18 auxiliary observables moves a heavy-ion-like closure test from 10-20% agreement to percent-level agreement with truth. The genuinely new pieces are the explicit treatment of fakes and trash in the derived algorithm (Ref. [27] had the idea without the derivation), the correlation-clustering strategy for selecting auxiliary observables, and a comparison showing that a simplified JES/JER calibration which decorrelates observables actually degrades high-dimensional unfolding. The event-level unfolding of an observable not in the training set (n_rsd) is a nice bonus. Code and data are public.

The closure test is strong: unfolding Herwig truth with a Pythia-based response is an independent check. The math in Sec. 2 is coherent, and the interpretation of the NN loss functions as likelihood-ratio estimators is clear. Credit where due: this is a serious, well-executed study.

Now the soft spots, in proportion. (1) The comparison to 'traditional 1D' is not iteration-controlled: Fig. 4 uses three iterations, Fig. 6 uses five. That's apples-to-oranges. However, the central auxiliary-observable claim does not depend on that comparison — within Fig. 6, 3D, 7D, 12D, and 18D are all at five iterations, and the gains appear as dimensionality increases. So the stress-test worry that the headline improvement might just be extra convergence does not hold up for the main claim; it only affects the 1D side comparison. Showing a 1D or 3D run at five iterations would make the paper cleaner. (2) There is no quantitative goodness-of-fit metric; performance is read off ratio plots. A chi-square or similar would let readers judge the size of the effect rather than eyeball it. (3) The calibration study sets sigma_meas^2 = 2 sigma_mc^2 as an ad hoc assumption. The authors flag it, but it limits the reach of that comparison. (4) Auxiliary-observable selection uses truth-level correlations. That is standard in MC-based unfolding — you have simulation truth — and it is not a circular use of the target data, but the paper should say this explicitly. (5) The statistical-uncertainty framework is interesting, but the authors honestly note that the connection to IBU uncertainties is not yet fully understood. That is not a flaw, just a limitation worth knowing.

Who gets value from this: hep-ph readers in jet substructure, heavy-ion phenomenology, and anyone applying ML unfolding beyond standard OmniFold. It deserves a serious referee. I would send it to peer review with a request for an iteration-controlled baseline and a quantitative agreement metric.

Referee Report

4 major / 5 minor

Summary. This paper introduces OmniFold-HI, an extension of the OmniFold unfolding algorithm that incorporates background, fake signals, detector acceptance/efficiency, and uncertainty propagation, and derives its equivalence to expectation-maximization and iterative Bayesian unfolding (IBU). The authors validate the method in a closure-style study using Pythia-based response and prior with Herwig-based truth and measurement, and demonstrate multidimensional unfolding of jet observables with up to 18 input dimensions. They further study the interplay of jet calibration, particle-level background subtraction, and unfolding, arguing that unfolding directly from reconstruction level outperforms workflows based on simplified JES/JER calibration. The paper includes public code and data, and explicitly acknowledges several limitations of the simulation setup.

Significance. If the central empirical claim holds, this is a valuable contribution: it would show that including auxiliary observables in ML-based unfolding can substantially reduce unfolding uncertainties in dense environments such as heavy-ion collisions and high-luminosity LHC running. The theoretical derivation clarifying that OmniFold-HI is an EM/IBU algorithm is useful and goes beyond earlier treatments by explicitly handling fakes, trash, and efficiency. The validation is designed to avoid circularity, since the unfolding uses a Pythia-based response and prior while the measurement and target truth are Herwig-based. The public release of code and data is a further strength. However, the main performance claim is currently supported by qualitative ratio plots and, more importantly, by a comparison of runs with different iteration counts; the calibration comparison also relies on an ad hoc modeling assumption. These issues are addressable but need to be fixed before the central claims can be fully assessed.

major comments (4)

[§3.3 vs §3.2, Fig. 6 vs Fig. 4] The central evidence for the benefit of auxiliary observables is the comparison between high-dimensional unfolding in Fig. 6 and the 1D/3D baselines in Fig. 4, but these runs use different numbers of iterations: Fig. 4 is explicitly described as 'after three iterations', while Fig. 6 is 'after five unfolding iterations, that is used from now on'. Since OmniFold-HI is an iterative EM/IBU algorithm, and Sec. 3.2 states that the residual imperfections in Fig. 4 are 'partially due to remaining prior biases (finite number of iterations)', the observed improvement from 10–20% accuracy to percent-level accuracy could be partly a convergence effect rather than an effect of dimensionality. Please add 1D and 3D unfolding runs at five iterations (and ideally an iteration scan for each dimensionality) so that the dimensionality dependence is cleanly isolated from the iteration dependence.
[§3.2–§3.3] The performance claims, including '10-20% accuracy' for 1D unfolding and 'percent level accuracy' for high-dimensional unfolding, are read off ratio panels and are not supported by a quantitative goodness-of-fit metric. Because these numbers are the quantitative basis for the abstract's central claim, please report a standard metric (e.g., chi2/ndf, Kolmogorov-Smirnov distance, or integrated absolute deviation) for each dimensionality and iteration count, ideally with statistical and network uncertainties on the metric itself.
[§3.4, calibration step 2] The conclusion that applying calibration before unfolding degrades high-dimensional performance rests on the assumption σ_meas^2 = 2 σ_mc^2, stated in Sec. 3.4 without justification or sensitivity studies. The size of the induced smearing directly controls how much physical correlation is removed, so the comparison in Fig. 8 is only demonstrated for one arbitrary calibration scenario. Please test the robustness of the conclusion over a plausible range of σ_meas/σ_mc values, or use a physics-motivated JER parametrization; otherwise the claim that 'traditional calibration techniques have to be reexamined' is not quantitatively supported.
[§3.3, Fig. 7] The proposed 'optimal unfolding strategy' for selecting auxiliary observables uses the Pearson correlation matrix computed from Herwig truth-level events, i.e., from the very distribution that is the target of the unfolding. In a real analysis, such truth-level correlations are not known, so the demonstrated convergence gains may be optimistic. Please show that the strategy gives similar gains when the observable ordering is based on reconstructed-level information or on a fixed a priori ordering, or explicitly frame the current result as an optimistic upper benchmark.

minor comments (5)

[§3.1] There are minor typographical errors: 'retined' should be 'retained', and 'for instead' should be 'for instance'.
[§2.2, Eq. (2.20)] The notation in the sums 'meas+mc' and 'mc+mc' is confusing at first reading; please clarify that the two terms refer to the measured sample and the two MC samples used in the two classifier steps.
[Fig. 7] The label 'RakT' in the left panel appears to be a typo for 'R_akt' or 'R_akt=0.4'; please correct it.
[§3.3] The statement that extending to more dimensions has 'minimal impact on computational runtime' is asserted but not demonstrated; a short runtime benchmark for the different dimensionalities would make this claim precise.
[Abstract and §4] The abstract says 'enhances full-event unfolding', but the demonstrated event-level result is limited to one auxiliary observable (n_rsd) not included in training; consider softening the wording to 'event-level unfolding' to match the scope of the demonstration.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the unfolding derivation is self-contained and the central performance claim is benchmarked against external Herwig truth; the noted caveats are experimental-control concerns, not circular steps.

full rationale

The derivation chain is not circular. Section 2.1 starts from the IBU recursion (Eq. 2.4) and proves its EM/maximum-likelihood character via Jensen's inequality (Eqs. 2.8-2.12). Section 2.2 then rewrites the unbinned IBU equation (Eq. 2.14) in terms of likelihood ratios (Eq. 2.16), and shows that the OmniFold-HI classifier losses (Eqs. 2.17-2.22) evaluate exactly those ratios; the neural networks are thus computational estimators of the same unfolding recursion, not fitted answers. The main performance claim (Fig. 6) is validated by unfolding a Herwig 'truth/measured' sample with a Pythia + Delphes + JetToyHI response and prior, which is an external benchmark rather than an input fitted to the target. The uncertainty-refolding procedure is explicitly acknowledged to be 'formally equivalent to the Poisson bootstrap' (Sec. 2.3.1), an honest statement of equivalence rather than a disguised prediction. The paper's own stated limitations are real but do not create circularity: Sec. 3.1 notes that 'differences between generators provide fundamental limitations in the unfolding performance'; Sec. 3.2 attributes residual imperfections 'partially due to remaining prior biases (finite number of iterations)'; and Fig. 7 selects auxiliary observables using Herwig truth-level correlations, which is a mild target-information leakage in that demonstration. Additionally, the headline comparison contrasts five-iteration high-dimensional results (Sec. 3.3, Fig. 6) with three-iteration 1D/3D baselines (Sec. 3.2, Fig. 4), so iteration count is not controlled. These issues affect the strength and interpretation of the empirical comparison, but no predicted distribution is equal by construction to the inputs, so no circular step is identified.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

No new physical entities are introduced. The main assumptions are the standard unfolding response-model assumption, deterministic one-to-one MC pairing, and the ad hoc calibration variance ratio. The free parameters are algorithm regularizers and settings, not fitted physical constants.

free parameters (4)

Calibration variance ratio r = sigma_meas^2 / sigma_mc^2 = 2 (assumed for all pT bins)
Sec. 3.4 step 2 states 'we assume simply sigma_meas^2 = 2 sigma_mc^2'; this ad hoc choice drives the calibration comparison and is not derived from data or a detector study.
Number of unfolding iterations n = 3 in Figs. 4-5, 5 in Figs. 6-9
Iteration count is a regularization choice that controls the bias-variance tradeoff; results depend on it, and IBU uncertainty grows with iteration.
NN hyperparameters = 2 hidden layers of 200 nodes, ReLU, Adam, 20 epochs, batch size 8192
Sec. 3.2 describes exploring several architectures; the chosen settings affect performance and the quoted NN systematic uncertainties.
ICS background estimation parameters = Grid size 0.5, ghost area 0.01, subtraction distances (0.1, 0.2), alpha = 1
Sec. 3.5 lists these settings for particle-level background subtraction; results may depend on them.

assumptions (7)

standard math Bayes theorem and Jensen's inequality hold for the relevant probability densities.
Used in Sec. 2.1 to derive the IBU recursion and in Eq. (2.8) for the EM lower bound.
standard math The EM algorithm monotonically increases the likelihood toward a maximum.
Invoked in Sec. 2.1 to argue that iterative Bayesian unfolding converges to the maximum likelihood solution.
standard math Neural networks can approximate the optimal classifier (universal approximation).
Used in Sec. 2.2 to replace histogram ratios with trained classifiers.
domain assumption The MC simulation response approximates the true detector response: p(E|C) approx p(E|C,mc).
Stated in Sec. 2.1 as the standard unfolding assumption; the entire closure test relies on it.
domain assumption MC events pass through simulation one-by-one, so p(m_i|t_j) = delta_ij and efficiency epsilon(t) is 0 or 1.
Used in Sec. 2.2 to justify the Monte Carlo evaluation of the loss functionals and the efficiency factor.
domain assumption Pythia plus Delphes plus JetToyHI provides adequate phase-space coverage for the 18-dimensional unfolding.
Secs. 3.1 and 3.3 rely on this coverage; the authors note that phase-space gaps are a known issue left for future work.
ad hoc to paper The simplified calibration with sigma_meas^2 = 2 sigma_mc^2 approximates real JES and JER corrections.
Sec. 3.4 introduces this assumption without motivation or sensitivity study, and it drives the comparison between calibration-first unfolding and direct unfolding.

how reviews work

0 comments

Cite this review

Pith. "Pith review of High-Dimensional Unfolding in Large Backgrounds." pith.science (2026). https://pith.science/paper/ZGFOX6IJ

@misc{pith2026250706291,
  author       = {Pith},
  title        = {Pith review of: High-Dimensional Unfolding in Large Backgrounds},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZGFOX6IJ}},
  note         = {Machine review of arXiv:2507.06291}
}

read the original abstract

We propose new methodologies in multi-dimensional unfolding in dense environments, and show that incorporating auxiliary observables can significantly improve performance. Our approach builds on the ML-based OmniFold algorithm, which we extend to account for background, detector acceptance, efficiency, and uncertainties, enabling its application in high-luminosity and heavy-ion collision settings. We derive this algorithm and demonstrate its mathematical and numerical equivalence to expectation-maximization and Iterative Bayesian Unfolding (IBU). We illustrate our method with a realistic jet substructure analysis incorporating both large background and detector simulation. Our analysis includes up to 18 observables, leading to significantly improved performance in the unfolding. We propose a method that integrates calibration and unfolding into a single, consistent framework, and demonstrate enhanced performance relative to traditional methods. These developments lay the groundwork for robust, high-dimensional, ML-based unfolding and calibration in complex collider environments across a wide range of analyses.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Toward an event-level analysis of hadron structure using differential programming
hep-ph 2025-07 conditional novelty 4.0 of 10

LOITS is a differentiable sampling method, demonstrated in a GAN closure test, that maps sampled events back to the parameters of a target density for event-level inference.

Reference graph

Works this paper leans on

85 extracted references · 8 canonical work pages · cited by 1 Pith paper

[27]

Andreassen, P

A. Andreassen, P. T. Komiske, E. M. Metodiev, B. Nachman, A. Suresh, and J. Thaler, Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution, in9th International Conference on Learning Representations, 5, 2021.arXiv:2105.04448

arXiv 2021
[1]

G. P. Salam,Towards Jetography,Eur. Phys. J. C67(2010) 637–686, [arXiv:0906.1833]

arXiv 2010
[2]

A. J. Larkoski, I. Moult, and B. Nachman,Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning,Phys. Rept.841(2020) 1–63, [arXiv:1709.04464]

arXiv 2020
[3]

Marzani, G

S. Marzani, G. Soyez, and M. Spannowsky,Looking inside jets: an introduction to jet substructure and boosted-object phenomenology, vol. 958. Springer, 2019. – 26 – 0.9 1.0 1.1 OF-HI ratio to truth Poisson bootstrap (BS) Direct unfolding 250 450 650 pT [GeV] 0.9 1.0 1.1 OF-HI stat. unc. ratio to truth statistical uncertainty F T 0.9 1.0 1.1 Truth stat. unc...

2019
[4]

Kogler et al.,Jet Substructure at the Large Hadron Collider: Experimental Review,Rev

R. Kogler et al.,Jet Substructure at the Large Hadron Collider: Experimental Review,Rev. Mod. Phys.91(2019), no. 4 045003, [arXiv:1803.06991]

arXiv 2019
[5]

d’Enterria,Jet quenching,Landolt-Bornstein23(2010) 471, [arXiv:0902.2011]

D. d’Enterria,Jet quenching,Landolt-Bornstein23(2010) 471, [arXiv:0902.2011]

arXiv 2010
[6]

Connors, C

M. Connors, C. Nattrass, R. Reed, and S. Salur,Jet measurements in heavy ion physics, Rev. Mod. Phys.90(2018) 025005, [arXiv:1705.01974]

arXiv 2018
[7]

Cunqueiro and A

L. Cunqueiro and A. M. Sickles,Studying the QGP with Jets at the LHC and RHIC,Prog. Part. Nucl. Phys.124(2022) 103940, [arXiv:2110.14490]

arXiv 2022

Show all 85 references

[8]

Zurbano Fernandez et al.,High-Luminosity Large Hadron Collider (HL-LHC): Technical design report,

I. Zurbano Fernandez et al.,High-Luminosity Large Hadron Collider (HL-LHC): Technical design report,
[9]

Cacciari and G

M. Cacciari and G. P. Salam,Pileup subtraction using jet areas,Phys. Lett. B659(2008) 119–126, [arXiv:0707.1378]

2008 arXiv
[10]

Berta, M

P. Berta, M. Spousta, D. W. Miller, and R. Leitner,Particle-level pileup subtraction for jets and jet shapes,JHEP06(2014) 092, [arXiv:1403.3108]

2014 arXiv
[11]

Cacciari, G

M. Cacciari, G. P. Salam, and G. Soyez,SoftKiller, a particle-level pileup removal method, Eur. Phys. J. C75(2015), no. 2 59, [arXiv:1407.0408]

2015 arXiv
[12]

Bertolini, P

D. Bertolini, P. Harris, M. Low, and N. Tran,Pileup Per Particle Identification,JHEP10 (2014) 059, [arXiv:1407.6013]. [13]ST ARCollaboration, L. Adamczyk et al.,Measurements of jet quenching with semi-inclusive hadron+jet distributions in Au+Au collisions at√sN N= 200 GeV,Phys...

2014 arXiv
[14]

Arjona Martínez, O

J. Arjona Martínez, O. Cerri, M. Pierini, M. Spiropulu, and J.-R. Vlimant,Pileup mitigation at the Large Hadron Collider with graph neural networks,Eur. Phys. J. Plus134 (2019), no. 7 333, [arXiv:1810.07988]

2019 arXiv
[15]

Berta, L

P. Berta, L. Masetti, D. W. Miller, and M. Spousta,Pileup and Underlying Event Mitigation with Iterative Constituent Subtraction,JHEP08(2019) 175, [arXiv:1905.03470]

2019 arXiv
[16]

Soyez,Pileup mitigation at the LHC: A theorist’s view,Phys

G. Soyez,Pileup mitigation at the LHC: A theorist’s view,Phys. Rept.803(2019) 1–158, [arXiv:1801.09721]. – 27 – [17]CMSCollaboration, S. Chatrchyan et al.,Determination of Jet Energy Calibration and Transverse Momentum Resolution in CMS,JINST6(2011) P11002, [arXiv:1107.4277]. ...

2019 arXiv
[22]

Mehtar-Tani, J

Y. Mehtar-Tani, J. G. Milhano, and K. Tywoniuk,Jet physics in heavy-ion collisions,Int. J. Mod. Phys. A28(2013) 1340013, [arXiv:1302.2579]

2013 arXiv
[23]

Blaizot and Y

J.-P. Blaizot and Y. Mehtar-Tani,Jet Structure in Heavy Ion Collisions,Int. J. Mod. Phys. E24(2015), no. 11 1530012, [arXiv:1503.05958]

2015 arXiv
[24]

S. Cao, A. Majumder, R. Modarresi-Yazdi, I. Soudi, and Y. Tachibana,Jet Quenching: From Theory to Simulation,Int. J. Mod. Phys. E33(2024) 2430002, [arXiv:2401.10026]

2024 arXiv
[25]

Cao and X.-N

S. Cao and X.-N. Wang,Jet quenching and medium response in high-energy heavy-ion collisions: a review,Rept. Prog. Phys.84(2021), no. 2 024301, [arXiv:2002.04028]

2021 arXiv
[26]

Andreassen, P

A. Andreassen, P. T. Komiske, E. M. Metodiev, B. Nachman, and J. Thaler,OmniFold: A Method to Simultaneously Unfold All Observables,Phys. Rev. Lett.124(2020), no. 18 182001, [arXiv:1911.09107]

2020 arXiv
[28]

Bellagente, A

M. Bellagente, A. Butter, G. Kasieczka, T. Plehn, A. Rousselot, R. Winterhalder, L. Ardizzone, and U. Köthe,Invertible Networks or Partons to Detector and Back Again, SciPost Phys.9(2020) 074, [arXiv:2006.06685]

2020 arXiv
[29]

Backes, A

M. Backes, A. Butter, M. Dunford, and B. Malaescu,An unfolding method based on conditional invertible neural networks (cINN) using iterative training,SciPost Phys. Core7 (2024), no. 1 007, [arXiv:2212.08674]

2024 arXiv
[30]

Backes, A

M. Backes, A. Butter, M. Dunford, and B. Malaescu,Event-by-event comparison between machine-learning- and transfer-matrix-based unfolding methods,Eur. Phys. J. C84(2024), no. 8 770, [arXiv:2310.17037]

2024 arXiv
[31]

Diefenbacher, G.-H

S. Diefenbacher, G.-H. Liu, V. Mikuni, B. Nachman, and W. Nie,Improving generative model-based unfolding with Schrödinger bridges,Phys. Rev. D109(2024), no. 7 076011, [arXiv:2308.12351]

2024
[32]

K. Zhou, L. Wang, L.-G. Pang, and S. Shi,Exploring QCD matter in extreme conditions with Machine Learning,Prog. Part. Nucl. Phys.135(2024) 104084, [arXiv:2303.15136]. – 28 –

2024 arXiv
[33]

A. J. Larkoski,QCD masterclass lectures on jet physics and machine learning,Eur. Phys. J. C84(2024), no. 10 1117, [arXiv:2407.04897]

2024 arXiv
[34]

Hep ml living review

“Hep ml living review.”https://iml-wg.github.io/HEPML-LivingReview. Accessed: 2023-11-28. [35]H1Collaboration, V. Andreev et al.,Measurement of Lepton-Jet Correlation in Deep-Inelastic Scattering with the H1 Detector Using Machine Learning for Unfolding, Phys. Rev. Lett.128(20...

2022
[43]

G. D’Agostini,A multidimensional unfolding method based on bayes’ theorem,Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment362(1995), no. 2 487–498

1995
[44]

D’Agostini,Improved iterative Bayesian unfolding,arXiv e-prints(Oct., 2010) arXiv:1010.0632, [arXiv:1010.0632]

G. D’Agostini,Improved iterative Bayesian unfolding,arXiv e-prints(Oct., 2010) arXiv:1010.0632, [arXiv:1010.0632]

2010 arXiv
[45]

OmniFold-HI GitHub repository

A. F. Falcão and A. Takacs, “OmniFold-HI GitHub repository.” https://github.com/OmniFoldHI/OmniFoldHI, 2025. Accessed: (14.04.2025). [46]CMSCollaboration, A. M. Sirunyan et al.,Particle-flow reconstruction and global event description with the CMS detector,JINST12(2017), no. 1...

2017 arXiv
[48]

P. T. Komiske, E. M. Metodiev, and J. Thaler,Metric Space of Collider Events,Phys. Rev. Lett.123(2019), no. 4 041801, [arXiv:1902.02346]

2019 arXiv
[49]

P. T. Komiske, E. M. Metodiev, and J. Thaler,The Hidden Geometry of Particle Collisions,JHEP07(2020) 006, [arXiv:2004.04159]

2020 arXiv
[50]

A. J. Larkoski and J. Thaler,A spectral metric for collider geometry,JHEP08(2023) 107, [arXiv:2305.03751]. – 29 –

2023 arXiv
[51]

A. J. Larkoski and E. M. Metodiev,A Theory of Quark vs. Gluon Discrimination,JHEP 10(2019) 014, [arXiv:1906.01639]

2019 arXiv
[52]

F. A. Dreyer, G. P. Salam, and G. Soyez,The Lund Jet Plane,JHEP12(2018) 064, [arXiv:1807.04758]

2018 arXiv
[53]

F. A. Dreyer, G. Soyez, and A. Takacs,Quarks and gluons in the Lund plane,JHEP08 (2022) 177, [arXiv:2112.09140]

2022 arXiv
[54]

Brewer, J

J. Brewer, J. G. Milhano, and J. Thaler,Sorting out quenched jets,Phys. Rev. Lett.122 (2019), no. 22 222301, [arXiv:1812.05111]

2019 arXiv
[55]

Takacs and K

A. Takacs and K. Tywoniuk,Quenching effects in the cumulative jet spectrum,JHEP10 (2021) 038, [arXiv:2103.14676]

2021 arXiv
[56]

Y.-L. Du, D. Pablos, and K. Tywoniuk,Deep learning jet modifications in heavy-ion collisions,JHEP21(2020) 206, [arXiv:2012.07797]

2020 arXiv
[57]

Y.-L. Du, D. Pablos, and K. Tywoniuk,Jet Tomography in Heavy-Ion Collisions with Deep Learning,Phys. Rev. Lett.128(2022), no. 1 012301, [arXiv:2106.11271]

2022 arXiv
[58]

Y. S. Lai, J. Mulligan, M. Płoskoń, and F. Ringer,The information content of jet quenching and machine learning assisted observable design,JHEP10(2022) 011, [arXiv:2111.14589]

2022 arXiv
[59]

Crispim Romão, J

M. Crispim Romão, J. G. Milhano, and M. van Leeuwen,Jet substructure observables for jet quenching in quark gluon plasma: A machine learning driven analysis,SciPost Phys.16 (2024), no. 1 015, [arXiv:2304.07196]

2024 arXiv
[60]

Nachman and J

B. Nachman and J. Thaler,Learning from many collider events at once,Phys. Rev. D103 (2021), no. 11 116013, [arXiv:2101.07263]

2021 arXiv
[61]

Rizvi, M

S. Rizvi, M. Pettee, and B. Nachman,Learning likelihood ratios with neural network classifiers,JHEP02(2024) 136, [arXiv:2305.10500]

2024 arXiv
[62]

Nachman and J

B. Nachman and J. Thaler,Neural resampler for Monte Carlo reweighting with preserved uncertainties,Phys. Rev. D102(2020), no. 7 076004, [arXiv:2007.11586]

2020 arXiv
[63]

R. Liaw, E. Liang, R. Nishihara, P. Moritz, J. E. Gonzalez, and I. Stoica,Tune: A research platform for distributed model selection and training,arXiv preprint arXiv:1807.05118 (2018)

2018 arXiv
[64]

Plehn, A

T. Plehn, A. Butter, B. Dillon, T. Heimel, C. Krause, and R. Winterhalder,Modern Machine Learning for LHC Physicists,arXiv:2211.01421

arXiv
[65]

Skands, S

P. Skands, S. Carrazza, and J. Rojo,Tuning PYTHIA 8.1: the Monash 2013 Tune,Eur. Phys. J. C74(2014), no. 8 3024, [arXiv:1404.5630]

2014 arXiv
[66]

Sjöstrand, S

T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands,An introduction to PYTHIA 8.2,Comput. Phys. Commun.191(2015) 159–177, [arXiv:1410.3012]

2015 arXiv
[67]

Bellm et al.,Herwig 7.0/Herwig++ 3.0 release note,Eur

J. Bellm et al.,Herwig 7.0/Herwig++ 3.0 release note,Eur. Phys. J. C76(2016), no. 4 196, [arXiv:1512.01178]

2016 arXiv
[68]

Bewick et al.,Herwig 7.3 release note,Eur

G. Bewick et al.,Herwig 7.3 release note,Eur. Phys. J. C84(2024), no. 10 1053, [arXiv:2312.05175]

2024 arXiv
[69]

JetToyHI GitHub repository

JetToyHI, “JetToyHI GitHub repository.”https://github.com/mverwe/JetToyHI, 2025. Accessed: (07.03.2025). – 30 –

2025
[70]

H. A. Andrews et al.,Novel tools and observables for jet physics in heavy-ion collisions,J. Phys. G47(2020), no. 6 065102, [arXiv:1808.03689]

2020 arXiv
[71]

Hughes, A

C. Hughes, A. C. Oliveira Da Silva, and C. Nattrass,Model studies of fluctuations in the background for jets in heavy ion collisions,Phys. Rev. C106(2022), no. 4 044915, [arXiv:2005.02320]. [72]DELPHES 3Collaboration, J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lema...

2022 arXiv
[73]

Cacciari, G

M. Cacciari, G. P. Salam, and G. Soyez,The anti-kt jet clustering algorithm,JHEP04 (2008) 063, [arXiv:0802.1189]

2008 arXiv
[74]

Cacciari, G

M. Cacciari, G. P. Salam, and G. Soyez,FastJet User Manual,Eur. Phys. J. C72(2012) 1896, [arXiv:1111.6097]

2012 arXiv
[75]

OmniFold GitHub repository

A. Andreassen, P. T. Komiske, E. M. Metodiev, B. Nachman, and J. Thaler, “OmniFold GitHub repository.”https://github.com/hep-lbdl/OmniFold, 2025. Accessed: (07.03.2025)

2025
[76]

Mehtar-Tani, A

Y. Mehtar-Tani, A. Soto-Ontoso, and K. Tywoniuk,Dynamical grooming of QCD jets, Phys. Rev. D101(2020), no. 3 034004, [arXiv:1911.00375]

2020 arXiv
[77]

Caucal, A

P. Caucal, A. Soto-Ontoso, and A. Takacs,Dynamical Grooming meets LHC data,JHEP07 (2021) 020, [arXiv:2103.06566]

2021 arXiv
[78]

A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler,Soft Drop,JHEP05(2014) 146, [arXiv:1402.2657]

2014 arXiv
[79]

F. A. Dreyer, L. Necib, G. Soyez, and J. Thaler,Recursive Soft Drop,JHEP06(2018) 093, [arXiv:1804.03657]

2018 arXiv
[80]

Thaler and K

J. Thaler and K. Van Tilburg,Identifying Boosted Objects with N-subjettiness,JHEP03 (2011) 015, [arXiv:1011.2268]

2011 arXiv
[81]

Caucal, A

P. Caucal, A. Soto-Ontoso, and A. Takacs,Dynamically groomed jet radius in heavy-ion collisions,Phys. Rev. D105(2022), no. 11 114046, [arXiv:2111.14768]

2022 arXiv
[82]

Wang, J.-W

L. Wang, J.-W. Kang, Q. Zhang, S. Shen, W. Dai, B.-W. Zhang, and E. Wang,Jet Radius and Momentum Splitting Fraction with Dynamical Grooming in Heavy-Ion Collisions,Chin. Phys. Lett.40(2023), no. 3 032101, [arXiv:2211.13674]

2023 arXiv
[83]

Cunqueiro, D

L. Cunqueiro, D. Pablos, A. Soto-Ontoso, M. Spousta, A. Takacs, and M. Verweij,Isolating perturbative QCD splittings in heavy-ion collisions,Phys. Rev. D110(2024), no. 1 014015, [arXiv:2311.07643]. [84]ALICECollaboration, S. Acharya et al.,Search for quasi-particle scattering ...

2024 arXiv
[89]

Chollet et al., “Keras.”https://keras.io, 2015

F. Chollet et al., “Keras.”https://keras.io, 2015. [90]CMSCollaboration,A new method for correcting the substructure of multi-prong jets using Lund jet plane reweighting in the CMS experiment, tech. rep., CERN, Geneva, 2025. [91]CMSCollaboration, A. M. Sirunyan et al.,Study of...

2018 arXiv
[97]

Haake and C

R. Haake and C. Loizides,Machine Learning based jet momentum reconstruction in heavy-ion collisions,Phys. Rev. C99(2019), no. 6 064904, [arXiv:1810.06324]

2019 arXiv
[98]

P. T. Komiske, E. M. Metodiev, and J. Thaler,Energy Flow Networks: Deep Sets for Particle Jets,JHEP01(2019) 121, [arXiv:1810.05165]

2019 arXiv
[99]

P. T. Komiske, S. Kryhin, and J. Thaler,Disentangling quarks and gluons in CMS open data,Phys. Rev. D106(2022), no. 9 094021, [arXiv:2205.04459]

2022 arXiv
[100]

D. Ba, A. S. Dogra, R. Gambhir, A. Tasissa, and J. Thaler,SHAPER: can you hear the shape of a jet?,JHEP06(2023) 195, [arXiv:2302.12266]

2023 arXiv
[101]

Athanasakos, A

D. Athanasakos, A. J. Larkoski, J. Mulligan, M. Płoskoń, and F. Ringer,Is infrared-collinear safe information all you need for jet classification?,JHEP07(2024) 257, [arXiv:2305.08979]

2024 arXiv
[102]

Maier, S

B. Maier, S. M. Narayanan, G. de Castro, M. Goncharov, C. Paus, and M. Schott,Pile-up mitigation using attention,Mach. Learn. Sci. Tech.3(2022), no. 2 025012, [arXiv:2107.02779]

2022 arXiv
[103]

Quétant, J

G. Quétant, J. A. Raine, M. Leigh, D. Sengupta, and T. Golling,Generating variable length full events from partons,Phys. Rev. D110(2024), no. 7 076023, [arXiv:2406.13074]

2024 arXiv
[104]

Algren, C

M. Algren, C. Pollard, J. A. Raine, and T. Golling,Variational inference for pile-up removal at hadron colliders with diffusion models,arXiv:2410.22074. – 32 –

arXiv
[105]

Torbunov, Y

D. Torbunov, Y. Huang, M. Lin, Y. Ren, Y. Go, T. Rinn, H. Yu, B. Viren, and J. Huang, Effectiveness of denoising diffusion probabilistic models for fast and high-fidelity whole-event simulation in high-energy heavy-ion experiments,Phys. Rev. C110(2024), no. 3 034912, [arXiv:24...

2024 arXiv
[106]

Steffanic, C

P. Steffanic, C. Hughes, and C. Nattrass,Separating signal from combinatorial jets in a high-background environment,Phys. Rev. C108(2023), no. 2 024909, [arXiv:2301.09148]

2023 arXiv
[107]

Mengel, P

T. Mengel, P. Steffanic, C. Hughes, A. C. O. Da Silva, and C. Nattrass,Multiplicity Based Background Subtraction for Jets in Heavy Ion Collisions,arXiv:2402.10945

arXiv
[108]

Stewart and J

D. Stewart and J. Putschke,Neural network biased corrections: Cautionary study in background corrections for quenched jets,arXiv:2412.15440

arXiv
[109]

Bierlich, P

C. Bierlich, P. Ilten, T. Menzo, S. Mrenna, M. Szewc, M. K. Wilkinson, A. Youssef, and J. Zupan,Describing hadronization via histories and observables for Monte-Carlo event reweighting,SciPost Phys.18(2025), no. 2 054, [arXiv:2410.06342]

2025 arXiv
[110]

Cranmer, J

K. Cranmer, J. Brehmer, and G. Louppe,The frontier of simulation-based inference, Proceedings of the National Academy of Science117(Dec., 2020) 30055–30062, [arXiv:1911.01429]

2020 arXiv
[111]

Adye,Unfolding algorithms and tests using RooUnfold, inPHYSTAT 2011, (Geneva), pp

T. Adye,Unfolding algorithms and tests using RooUnfold, inPHYSTAT 2011, (Geneva), pp. 313–318, CERN, 2011.arXiv:1105.1160

2011 arXiv
[112]

Brenner, R

L. Brenner, R. Balasubramanian, C. Burgard, W. Verkerke, G. Cowan, P. Verschuuren, and V. Croft,Comparison of unfolding methods using RooFitUnfold,Int. J. Mod. Phys. A35 (2020), no. 24 2050145, [arXiv:1910.14654]

2020 arXiv
[113]

Huetsch et al.,The landscape of unfolding with machine learning,SciPost Phys.18 (2025), no

N. Huetsch et al.,The landscape of unfolding with machine learning,SciPost Phys.18 (2025), no. 2 070, [arXiv:2404.18807]

2025 arXiv
[114]

Milton, V

R. Milton, V. Mikuni, T. Lee, M. Arratia, T. Wamorkar, and B. Nachman,Tools for unbinned unfolding,JINST20(2025), no. 05 P05034, [arXiv:2503.09720]. – 33 –

2025 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [27]

Andreassen, P

A. Andreassen, P. T. Komiske, E. M. Metodiev, B. Nachman, A. Suresh, and J. Thaler, Scaffolding Simulations with Deep Learning for High-dimensional Deconvolution, in9th International Conference on Learning Representations, 5, 2021.arXiv:2105.04448

arXiv 2021

[2] [1]

G. P. Salam,Towards Jetography,Eur. Phys. J. C67(2010) 637–686, [arXiv:0906.1833]

arXiv 2010

[3] [2]

A. J. Larkoski, I. Moult, and B. Nachman,Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning,Phys. Rept.841(2020) 1–63, [arXiv:1709.04464]

arXiv 2020

[4] [3]

Marzani, G

S. Marzani, G. Soyez, and M. Spannowsky,Looking inside jets: an introduction to jet substructure and boosted-object phenomenology, vol. 958. Springer, 2019. – 26 – 0.9 1.0 1.1 OF-HI ratio to truth Poisson bootstrap (BS) Direct unfolding 250 450 650 pT [GeV] 0.9 1.0 1.1 OF-HI stat. unc. ratio to truth statistical uncertainty F T 0.9 1.0 1.1 Truth stat. unc...

2019

[5] [4]

Kogler et al.,Jet Substructure at the Large Hadron Collider: Experimental Review,Rev

R. Kogler et al.,Jet Substructure at the Large Hadron Collider: Experimental Review,Rev. Mod. Phys.91(2019), no. 4 045003, [arXiv:1803.06991]

arXiv 2019

[6] [5]

d’Enterria,Jet quenching,Landolt-Bornstein23(2010) 471, [arXiv:0902.2011]

D. d’Enterria,Jet quenching,Landolt-Bornstein23(2010) 471, [arXiv:0902.2011]

arXiv 2010

[7] [6]

Connors, C

M. Connors, C. Nattrass, R. Reed, and S. Salur,Jet measurements in heavy ion physics, Rev. Mod. Phys.90(2018) 025005, [arXiv:1705.01974]

arXiv 2018

[8] [7]

Cunqueiro and A

L. Cunqueiro and A. M. Sickles,Studying the QGP with Jets at the LHC and RHIC,Prog. Part. Nucl. Phys.124(2022) 103940, [arXiv:2110.14490]

arXiv 2022