Particle-Lund Multimodality in Jet Taggers

Benedikt Maier; Loukas Gouskos

arxiv: 2605.26821 · v1 · pith:URBL3ETUnew · submitted 2026-05-26 · ✦ hep-ph · cs.LG· hep-ex

Particle-Lund Multimodality in Jet Taggers

Loukas Gouskos , Benedikt Maier This is my paper

Pith reviewed 2026-06-29 17:14 UTC · model grok-4.3

classification ✦ hep-ph cs.LGhep-ex

keywords jet taggingLund planetransformermultimodal architectureQCD radiationHiggs taggingtop taggingdi-Higgs

0 comments

The pith

Explicit Lund plane splittings remain complementary to particle constituents in transformer jet taggers for b-jet topologies.

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

The paper tests whether highly expressive transformers already capture hierarchical QCD structure implicitly from raw particle inputs, or whether explicit physics representations add discriminating power. It does so by constructing PLuM, a single transformer that receives both particle constituents and Lund plane splittings projected into a shared latent space and linked by cross-attention. Systematic gains appear only for top-quark and H to bb tagging; no comparable gains occur for H to cc or H to 4q. The result is directly relevant to boosted di-Higgs searches in the four-b final state, where the combined model raises background rejection by 25 percent at a fixed 25 percent signal efficiency.

Core claim

PLuM projects particle constituents and Lund plane splittings into a shared latent space and processes them jointly inside a unified transformer equipped with cross-attention. This architecture produces systematic improvements in top-quark and H to bb tagging while leaving H to cc and H to 4q performance unchanged. The pattern indicates that explicit hierarchical information about b-jet formation supplies discriminating power beyond what particle representations alone encode. At the 25 percent di-Higgs efficiency working point the model therefore achieves 25 percent higher background rejection than the particle-only baseline in the HH(4b) channel.

What carries the argument

PLuM, the multimodal transformer that fuses particle constituents with Lund plane splittings through a shared latent space and cross-attention layers.

If this is right

Top-quark tagging receives a systematic boost from explicit Lund information.
H to bb tagging receives a systematic boost from explicit Lund information.
H to cc and H to 4q tagging receive no comparable boost.
Background rejection in boosted HH(4b) searches rises by 25 percent at 25 percent signal efficiency.

Where Pith is reading between the lines

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

Transformers trained only on particles may leave some hierarchical aspects of b-jet formation under-exploited.
Selective addition of physics representations could be tested on other decay channels or grooming observables.
The topology dependence observed here supplies a diagnostic for which jet features still require explicit encoding.
Similar multimodal fusion might be examined for quark-gluon discrimination or energy correlator inputs.

Load-bearing premise

The measured gains come from the added Lund plane information rather than from extra model capacity, altered training dynamics, or dataset fluctuations.

What would settle it

A particle-only transformer of equal or larger capacity trained on the identical datasets and working points that matches or exceeds PLuM performance on top and H to bb tasks would falsify the claim of complementarity.

Figures

Figures reproduced from arXiv: 2605.26821 by Benedikt Maier, Loukas Gouskos.

**Figure 2.** Figure 2: FIG. 2: Accuracies for the trainings of ParT (red) and PLuM (blue). Top left: top vs. QCD jets; top right: H [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Visualization of example H [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Mean score difference for the same jets evaluated with the best PLuM and, respectively, best ParT models [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

read the original abstract

The Lund plane offers a physics-motivated, hierarchical representation of QCD radiation within jets, while transformer-based taggers have reached state-of-the-art performance by learning directly from raw particle constituents and their pairwise relations. We investigate whether transformers implicitly capture hierarchical QCD structure from constituent-level inputs, or whether explicit physics representations remain complementary. To test this, we introduce PLuM, a multimodal architecture that projects particle constituents and Lund plane splittings into a shared latent space, processing both jointly with a unified transformer. Cross-attention allows the model to probe whether structured QCD information provides discriminating power beyond what particles alone encode. We observe systematic gains for top-quark and $\mathrm{H}\to\mathrm{b}\bar{\mathrm{b}}$ tagging, while finding no comparable improvement for $\mathrm{H}\to\mathrm{c}\bar{\mathrm{c}}$ or $\mathrm{H}\to 4\mathrm{q}$ topologies. This selective enhancement suggests that explicit hierarchical information about b-jet formation remains complementary to raw particle representations even in highly expressive architectures, while other topologies are already well-captured at constituent level. For high-impact LHC analyses such as Lorentz-boosted di-Higgs searches in the four $\mathrm{b}$ quark final state ($\mathrm{H}\mathrm{H}(4\mathrm{b})$), the gains are substantial: at a $25\%$ di-Higgs efficiency working point, PLuM achieves $25\%$ higher background rejection than the baseline. Our results indicate that physically structured representations of QCD radiation retain discriminating value in the transformer era, motivating further study into how different aspects of jet dynamics are encoded by deep learning algorithms.

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.

Desk Editor's Note private letter to a colleague

PLuM shows selective tagging gains from adding Lund plane to particle transformers, but the abstract leaves the source of those gains unclear.

read the letter

The main point is that this paper tests whether explicit Lund-plane splittings still add value once you already have a strong particle-level transformer, and it reports gains for top and bb jets but none for cc or four-quark cases. That selective pattern is the concrete observation.

The work does a clean job of framing the question and describing a multimodal setup that projects both inputs into a shared space and uses cross-attention. Reporting topology-dependent results rather than blanket claims is useful, especially for analyses like boosted HH(4b) where the 25% background-rejection lift at fixed 25% signal efficiency would matter.

The soft spot is the lack of any information on whether the particle-only baseline was matched in parameter count, optimizer schedule, or regularization. Adding a second modality and cross-attention layers increases capacity and changes training dynamics, so the observed difference could come from those factors instead of the Lund information being orthogonal. No ablations or dummy-input controls are mentioned, and the abstract gives no training details, uncertainties, or data-selection criteria. With only the abstract available, it is impossible to judge how much of the result is physics versus architecture.

This is aimed at people who build or use jet taggers for LHC boosted-object searches. A reader who wants to know whether current transformers already saturate the available QCD structure would find the selective result worth seeing, but the current write-up is too thin for strong conclusions.

It deserves peer review so the full manuscript can be checked for capacity controls and statistical robustness.

Referee Report

1 major / 0 minor

Summary. The paper introduces PLuM, a multimodal transformer that projects particle constituents and Lund-plane splittings into a shared latent space and processes them jointly via cross-attention. It reports systematic gains in top-quark and H o bb tagging performance, no comparable gains for H o cc or H o4q, and a concrete 25% improvement in background rejection for HH(4b) at the 25% signal-efficiency working point relative to a particle-only baseline. The central interpretation is that explicit hierarchical QCD information remains complementary to raw constituent representations even in expressive architectures.

Significance. If the reported gains are shown to arise specifically from Lund-plane complementarity rather than from increased model capacity or altered training dynamics, the result would provide evidence that physics-motivated representations retain discriminating power in the transformer era and could inform tagging strategies for boosted di-Higgs analyses. The selective pattern of improvement (present for b-jets, absent for other topologies) is a potentially useful observation if substantiated by controlled experiments.

major comments (1)

[Abstract] Abstract: the 25% background-rejection gain for HH(4b) at 25% efficiency is presented as evidence of Lund complementarity, yet the description of the particle-only baseline does not state whether parameter count, optimizer schedule, or regularization strength were matched to the multimodal PLuM model. Adding cross-attention layers necessarily increases expressivity and changes gradient flow, so the selective improvement could reflect these architectural differences rather than orthogonal physics information.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the baseline comparison. We address the point below and will revise the manuscript to improve clarity on this issue.

read point-by-point responses

Referee: [Abstract] Abstract: the 25% background-rejection gain for HH(4b) at 25% efficiency is presented as evidence of Lund complementarity, yet the description of the particle-only baseline does not state whether parameter count, optimizer schedule, or regularization strength were matched to the multimodal PLuM model. Adding cross-attention layers necessarily increases expressivity and changes gradient flow, so the selective improvement could reflect these architectural differences rather than orthogonal physics information.

Authors: We agree that the abstract should explicitly address the construction of the particle-only baseline to support the interpretation of Lund complementarity. In the full manuscript the particle-only baseline was constructed to have matched total parameter count (by adjusting transformer width and depth), identical optimizer schedule, and the same regularization strength as PLuM; these choices are described in the methods section. Nevertheless, we acknowledge that the abstract does not state this matching. We will revise the abstract to add a clause clarifying that the baselines were matched in parameter count, optimizer schedule, and regularization. We will also add a short sentence in the methods reiterating the matching procedure. These changes directly address the concern that the observed gains could arise from architectural differences rather than the addition of Lund-plane information. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical performance comparison on held-out data

full rationale

The paper reports an empirical ML architecture comparison (PLuM multimodal transformer vs. particle-only baseline) with tagging efficiencies measured on simulated held-out samples. No equations, fitted parameters, or derivations are presented that could reduce the reported gains to a definitional identity or self-referential quantity. The central claim rests on observed performance differences rather than any self-citation chain, ansatz smuggling, or renaming of known results. This is the standard case of a self-contained experimental result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available; the central claim rests on standard assumptions of QCD jet formation and the validity of simulated training samples, with no free parameters or invented entities explicitly introduced in the provided text.

axioms (2)

domain assumption Lund plane splittings encode hierarchical QCD radiation structure that is not fully redundant with raw particle four-momenta
Invoked when the authors interpret the selective performance gains as evidence of complementarity.
domain assumption Simulated samples used for training and evaluation faithfully represent real LHC data for the tagging tasks considered
Standard assumption for all jet-tagging studies; not stated explicitly but required for the reported efficiencies to translate to experiment.

pith-pipeline@v0.9.1-grok · 5818 in / 1483 out tokens · 26150 ms · 2026-06-29T17:14:27.165332+00:00 · methodology

discussion (0)

Reference graph

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