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arxiv: 2512.07420 · v2 · pith:7ZBIHT5Inew · submitted 2025-12-08 · ✦ hep-ph · cs.LG· hep-ex

E-PCN: Jet Tagging with Explainable Particle Chebyshev Networks Using Kinematic Features

Md Raqibul Islam , Adrita Khan , Mir Sazzat Hossain , Choudhury Ben Yamin Siddiqui , Md. Zakir Hossan , Tanjib Khan , M. Arshad Momen , Amin Ahsan Ali
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AKM Mahbubur Rahman
This is my paper

Pith reviewed 2026-05-17 01:01 UTC · model grok-4.3

classification ✦ hep-ph cs.LGhep-ex
keywords jet tagginggraph neural networksexplainable AIkinematic featuresGrad-CAMparticle physicsJetClass datasetchebyshev networks
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The pith

E-PCN classifies jets by building four graphs each weighted by a different kinematic variable and uses Grad-CAM to show angular separation plus transverse momentum drive 76 percent of decisions.

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

The paper introduces the Explainable Particle Chebyshev Network to classify particle jets while making the model's feature use explicit. It represents each jet as four separate graphs, one weighted by angular separation, one by transverse momentum, one by momentum fraction, and one by invariant mass squared. Grad-CAM then measures how much each weighted graph influences the final classification. On the JetClass dataset spanning ten jet types this yields measurable gains over the plain Particle Chebyshev Network and identifies which physical quantities the network actually relies on. A reader would care because collider experiments generate enormous data volumes and physicists need to know whether learned models are using the same kinematic information that traditional physics algorithms employ.

Core claim

E-PCN constructs four graph representations per jet, each weighted by one of angular separation Δ, transverse momentum k_T, momentum fraction z, or invariant mass squared m². Application of Grad-CAM reveals that Δ and k_T together account for approximately 76 percent of classification decisions. On the JetClass dataset with ten signal classes the network reaches 94.67 percent macro-accuracy, 96.78 percent macro-AUC, and 86.79 percent macro-AUPR, improving on the baseline PCN by 2.36 percent, 4.13 percent, and 24.88 percent respectively while supplying physically interpretable attributions.

What carries the argument

Four kinematic-weighted graph representations of each jet together with Grad-CAM attribution, allowing separate measurement of how much each kinematic variable contributes to the output class scores.

If this is right

  • Macro accuracy, AUC, and AUPR all rise relative to the baseline Particle Chebyshev Network on the ten-class JetClass task.
  • Angular separation receives 40.72 percent and transverse momentum 35.67 percent of the total attribution weight.
  • The remaining 24 percent of decisions are attributed to momentum fraction and invariant mass squared combined.
  • The learned representations remain directly tied to measurable particle kinematics rather than opaque latent embeddings.
  • The same four-graph construction can be applied to other graph neural networks used for jet substructure analysis.

Where Pith is reading between the lines

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

  • Physicists could use the same weighting scheme to test whether traditional jet algorithms already capture the same dominant variables that the network discovers.
  • If the attributions remain stable across detector variations, the approach might reduce the number of kinematic inputs needed for future real-time triggers.
  • Similar four-graph constructions could be tested on other high-energy datasets to see whether the 76 percent dominance of angular and transverse momentum variables generalizes.
  • Direct comparison of Grad-CAM maps against permutation-based feature importance would provide an independent check on the explanation quality.

Load-bearing premise

Grad-CAM attributions computed on the four kinematic-weighted graphs accurately reflect the causal importance of those variables inside the model's decision process rather than artifacts of the explanation method.

What would settle it

An ablation that removes angular separation and transverse momentum features while keeping the other two, then checks whether the measured performance drop is at least three times larger than the drop obtained by removing only momentum fraction and invariant mass.

read the original abstract

The identification and classification of collimated particle sprays, or jets, are essential for interpreting data from high-energy collider experiments. While deep learning has improved jet classification, it often lacks interpretability. We introduce the Explainable Particle Chebyshev Network (E-PCN), a graph neural network extending the Particle Chebyshev Network (PCN). E-PCN integrates kinematic variables into jet classification by constructing four graph representations per jet, each weighted by a distinct variable: angular separation ($\Delta$), transverse momentum ($k_T$), momentum fraction ($z$), and invariant mass squared ($m^2$). We use the concept of Gradient-weighted Class Activation Mapping (Grad-CAM) to determine which kinematic variables dominate classification outcomes. Analysis reveals that angular separation and transverse momentum collectively account for approximately 76% of classification decisions (40.72% and 35.67%, respectively), with momentum fraction and invariant mass contributing the remaining 24%. Evaluated on the JetClass dataset with 10 signal classes, E-PCN achieves a macro-accuracy of 94.67%, macro-AUC of 96.78%, and macro-AUPR of 86.79%, representing improvements of 2.36%, 4.13%, and 24.88% respectively over the baseline PCN implementation, while demonstrating physically interpretable feature learning.

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 / 1 minor

Summary. The paper introduces the Explainable Particle Chebyshev Network (E-PCN) as an extension of the Particle Chebyshev Network (PCN) for jet tagging. E-PCN constructs four graph representations per jet weighted by distinct kinematic variables: angular separation (Δ), transverse momentum (k_T), momentum fraction (z), and invariant mass squared (m²). It employs Grad-CAM to identify dominant features, reporting that angular separation and transverse momentum account for approximately 76% of classification decisions. On the JetClass dataset with 10 signal classes, E-PCN achieves a macro-accuracy of 94.67%, macro-AUC of 96.78%, and macro-AUPR of 86.79%, with improvements of 2.36%, 4.13%, and 24.88% over the baseline PCN.

Significance. If the interpretability claims hold, this contributes meaningfully to developing transparent ML models for high-energy physics applications. Jet tagging benefits from models that not only perform well but also provide insights aligned with physical quantities. The multi-graph approach using kinematic weights is a logical extension, and the reported metrics indicate competitive performance, though the explainability is the key differentiator.

major comments (2)
  1. [§4 (Performance Evaluation)] The abstract and results report specific performance numbers (e.g., 94.67% macro-accuracy) without error bars, standard deviations from multiple runs, or details on the training configuration and hyperparameter search. This makes it hard to evaluate the robustness of the claimed improvements over PCN and whether they are statistically meaningful.
  2. [§3.2 (Grad-CAM Analysis)] The central claim regarding feature importance (angular separation 40.72%, pT 35.67%) is based on Grad-CAM applied to the four kinematic-weighted graphs. No validation is described for the faithfulness of these attributions, such as checks against gradient saturation, ablation of individual graphs, or comparison to alternative explanation techniques. This is load-bearing for the novelty of 'physically interpretable feature learning' and requires additional evidence to support that the attributions reflect causal usage in the model rather than artifacts.
minor comments (1)
  1. Consider adding a brief explanation or reference for the choice of the four specific kinematic variables (Δ, k_T, z, m²) and how they relate to standard jet substructure observables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important aspects of robustness and the validation of interpretability claims. We address each major comment below and outline the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [§4 (Performance Evaluation)] The abstract and results report specific performance numbers (e.g., 94.67% macro-accuracy) without error bars, standard deviations from multiple runs, or details on the training configuration and hyperparameter search. This makes it hard to evaluate the robustness of the claimed improvements over PCN and whether they are statistically meaningful.

    Authors: We agree that reporting error bars and experimental details is necessary to allow proper evaluation of statistical significance and robustness. In the revised manuscript we will add standard deviations obtained from multiple independent training runs using different random seeds. We will also expand Section 4 to include the complete training configuration (optimizer, learning-rate schedule, batch size, number of epochs) and a description of the hyperparameter search procedure. revision: yes

  2. Referee: [§3.2 (Grad-CAM Analysis)] The central claim regarding feature importance (angular separation 40.72%, pT 35.67%) is based on Grad-CAM applied to the four kinematic-weighted graphs. No validation is described for the faithfulness of these attributions, such as checks against gradient saturation, ablation of individual graphs, or comparison to alternative explanation techniques. This is load-bearing for the novelty of 'physically interpretable feature learning' and requires additional evidence to support that the attributions reflect causal usage in the model rather than artifacts.

    Authors: We acknowledge that additional validation of the Grad-CAM attributions would strengthen the interpretability claims. The present manuscript applies Grad-CAM but does not report explicit faithfulness checks. In the revision we will include an ablation study that removes or masks each kinematic-weighted graph in turn and quantifies the resulting drop in classification metrics. We will also add a brief discussion of known Grad-CAM limitations such as gradient saturation and, space permitting, a comparison with a perturbation-based attribution method. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected; results are empirical evaluations on held-out data

full rationale

The paper reports empirical performance (94.67% macro-accuracy, etc.) from training E-PCN on the JetClass dataset and evaluating on its test split, plus post-hoc Grad-CAM attributions on the four kinematic-weighted graphs that yield the 76% figure. These quantities are measured outputs, not quantities that reduce by construction to the model definition or to fitted parameters. No derivation chain, uniqueness theorem, or self-citation is shown to be load-bearing for the accuracy or attribution numbers. The architecture choice of four separate graphs is an explicit modeling decision whose consequences are tested externally rather than presupposed.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of graph neural networks and the faithfulness of Grad-CAM explanations; no new physical entities or free parameters are introduced beyond typical ML hyperparameters.

free parameters (1)
  • graph construction and weighting hyperparameters
    Parameters controlling how the four kinematic graphs are built and combined are chosen or tuned during development.
axioms (1)
  • domain assumption Grad-CAM produces faithful feature attributions for the GNN classifier
    Invoked to interpret which kinematic variables dominate decisions without independent validation in the abstract.

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discussion (0)

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Forward citations

Cited by 1 Pith paper

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    Explainability techniques applied to LundNet show that assigned node importance correlates with classical jet substructure observables such as N-subjettiness ratios and energy correlation functions, with shifts across...

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