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How to GAN away Detector Effects

Marco Bellagente, Anja Butter, Gregor Kasieczka, Tilman Plehn, Ramon Winterhalder

arXiv:1912.00477v4hep-phcs.LG

TL;DR

Practical inversion of LHC Monte Carlo simulations remains approximate, limiting quantitative interpretation in hard-process terms. The paper uses conditional generative networks to invert detector effects; its FCGAN reproduces key invariant-mass peak features to about 90% and handles tested phase-space differences.

  • Problem

    Practical Monte Carlo inversion requires approximations, limiting access to hard-process likelihood ratios and perturbative-QCD observables.

    Source: §1 · p. 2

  • Method

    The paper trains a fully conditional GAN on paired parton-level and detector-level events to invert fast detector simulation, using MMD to compare predefined distributions.

    Source: §2 · pp. 3–4, §3 · p. 7

  • Results

    About 90%: the FCGAN reproduces the invariant W-mass peak position, width, and shape, and reconstructs tested pT,jj patterns under jet cuts.

    Source: §3 · pp. 8–9

  • Takeaways & Limitations

    The results illustrate that fully conditional generative networks can statistically invert Monte Carlo simulations and reconstruct parton-level information from measured events.

    Source: §1 · p. 2, §3 · p. 8

    Detector unfolding to a hard process is model-dependent because it requires a model hypothesis for the parton-level and detector-level events.

    Source: §2 · p. 3

Abstract

from arXiv · show

LHC analyses directly comparing data and simulated events bear the danger of using first-principle predictions only as a black-box part of event simulation. We show how simulations, for instance, of detector effects can instead be inverted using generative networks. This allows us to reconstruct parton level information from measured events. Our results illustrate how, in general, fully conditional generative networks can statistically invert Monte Carlo simulations. As a technical by-product we show how a maximum mean discrepancy loss can be staggered or cooled.

1 Introduction

The LHC simulation chain provides efficient first-principles predictions, but practical inversion remains approximate and limits quantitative interpretation in hard-process terms. The paper proposes GAN-based Monte Carlo inversion, including a fully conditional GAN for detector effects that preserves local structures during unfolding.

1 Introduction

  • The LHC simulation chain runs from perturbative-QCD hard processes through showering, fragmentation, hadronization, and detector simulation, using efficient Monte Carlo techniques.Source: §1 · p. 2
  • Practical inversion of that chain remains approximate, limiting access to hard-process likelihood ratios and straightforward interpretation through perturbative-QCD observables.Source: §1 · p. 2
  • GANs are proposed to invert Monte Carlo simulations, with a fully conditional GAN introduced for fast detector-simulation inversion.Source: §1 · p. 2
  • The approach is not intended to combine detector unfolding with optimized inference, and is also discussed for direct QCD comparisons and advanced techniques such as the matrix element method.Source: §1 · p. 2
  • The FCGAN is presented as an example for understanding direct data–simulation comparisons, with preserved local structures supporting a large degree of model independence in unfolding.Source: §1 · p. 2

2 GAN unfolding

The section tests whether generative networks can statistically invert detector simulation to recover parton-level information. A naive GAN reproduces distributions when training and test samples are statistically equivalent, but fails when unfolding restricted phase space.

2 GAN unfolding

  • Unfolding detector effects requires a model hypothesis and is meaningful only for sufficiently large event samples.The passage illustrates the hypothesis with a detector-broadened Z peak whose preferred invariant mass is the parton-level mZ.Source: §2 · p. 3
  • The setup maps batches of detector-level events to parton-level events, while a discriminator distinguishes generated samples from parton-level target samples.The example assumes a correspondence between hard partons and hadronic final states reconstructed with a jet algorithm.Source: §2 · pp. 3–4
  • The generator loss can include maximum mean discrepancy (MMD) to compare predefined distributions, including intermediate-particle invariant mass; its kernel width is inefficient early in training when generated masses are nearly random.The MMD loss is used instead of MMD squared to enhance model sensitivity.Source: §2 · pp. 4–5
  • The GAN-inverted pT,j1 and mjj distributions agree well with parton-level truth when evaluated on statistically independent but simulation-wise identical detector-level samples.The comparison benchmarks statistical inversion of the detector effect.Source: Figure 3 · p. 5, §2 · p. 6
  • GAN training uses independently chosen batches from parton-level and detector-level samples, so event-by-event matched samples are not strictly required.Within memory limits, larger batches reduce statistical uncertainties and can improve training.Source: §2 · p. 6
  • When trained on full phase space but tested on restricted phase space, the naive GAN strongly sculpts the GANned pT,j distribution and no longer reliably unfolds the sample.The two test cuts retain 88% and 38% of events, respectively.Source: §2 · p. 6, Figure 4 · p. 7

3 Fully conditional GAN

The fully conditional GAN (FCGAN) uses random input while conditioning on detector-level events, aiming to preserve the statistical nature of detector inversion. It reproduces parton-level distributions across several train/test phase-space mismatches, with a boundary when low-transverse-momentum events are removed.

3 Fully conditional GAN

  • Random numbers and detector-level events condition the generator’s parton-level output, while training requires event-by-event detector/parton matching.The discriminator is also conditioned on detector-level data.Source: §3 · pp. 7–8, Figure 5 · p. 8
  • FCGAN inversion reproduces the full-phase-space parton-level distributions better than the naive GAN, eliminating its systematic tail-rate underestimation.The reconstructed W-mass peak position, width, and shape are reproduced to about 90%.Source: §3 · p. 8, Figure 6 · p. 9
  • With training on the full sample, FCGAN reconstructs parton-level patterns under restricted test cuts, including when only 38% of events pass.The pT,jj distribution is reported to reproduce the true parton-level patterns perfectly.Source: §3 · p. 9, Figure 7 · p. 10
  • For the harsher Cut III sample, comprising 14% of events, the FCGAN reproduces the true distributions extremely well despite the reduced test fraction.The passage reports that the result appears largely insensitive to the training/test fraction correspondence.Source: §3 · pp. 9–10, Figure 8 · p. 11
  • Cut IV retains 39% of events but removes low-pT events; this breaks mjj reconstruction, while other shown kinematic variables remain stable.The authors attribute the mass-distribution failure to their nonconditional MMD loss implementation.Source: §3 · p. 10, Figure 8 · p. 11
  • Across two-dimensional distributions, FCGAN closely reproduces parton-level truth, with larger relative deviations only at low Ej1 where training events are extremely sparse.Source: §3 · p. 11

4 New physics injection

The section tests whether an FCGAN trained on Standard Model data can unfold a sample containing a 10% W′ signal. It reproduces the signal’s mass peak while overestimating its width, supporting the authors’ claim that the mapping retains local phase-space structure.

4 New physics injection

  • The test asks whether an FCGAN trained on Standard Model events can map local phase-space structures when applied to an alternative hypothesis.The alternative is a triplet-extension W′ signal injected into the test data.Source: §4 · pp. 11–12
  • The Standard-Model-trained FCGAN reproduces the injected W′ mass peak and its central position, but overestimates the width.The test sample combines 90% Standard Model events with 10% W′ events; the W′ mass is 1.3 TeV and its width is 15 GeV.Source: §4 · pp. 12–13, Figure 10 · p. 13
  • Leading-jet and lepton transverse-momentum distributions, as well as the hadronic W-boson invariant mass, remain essentially identical between truth and FCGAN output.The hadronic W mass also serves as a stability check for training and testing.Source: §4 · p. 13
  • The injected W′ peak is a localized structure in the full phase space, not merely a one-dimensional feature, which the authors associate with model independence.The test deliberately uses a narrow W′ width, ΓW′/MW′ ∼1%.Source: §4 · pp. 12–13

5 Outlook

The paper demonstrates statistical inversion of a fast detector simulation with a fully conditional GAN, and finds that the approach handles differing samples and injected local signals within the tested setup. It presents OmniFold as a complementary route to extracting hard-process information.

5 Outlook

  • A fully conditional GAN can invert the Delphes fast detector simulation; a naive GAN works extremely well when training and test samples are similar, without event-by-event matching.The example process is WZ → (jj)(ℓℓ) at the LHC.Source: §5 · p. 14
  • When training and test samples differ significantly, the FCGAN gives more stable tail predictions and can be applied to smaller phase-space regions, including cuts in main kinematic features.The approach eventually breaks in this setup because the MMD loss for narrow Breit-Wigner propagators is not conditional.Source: §5 · p. 14
  • The network reproduces an injected new-physics signal as a local phase-space structure, which the authors connect to structured mapping between linked phase spaces.Source: §5 · p. 14
  • FCGAN inverts the Delphes simulation, whereas OmniFold iteratively translates both sides of matched simulated events toward measured events; both aim to extract hard-process information.The authors state that both approaches assume understanding the relation between perturbative QCD predictions and Monte Carlo events.Source: Figure 11 · p. 14, §5 · p. 15

A Performance

The appendix compares FCGAN-inverted kinematics with parton-level truth and Delphes events, finding closer reconstruction with FCGAN. The migration matrix also shows narrow diagonal correlations between true and reconstructed parton-level kinematics.

A Performance

  • For all shown distributions, especially reconstructed W mass, FCGAN reconstruction is significantly closer to parton-level truth than Delphes events.Normalized deviations have narrow peaks around zero, with widths in the ±10% range for jet momenta and narrower for leptons.Source: A Performance · pp. 16–17, Figure 12 · p. 16
  • The migration matrix shows narrow diagonal lines between true and reconstructed parton-level kinematics.Source: A Performance · p. 17, Figure 13 · p. 17

B Staggered vs cooling MMD

The appendix addresses weak early-training gradients in the MMD loss by comparing multiple-kernel, cooling-kernel, and augmented-kernel implementations. Cooling adapts kernel width to the generated mass distribution, while augmentation adds detector-level invariant-mass information.

B Staggered vs cooling MMD

  • A fixed kernel width chosen to match an on-shell particle’s width gives little to no gradient when generated masses are initially broad and nearly uniform.In this regime, squared sample distances greatly exceed the kernel-width squared.Source: B Staggered vs cooling MMD · p. 17
  • Multiple kernels with decreasing widths let wide kernels drive early training, but only kernels near the evolving generated-mass width provide a non-negligible gradient.Source: B Staggered vs cooling MMD · p. 17
  • A cooling kernel shrinks from a large initial width toward the particle width; setting its width to a fixed fraction of the generated-mass standard deviation avoids hand-tuning the cooling schedule.The standard deviation can be replaced by measures such as full width at half maximum, and the tests find performance largely insensitive to the chosen fraction.Source: B Staggered vs cooling MMD · pp. 17–18
  • Augmented MMD compares generated and true invariant masses together with detector-level invariant mass, adding physical information without making the loss conditional.Figure 14 compares the invariant-mass distributions from the different MMD implementations.Source: B Staggered vs cooling MMD · p. 18, Figure 14 · p. 18
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