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This paper demonstrates that machine-learning anomaly detectors trained without labeled signal examples can pull rare boosted top quarks out of 138 fb⁻¹ of LHC collisions, and that five such model-agnostic methods all exceed the sensitivity

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2026-08-03 14:22 UTC pith:WZVWKJQZ

load-bearing objection A careful, genuinely useful CMS methods paper with a real data-level comparison of modern anomaly detectors; the only notable gap is the missing closure test for mass sculpting in the sideband-based methods. the 2 major comments →

arxiv 2512.20395 v2 pith:WZVWKJQZ submitted 2025-12-23 hep-ex

Machine-learning techniques for model-independent searches in dijet final states

CMS Collaboration This is my paper
classification hep-ex
keywords anomaly detectionweakly supervised learningjet substructuredijet resonance searchmodel-agnostic searchlikelihood ratiovariational autoencodertop quark tagging
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that a new class of machine-learning searches can find rare, unexpected objects in collider data without ever being shown an example of the signal. Five anomaly-detection schemes, trained only on unlabeled collisions and on background estimates from mass sidebands, all outperform a simple inclusive scan for representative new-physics signals in 13 TeV data. As a proof in real data, a weakly supervised tagger separates hadronically decaying boosted top quarks—roughly 1% of the sample—from overwhelming background, reaching a significance improvement only about 15% below a fully supervised classifier using the same inputs. If true, model-agnostic anomaly detection becomes a practical tool for searches at the Large Hadron Collider, since it does not require a specific theory model to be written down in advance.

Core claim

The paper's central claim is that machine-learning anomaly detection can serve as a practical, model-independent search strategy for new particles decaying to a pair of large-radius jets. Using 138 fb⁻¹ of 13 TeV proton-proton collisions, the authors deploy five methods—a variational autoencoder with quantile regression, two weakly supervised classifiers (CWoLa Hunting and Tag N' Train), a generative-model-based classifier (CATHODE, plus a b-tagging variant), and a semi-supervised method that uses signal priors (QUAK). Every anomaly-detection method is shown to improve sensitivity over an inclusive resonance search for a 2-prong and a 3-prong benchmark signal, while no single method dominate

What carries the argument

The load-bearing mechanism is the unlabeled likelihood-ratio estimator. Under weak supervision, a classifier is trained to tell apart events from the signal region (data that may contain signal) and events from background sidebands in the dijet invariant mass. Because the signal-region density is a mixture of background and signal, the learned score is monotonically related to the optimal signal-to-background ratio, so no signal labels are needed. To prevent the classifier from learning mass-dependent features and sculpting a fake bump, the methods reweight jet transverse momentum, combine per-jet scores through percentiles, use quantile regression for the autoencoder approach, or interpolat

Load-bearing premise

The sidebands are a good model for the signal-region background: specifically, the jet-substructure features used by the classifier must be statistically independent of the mass variable after the decorrelation measures, otherwise the tagger can sculpt an artificial bump and create a false signal.

What would settle it

Run the weakly supervised tagger on a background-only control dataset (for example the high-rapidity-difference sideband) and inspect the selected-event mass distribution: a resonant bump there would mean the decorrelation failed. A complementary decisive test is to inject a known small signal into simulated collisions, retrain the tagger exactly as described, and verify that the measured signal-selection efficiency and final significance improvement over the inclusive search match the quoted values; if the tagger does not beat the inclusive search for both benchmark signals, the paper's centr

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A single search can cover a wide range of unknown resonance masses by training the tagger in overlapping mass windows rather than committing to one theory.
  • Weakly supervised anomaly detection works on real data, not only simulation: recovering boosted top quarks in roughly 1% abundance validates the approach on actual collision events.
  • Because anomaly scores across methods are weakly correlated, combining selections from different methods is a promising route to higher generic sensitivity, as the paper itself points out.
  • Input-feature choice, not just the algorithm, sets the achievable gain; uninformative features can actively hurt weakly supervised classifiers, so feature curation is part of the method.
  • A model-agnostic tagger can be repurposed from a resonant dijet search to a nonresonant pair-production search by switching the mass variable and reusing the same weakly supervised machinery.

Where Pith is reading between the lines

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

  • The same sideband-plus-generative-model recipe could be reused for nonresonant searches in other final states, where no sharp invariant-mass peak exists; the top-quark validation is implicitly a proof of concept for such searches.
  • Combining the weakly correlated anomaly scores—for example through a simple ensemble or a learned fusion—is a direct next step the paper does not develop; it could recover signals that any single method misses.
  • The released simulated dataset with full substructure and systematic variations lets other researchers benchmark new taggers against these five baselines, accelerating progress without needing detector access.
  • If these techniques generalize to higher-pileup running conditions, the same model-agnostic framework could become a standard first-pass search run before model-specific analyses are performed.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper describes the five machine-learning anomaly-detection techniques used in the CMS model-agnostic dijet search of Ref. [6]: VAE-QR (unsupervised), CWoLa Hunting, TNT, and CATHODE (weakly supervised), and QUAK (semi-supervised). Using 138 fb^-1 of 13 TeV CMS data and simulation, the paper compares the methods' sensitivity on a suite of BSM benchmark signals, studies complementarity of their anomaly scores, and investigates the role of input-feature choice. It also validates weakly supervised anomaly detection in real data by identifying boosted hadronically decaying top quarks, where the best model achieves a significance improvement only about 15% below a fully supervised classifier. A central methodological requirement is that the selection must not sculpt the m_jj spectrum; the paper describes explicit decorrelation countermeasures for the weakly supervised methods.

Significance. If the results hold, the paper provides one of the first multi-method, model-agnostic anomaly-detection studies on LHC collision data, with a compelling real-data validation. The strengths are the use of data sidebands for training, five-fold cross-validation, explicit decorrelation measures, a detailed signal-efficiency uncertainty procedure via repeated injection and selective retraining, a public companion dataset on Zenodo, and an honest comparison against supervised classifiers. The top-quark identification result in Section 7 is significant and supports the viability of weak supervision in a realistic hadronic channel.

major comments (2)
  1. [Section 5.2.1 and 5.2.2] The paper asserts that the per-jet pT reweighting 'has been shown to mitigate mass sculpting effects' (Section 5.2.1), but no supporting evidence or citation is provided in this manuscript. For CWoLa Hunting and TNT, no background-only closure test is shown demonstrating that the m_jj distribution after the anomaly selection is statistically consistent with the inclusive QCD background. Figure 5 provides such a test only for VAE-QR. Since the weakly supervised methods rely on m_jj sidebands to model the background, residual feature-m_jj correlations could cause the classifier to sculpt an artificial bump. This is a load-bearing point for the claim in Section 6.1 that all anomaly detection methods increase sensitivity. Please add a closure test (e.g., the selected m_jj spectrum compared to the inclusive spectrum in simulated background-only events) or explicitly cite the location of such
  2. [Section 5.2.3] CATHODE's background model is a conditional normalizing flow trained on sidebands and interpolated into the signal region. The manuscript states that this correctly accounts for correlations between x and m_jj, but no validation of the interpolation is shown. In particular, there is no closure test demonstrating that the generated background samples in the SR match observed data or an independent background simulation, nor that the selected m_jj spectrum after applying CATHODE's anomaly score is unchanged. Such a test would be analogous to Fig. 5 for VAE-QR and is needed to support the method's use in the resonant search.
minor comments (5)
  1. [Section 5.2.1] The phrase 'has been shown to mitigate mass sculpting effects' needs a reference or a brief explanation of the supporting study; as written it is an unsubstantiated assertion.
  2. [Section 5.3] The definition of the signed L5 norm, ||x||_5 = (x1^5 + ... + x6^5)^{1/5}, is ambiguous when the normalizing-flow NLL scores can be negative. Please specify whether absolute values are taken or clarify the handling of negative inputs.
  3. [Section 7.2] Typo: 'In the t t the signal, separate contributions...' should read 'In the tt signal, separate contributions...'.
  4. [Figure 9] The horizontal axis extends to negative cross sections. If this is intentional to show the zero-cross-section behavior, please add a note; otherwise consider starting the axis at zero for clarity.
  5. [Section 8] The summary states that the tt study 'constitutes a validation of resonant anomaly detection in collider data.' The tt validation uses a nonresonant split strategy applied to one jet's mass while scoring the other jet, explicitly avoiding sculpting. It does not exercise the m_jj sideband interpolation central to the resonant dijet search. The wording should be softened to 'validation of weakly supervised anomaly detection' or explicitly distinguish the nonresonant validation from the resonant search.

Circularity Check

0 steps flagged

No significant circularity: methods are benchmarked against injected signals and an independent data-based top-quark validation; QUAK's signal prior is explicitly disclosed and not used to mask model-agnostic claims.

full rationale

I walked the derivation chain of the paper. The central sensitivity claims (Section 6.1) are established by injecting benchmark signals into simulated background and running the full anomaly-detection pipeline, including training, event selection, and signal extraction; this is a genuine test, not a fit renamed as a prediction. The weakly supervised methods (CWoLa Hunting, TNT, CATHODE) do not use signal samples during training, so their improved sensitivity relative to the inclusive search is not forced by construction. QUAK is explicitly labeled semi-supervised and the paper states that targeted searches use the specific signal being tested as a prior, while also showing a generic QUAK variant; this is disclosed oracle-like benchmarking, not a hidden circularity. The data validation in Section 7.2 is independent of the resonant m_jj search: the weak tagger is applied to one randomly assigned jet (J2) while the signal is extracted from the other jet's soft-drop mass (J1), and the result is compared in simulation to a fully supervised classifier trained with the same features. The claim that the best weak model is only ~15% worse than the supervised classifier is therefore an external benchmark, not an equivalence to training inputs. The VAE-QR quantile regression is designed to produce a constant selection fraction; the resulting similarity of the m_jj shapes is a consistency check of that construction, not a prediction claimed as derived from first principles. Self-citations to Ref. [6] provide the parent search context and some fitting/limit-setting details, but no load-bearing uniqueness or ansatz is imported from that reference, and the method descriptions and top-quark validation are self-contained in this manuscript. The paper does state the sideband-decorrelation requirement for weak supervision and notes that the pT reweighting 'has been shown to mitigate mass sculpting effects' without showing the closure test in this paper; that is a validation gap and a potential correctness risk, but it is not a circular derivation. No step in the paper reduces a claimed result to its own input by definition or by self-citation.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The core methodological claims rest primarily on the assumption that sideband data can model the signal-region background after decorrelation; this is an explicitly acknowledged standard assumption in weak supervision. Hand-chosen selection thresholds and QUAK prior grouping affect absolute sensitivity but not the qualitative conclusions (improvement over inclusive, complementarity, near-supervised performance). No new physical entities are introduced.

free parameters (4)
  • Anomaly-score selection efficiencies per signal region = 1% (SRs up to B3), 3% (A4–B5), 5% (above); 0.1% in ttbar validation
    Hand-chosen to ensure sufficient event counts for the m_jj fit; not fitted to optimize a target result, but affects the absolute sensitivity in Section 6.1.
  • Quantile regression thresholds q = 10%, 5%, 1%
    Chosen for VAE-QR to define retained event fractions; the model-independent fit uses q<10% and limit-setting uses three categories. Not optimized against the central conclusions.
  • QUAK signal-prior grouping daughter masses = 80, 170, 400 GeV in six combinations
    Hand-chosen grouping of benchmark signals (Table 4) to define six normalizing-flow priors; affects QUAK sensitivity but not the model-agnostic conclusions.
  • Signal mass windows for ttbar validation = m_SD windows 65–150, 105–220, 145–250 GeV
    Selected without optimization ('These selection criteria were not optimized' in Section 7.1); the 105–220 and 145–250 windows align with the top mass and yield the successful tagging.
axioms (3)
  • domain assumption The background-only distribution of jet-substructure features in the signal region can be accurately estimated from m_jj sidebands (after reweighting or conditional generation).
    All weakly supervised methods assume feature transportability from sidebands to SR; if false, classifiers sculpt m_jj and create spurious signals. Stated in Section 5.2: 'these can serve as a good model for the background if the x features are statistically independent (decorrelated) from m_jj.'
  • domain assumption The simulated signal and background Monte Carlo samples accurately describe the physics and detector response.
    Used throughout Sections 4–6 for performance evaluation and benchmark sensitivities; a standard assumption in LHC analyses.
  • domain assumption Neural network generalization: models trained on finite samples generalize to the full population (i.i.d. assumption).
    All ML methods rely on standard supervised/unsupervised learning assumptions; implicit in training on sidebands/data and evaluating on signal regions.

pith-pipeline@v1.3.0-alltime-deepseek · 57084 in / 11186 out tokens · 119170 ms · 2026-08-03T14:22:48.799786+00:00 · methodology

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read the original abstract

Anomaly detection methods used in a recent search for new phenomena by CMS at the CERN LHC are presented. The methods use machine learning to detect anomalous jets produced in the decay of new massive particles without depending on a specific theory model. The effectiveness of these approaches in enhancing sensitivity to various signal samples is studied and compared using data collected in proton-proton collisions at a center-of-mass energy of 13 TeV. In an example analysis, the capabilities of anomaly detection methods are further demonstrated by identifying large-radius jets consistent with Lorentz-boosted hadronically decaying top quarks in a model-agnostic framework.

Figures

Figures reproduced from arXiv: 2512.20395 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: Diagram of the A → BC → 2 jets signal topology targeted in this work. The particle A is produced in a collision between two protons. Reproduced from Ref. [6]. The BSM particles (noted A) considered in this paper are not observed directly in the detectors. Instead, they decay almost instantly into a pair of lighter particles B and C, which in turn decay into SM particles, as shown in [PITH_FULL_IMAGE:figur… view at source ↗
Figure 2
Figure 2. Figure 2: The VAE architecture used for jet anomaly detection. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Jet pT (left) and η (right) distributions before and after resampling jets from the 2 < |∆ηjj| < 2.5 sideband (green) to match the distribution in the signal region (blue). The distributions of resampled jets are shown in orange. Histograms are normalized to unity. The details are given in the text [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Quality of jet constituent pT reconstruction for SM background jets (upper row), jets from a W′ → B ′ t → bZt decay (middle row), and jets from an X → YY′ → 4q decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient R between the input and output is also shown [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Simulated dijet invariant mass spectrum after selecting events based on the score of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A schematic showing the training algorithm for [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The three main steps of CATHODE. a) Given a signal mass hypothesis, mjj is used to define the signal region in which the signal would be localized. b) A background estimate for the input features x is obtained from events outside the signal region by training a generative model and interpolating it. c) A weakly supervised classifier is trained to distinguish between the interpolated background and the obse… view at source ↗
Figure 8
Figure 8. Figure 8: Signal selection efficiency of the weakly supervised classifier in the [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: CATHODE-b achieves the best results because, unlike TNT and CWoLa Hunting, it combines information from both jets to tag anomalous events. Among the per-jet methods, TNT outperforms CWoLa Hunting due to its additional preselection criteria. 6.2 Anomaly score correlations We also explore the correlation between the anomaly scores of the different methods on these two benchmark signals as well as background… view at source ↗
Figure 9
Figure 9. Figure 9: The p-values as a function of the injected signal cross sections for the different anal￾ysis procedures for two different signals. The upper panel shows results for the 2-prong X → YY′ → 4q signal with mX = 3 TeV and mY = mY′ = 170 GeV, while the lower panel shows results for the 3-prong W′ → B ′ t → bZt signal with mW′ = 3 TeV and mB′ = 400 GeV. Significance values larger than 7 standard deviations (σ) ar… view at source ↗
Figure 10
Figure 10. Figure 10: The p-values as a function of the injected signal cross sections for the different analy￾sis procedures modified to use a common set of input features, for two different signals: (upper) the 2-prong X → YY′ → 4q signal with mX = 3 TeV and mY = mY′ = 170 GeV, and (lower) 3-prong W′ → B ′ t → bZt signal with mW′ = 3 TeV and mB′ = 400 GeV. Significance values larger than 7 standard deviations (σ) are denoted… view at source ↗
Figure 11
Figure 11. Figure 11: Anomaly score correlations of different methods on the background sample. Scores [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Anomaly score correlations of different methods on the X [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Anomaly score correlations of different methods on the W [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Summary plots showing the Pearson correlation coefficient for each pair of anomaly [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Overlap between the events selected using the anomaly detection methods, for the [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Significance improvement obtained from supervised classifiers trained using the [PITH_FULL_IMAGE:figures/full_fig_p031_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Comparison of anomaly detection and supervised classification performance. The [PITH_FULL_IMAGE:figures/full_fig_p032_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Distribution of the J1 soft-drop mass after the basic (left) and b-tagged (right) prese [PITH_FULL_IMAGE:figures/full_fig_p034_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Post-fit plots of the fail (left) and pass (right) regions for the t [PITH_FULL_IMAGE:figures/full_fig_p036_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: A comparison of the top quark identification performance of classifiers trained in [PITH_FULL_IMAGE:figures/full_fig_p037_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Excess characterization for the weakly supervised anomaly detection strategy ap [PITH_FULL_IMAGE:figures/full_fig_p038_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Excess characterization for the weakly supervised anomaly detection strategy ap [PITH_FULL_IMAGE:figures/full_fig_p040_22.png] view at source ↗

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