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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, AKM Mahbubur Rahman

TL;DR

The Explainable Particle Chebyshev Network (E-PCN), a graph neural network extending the Particle Chebyshev Network, is introduced, a graph neural network extending the Particle Chebyshev Network that integrates kinematic variables into jet classification.

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 ($Δ$), 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.

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

TL;DR

The Explainable Particle Chebyshev Network (E-PCN), a graph neural network extending the Particle Chebyshev Network, is introduced, a graph neural network extending the Particle Chebyshev Network that integrates kinematic variables into jet classification.

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 (), transverse momentum (), momentum fraction (), and invariant mass squared (). 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.

Paper Structure

This paper contains 29 sections, 1 equation, 3 figures, 12 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Dataset
  5. Graph Representation of Jets
  6. Edge-Weighted Multi-Graph
  7. Neural Network Architecture
  8. Feature Extraction --
  9. Graph-Level Pooling --
  10. Multi-Graph Combination --
  11. Classification --
  12. Training Configuration
  13. Hyperparameters --
  14. Training Procedure --
  15. Kinematic Variable Importance
  16. ...and 14 more sections

Figures (3)

  • Figure 1: E-PCN, with integrated explainability analysis. Data is processed through four parallel GNNs, each weighted by a distinct kinematic variables: angular separation ($\boldsymbol{\Delta}$), transverse momentum ($\boldsymbol{k_T}$), momentum fraction ($\boldsymbol{z}$), and invariant mass squared ($\boldsymbol{m^{2}}$) of each pair of the particles involved. The embeddings from all GNNs are stacked and classified into jet classes. A detailed architectural diagram is provided in Figure \ref{['fig:model_architecture']}, and the model is formally described in Section \ref{['subsec:network_architecture']}.
  • Figure 2: Architecture of the proposed E-PCN model showing four parallel graph processing branches ($G_{\Delta}$, $G_{k_T}$, $G_{Z}$, $G_{m^2}$) with hybrid convolutional layers. Each branch processes a distinct graph representation through alternating Chebyshev graph convolutions (ChebConv) and edge convolutions (EdgeConv), generating 64-dimensional embeddings. The four embeddings are combined via 1D convolution and passed through fully connected layers for final classification into 10 jet categories.
  • Figure 3: Grad-CAM explainability analysis quantifying feature importance in E-PCN classification. (a) Four graph representations undergo parallel processing through specialized GNN branches. (b) Feature attribution analysis shows that angular separation ($\Delta$, 40.72%) and transverse momentum ($k_{T}$, 35.67%) dominate the classification decisions, while momentum fraction ($z$, 14.06%) and invariant mass ($m^{2}$, 9.54%) provide complementary information (Algorithm \ref{['alg:gradcam']}).