Source-linked AI summary
Jet-Images: Computer Vision Inspired Techniques for Jet Tagging
Josh Cogan, Michael Kagan, Emanuel Strauss, Ariel Schwartzman
TL;DR
The paper addresses discrimination of boosted heavy-particle jets from QCD jets by representing jets as images and processing them with a Fisher linear discriminant. In a W-versus-QCD case study, the computer-vision-inspired approach adds discriminating power, supports visual inspection of class differences, and is presented as flexible for other problems.
Problem
Boosted heavy-particle decay products can merge into single jets, creating a need to distinguish these jets from QCD-initiated quark and gluon jets.
Method
The method preprocesses jets into consistent images and applies a Fisher linear discriminant trained on Monte Carlo examples, without relying on an analytic description.
Results
The W-versus-QCD study finds additional discriminating power over other substructure approaches and identifies class-specific visual features in the Fisher-jet.
Takeaways & Limitations
Jet-images and Fisher-jets provide an inspectable tool for discovering discriminating differences in samples and a starting point for high-dimensional jet-classification problems.
Takeaways & Limitations
Preprocessing choices must be tailored to the system and environment, including grooming for pileup conditions and rotations for two- or three-prong decays.
Abstract
from arXiv · showhide
We introduce a novel approach to jet tagging and classification through the use of techniques inspired by computer vision. Drawing parallels to the problem of facial recognition in images, we define a jet-image using calorimeter towers as the elements of the image and establish jet-image preprocessing methods. For the jet-image processing step, we develop a discriminant for classifying the jet-images derived using Fisher discriminant analysis. The effectiveness of the technique is shown within the context of identifying boosted hadronic W boson decays with respect to a background of quark- and gluon- initiated jets. Using Monte Carlo simulation, we demonstrate that the performance of this technique introduces additional discriminating power over other substructure approaches, and gives significant insight into the internal structure of jets.
1 Introduction
Boosted heavy-particle decays can produce merged jets whose discrimination from QCD jets requires exploiting internal jet structure. The paper frames jet tagging as an image-recognition problem, using computer-vision-inspired preprocessing and a fast linear discriminant.
- Highly boosted heavy-particle decay products can merge into a single jet, motivating discrimination from QCD-initiated quark and gluon jets.
- Jet-substructure methods address this task by exploiting internal jet structure, alongside approaches including subjet finding, grooming, templates, energy flow, and probabilistic clustering.
- Its approach uses Monte Carlo-generated jet catalogs rather than relying on an analytic description such as color-flow information.
- After preprocessing, the method applies a fast, linear feature-extraction approach intended to support physical interpretation.
- The paper treats jet tagging as analogous to facial recognition and develops jet-specific computer-vision preprocessing and discrimination methods.
2 Algorithm
The paper represents calorimeter information as fixed-size jet-images, preprocesses them to reduce irrelevant variation, and classifies them with an interpretable Fisher discriminant. This computer-vision-inspired framework preserves low-level information while enabling fast comparison and visualization of discriminating features.
- Jets as Images: Jet-images are fixed-dimensional pixel grids formed from calorimeter towers within a square centered on each jet axis.The grid uses tower spacing Δη × Δφ = 0.1 × 0.1 and includes towers within a 2R by 2R square.
- Jets as Images: The representation retains total deposited transverse energy per pixel and permits rapid jet similarity calculations through standard linear algebra.The image can be flattened into an N^2-dimensional vector, making dot products available for comparing jets.
- Jet-Image Preprocessing: Preprocessing reduces pileup noise, identifies leading energy-deposition regions, and aligns primary features to consistent pixel locations.The alignment exploits η−φ symmetries; trimming is used for noise reduction and subjets locate points of interest.
- Jet-Image Processing: Constructing the Discriminant: Fisher’s Linear Discriminant maximizes class separation while minimizing within-class scatter, with regularization reducing training-sample fluctuations and overfitting.The resulting Fisher-jet has the same dimensionality as the example jet-images, and classification is performed by projection.
- Jet-Image Processing: Constructing the Discriminant: The Fisher-jet provides a fast, numerically cuttable classifier whose coefficients visualize which image features favor each jet class.Positive and negative coefficients indicate features associated with the two classes, while coefficient magnitude indicates classification strength.
3 Samples
The performance study uses Monte Carlo proton-proton samples at √s = 8 TeV, including no pileup and mean pileup μ = 30. Boosted W-jet events are reconstructed with Cambridge/Aachen jets and trimming, while pileup subtraction beyond trimming is not applied.
- Samples: Monte Carlo samples are generated with Pythia8, MadGraph, and Herwig++ for proton-proton collisions at √s = 8 TeV.Pileup is simulated by adding particles from additional Pythia8 minimum-bias interactions.
- Samples: The study considers samples with no pileup and with mean pileup μ = 30 interactions per bunch crossing.The number of additional interactions is sampled from a Poisson distribution.
- Samples: The signal sample is diboson WW production with one leptonic W decay and one hadronic W decay, selecting boosted jets in 50 GeV-wide pT windows.An example selection is 200 < pT < 250 GeV for the leading reconstructed jet.
- Samples: Jets are reconstructed from calorimeter-tower four-vectors with Cambridge/Aachen radius R = 1.2, retaining jets with pT > 25 GeV.Trimming uses kT subjets with R = 0.3 and fcut = 5% to reduce pileup effects.
- Samples: Trimming serves as the noise-reduction step, with no additional pileup subtraction performed.
4 Case Study: W Boson Jet Tagging
The case study applies separately trained Fisher linear discriminants to preprocessed, binned W- and QCD-jet images and compares their tagging performance with N-subjettiness. The discriminant also reveals class-specific spatial energy patterns and remains robust across generators and pileup conditions.
- Case-study setup: The study classifies boosted hadronic W→qq′ jets against QCD jets using 25×25 preprocessed jet-images and separate FLDs for each (pT, ∆Rjj) bin.Inputs are trimmed, aligned, translated, reflected, and equalized before training.
- Discriminating structure: A second hard subjet indicates a W-jet, whereas radiation surrounding the two subjets indicates a wider QCD jet.The primary hard subjet is nearly nondiscriminating because both classes contain one.
- Performance: FLD outperforms N-subjettiness across the full examined jet-pT range.Figure 3 compares rejection-efficiency curves and W-jet efficiency at fixed 10-fold QCD rejection.
- Performance: The Fisher-jet output correlates approximately 0.7 with N-subjettiness for both W and QCD jets, but only approximately -0.25 with jet mass.This indicates that FLD combines information related to N-subjettiness while retaining information distinct from mass.
- Robustness: No significant performance degradation is observed when Fisher-jets trained without pileup are applied to samples with pileup.The paper attributes this result likely to trimming, while leaving more detailed pileup studies for future work.
- Robustness: A Pythia8-trained Fisher-jet produces extremely similar W- and QCD-jet output distributions on Pythia8 and Herwig++ samples.The generator-dependence check uses jets with pT ∈[200, 250] GeV and ∆R ∈[0.6, 0.8].
5 Conclusion
The paper presents a flexible, inspectable jet-tagging method inspired by computer vision, using jet-images and Fisher discrimination to separate jet classes. It is competitive for boosted hadronic W versus QCD jets and supports visual study of discriminating features.
- The algorithm represents jets as images, preprocesses them consistently, and applies a Fisher linear discriminant trained on example jets.The discriminant projects classes toward opposite ends of its output spectrum for separation.
- The method is linear, easy to understand, requires little prior tuning knowledge, and does not rely on an analytic description of the studied system.
- The approach is competitive with N-subjettiness for separating hadronically decaying boosted W bosons from QCD jets.
- Visualized jet-images and Fisher-jets expose important and discriminating features in samples lacking a complete analytical description.This provides a starting point for simple answers to high-dimensional problems.
- The consistent jet-image representation permits extension to other classifiers and possible applications beyond W-versus-QCD discrimination.The paper mentions H →b¯b, hadronic top identification, and other imaging problems as possible applications.
- Jet-images connect particle physics with computer vision, while the paper identifies this approach as an initial step toward applying broader computer-vision techniques.
A Fisher Jet Images
Figure 6 presents Fisher linear discriminants as jet-images, or Fisher-jets, across several pT and ∆Rjj bins for jets with masses between 65 and 95 GeV.
- Fisher-jets are shown for several pT and ∆Rjj bins, restricting the jet mass to M ∈[65, 95] GeV.