Source-linked AI summary
Jet-Images -- Deep Learning Edition
Luke de Oliveira, Michael Kagan, Lester Mackey, Benjamin Nachman, Ariel Schwartzman
TL;DR
The paper addresses identifying highly boosted W bosons within jets, which can contain collimated decay products from heavy-particle decays amid overwhelming QCD backgrounds. It applies deep neural networks to jet images and develops visualization techniques to study learned physics information, finding that the networks outperform engineered jet features while not fully capturing jet mass.
Problem
Identifying boosted W-boson jets amid overwhelming QCD multijet backgrounds is important for searching for physics beyond the Standard Model at the LHC.
Method
The paper represents jets as images, trains modern deep neural networks for jet tagging, and quantifies and visualizes learned information by removing jet-mass and τ21 information.
Results
Deep neural networks identify boosted hadronically decaying W bosons from QCD multijet processes and outperform engineered features such as jet mass and n-subjettiness τ21, while not fully capturing jet mass.
Takeaways & Limitations
Jet-image deep learning has potential to improve tagging in LHC analyses using boosted hadronically decaying bosons and to reveal additional features of jet substructure.
Takeaways & Limitations
The study focuses on 250 GeV < pT,W < 300 GeV, and the networks studied do not fully capture the jet-mass variable.
Abstract
from arXiv · showhide
Building on the notion of a particle physics detector as a camera and the collimated streams of high energy particles, or jets, it measures as an image, we investigate the potential of machine learning techniques based on deep learning architectures to identify highly boosted W bosons. Modern deep learning algorithms trained on jet images can out-perform standard physically-motivated feature driven approaches to jet tagging. We develop techniques for visualizing how these features are learned by the network and what additional information is used to improve performance. This interplay between physically-motivated feature driven tools and supervised learning algorithms is general and can be used to significantly increase the sensitivity to discover new particles and new forces, and gain a deeper understanding of the physics within jets.
1 Introduction
The paper frames boosted-boson jet tagging as a key challenge in LHC searches because decay products can merge into a single jet amid overwhelming QCD backgrounds. It extends jet-image methods with deep neural networks to learn richer representations and connect performance gains to jet physics.
- Motivation: Boosted heavy particles can produce highly collimated decay products captured by one jet, making discrimination from QCD multijet backgrounds essential.The challenge arises because new heavy particles may decay to boosted W, Z, Higgs bosons, or top quarks.
- Motivation: Jet tagging has traditionally used physics-inspired features that exploit the rich internal substructure of jets.The introduction places this work within existing feature-driven approaches to jet substructure.
- Approach: Jets are represented as images whose pixel intensities encode particle energy depositions within the jet.This extends the earlier jet-images approach beyond its original linear Fisher-discriminant implementation.
- Approach: Modern deep neural networks are used to learn high-level jet-image representations and enhance discrimination power.The study examines both fully connected and convolutional architectures.
- Interpretation: Visualization techniques are developed to relate learned network features to the physical properties governing jet substructure.The stated goal is to understand what the networks learn rather than treating them only as classifiers.
2 Simulation Details and the Jet Image
The study simulates boosted W-boson jets and QCD multijet backgrounds, constructs detector-like jet images from calorimeter towers, and characterizes the physical variables used for tagging. The analysis focuses on W jets with 250 GeV < pT,W < 300 GeV, where the decay products have an angular spread of about ∆R ∼ 0.6.
- Simulation: Monte Carlo simulations generate boosted hadronic W bosons from hypothetical W′ decays and QCD multijet events as background.The invisible Z decay makes the highest-transverse-momentum jet the W-boson jet.
- Simulation: The analysis focuses on 250 GeV < pT,W < 300 GeV, corresponding to a W-decay-product angular spread of about ∆R ∼ 0.6.The signal and background are generated at √s = 14 TeV with Pythia 8.170.
- Detector and jets: Jets are clustered with anti-kt, trimmed using R = 0.3 kt subjets, and modeled with a calorimeter granularity of 0.1 × 0.1 in (η, φ).Trimming reduces contributions from the underlying event and pileup.
- Tagging features: Jet mass, τ21, and ∆R between trimmed subjets are identified as key features distinguishing W jets from QCD jets.Jet mass acts as a proxy for the boson mass in W events, while τ21 measures compatibility with two hard prongs.
- Tagging features: The signal is re-weighted to match the background pT distribution because several discriminating features depend strongly on transverse momentum.This controls the pT dependence when comparing signal and background.
- Jet images: Jet images discretize constituent energy into pixels in (η, φ), with each pixel intensity equal to the summed energy of constituents inside it.The study also investigates transverse-energy pixel intensities.
3 Pre-processing and the Symmetries of Space-time
Jet-image preprocessing standardizes translations, orientations, pixelation, and parity while attempting to preserve physically useful information. The procedure can clarify two-prong structure, but some choices broaden or otherwise alter the image-mass distribution.
- Preprocessing: Preprocessing applies translation, rotation, re-pixelation, and inversion so networks need not learn space-time symmetries.The leading subjet is translated to (η, φ) = (0, 0).
- Preprocessing: Rotation places a second subjet at −π/2, or aligns the first principal component vertically when no second subjet exists.Re-pixelation redistributes rotated-grid energy onto the original grid, followed by a parity flip.
- Visual structure: After preprocessing, the average W-jet image shows a localized second energy core, while QCD energy remains more diffuse.Before preprocessing, W jets exhibit a clearer annulus that is nearly absent in QCD jets.
- Normalization: L2 normalization can make training easier by reducing intensity-spread variations, but it can distort information encoded in the image.The study notes that ∆R remains invariant under preprocessing and normalization, whereas image mass does not.
- Mass preservation: Translations preserve image mass with the proper pixel intensity, whereas rotations, naive η translations, and L2 normalization can change or broaden its distribution.A π/2 rotation causes a small mass change, while naive translation and L2 normalization significantly broaden the distribution.
4 Network Architecture
The paper studies fully connected MaxOut and convolutional neural networks for jet-image classification, comparing architectures and preprocessing choices. Convolutional models use staged filtering, pooling, dropout, and dense layers, while the selected first-layer filter size is optimized empirically.
- Input representation: Jet images are sparse 25 × 25 single-channel transverse-energy-scale images, motivating specialized image-based network architectures.Only roughly 5–10% of pixels are active on average.
- Convolutional architecture: Convolutional networks apply local filters across image patches, use zero-padding at borders, and then apply nonlinear activations and down-sampling.The study uses the zero-padding option because it produced better performance and more physics-driven filters.
- MaxOut architecture: The MaxOut model uses two MaxOut fully connected layers followed by two ReLU layers and a sigmoid classification output.The MaxOut layers have 256 and 128 units with five piecewise components each; the ReLU layers have 64 and 25 units.
- Convolutional architecture: The deep convolutional model contains three convolution–max-pooling–dropout units, local response normalization, and two fully connected layers.Each convolutional layer uses 32 feature maps, with filter sizes 11 × 11, 3 × 3, and 3 × 3.
- Architectural selection: 11 × 11 is the optimal first-layer convolution size in the reported comparison, outperforming the smaller filter choices by Area Under the ROC Curve.The authors hypothesize that larger filters help capture sparse structures in jet images.
- Preprocessing comparison: The study compares an unnormalized ConvNet with a ConvNet-Norm trained on L2-normalized jet images, while using transverse energy for pixel intensities in both.This comparison isolates possible effects of normalization during preprocessing.
5 Analysis and Visualization
The study compares deep neural networks with physics-motivated jet features and examines which information the networks learn. Visualization and controlled reweighting show that the networks capture substructure-related information while retaining additional discrimination linked to jet mass and radiation patterns.
- 5.1 Studies in the General Phase Space: The DNNs significantly outperform individual and two-variable physics-inspired discriminators, with MaxOut outperforming ConvNet and normalized ConvNet training improving performance.The authors attribute MaxOut’s advantage partly to sparse jet images and normalized ConvNet’s advantage to easier training, despite normalization removing jet-mass information.
- 5.1 Studies in the General Phase Space: Adding ΔR or τ21 to DNN outputs does not improve performance, whereas adding jet mass produces a noticeable improvement.This indicates that relevant ΔR and τ21 information is largely learned by the networks, while some mass information remains unlearned.
- 5.1 Studies in the General Phase Space: The DNN output has a strong nonlinear relationship with τ21 and ΔR, while its relationship with jet mass is weaker.The conditional distributions support learned substructure information more directly than fully learned mass information.
- 5.2 Understanding what is learned: First-layer convolutional filters learn representations of subjets and distances between subjets, including circular features shaped by jet-image sparsity.Convolved signal-background differences show patterns near expected leading and subleading subjets.
- 5.2 Understanding what is learned: The diversity of convolved representations indicates that the DNN learns multiple descriptive features rather than relying on a single pattern.Node-activation visualizations further distinguish two-prong signal-like structures from one-prong diffuse background-like radiation.
- 5.4 Studies in the Uniform Phase Space: After reweighting to remove mass and τ21 discrimination, τ21 and mass become random-guess baselines, but the reweighted ConvNet retains significant discrimination beyond them.Performance is degraded relative to the unweighted ROC, improves when the same weighting is used during training, and remains better than random guessing.
6 Outlook and Conclusions
The study concludes that deep neural networks applied to jet images identify boosted hadronic W bosons effectively and outperform several engineered physics features. Visualization and reweighting analyses connect learned information to jet physics, while incomplete learning of jet mass remains an open issue.
- Deep neural networks applied directly to jet images identify boosted hadronically decaying W bosons from QCD multijet backgrounds.
- The networks outperform engineered features including jet mass and n-subjettiness τ21.
- Fully learning jet mass remains a goal for future work.
- Reweighting and redaction of jet mass and τ21 quantify discrimination beyond those features.
- Deep correlation jet images visualize correlations between network outputs and input pixels.
- Colorflow patterns account for at least part of the network’s unique information, but jet pull angle does not contain all of it.
A Image Sparsity
The appendix characterizes jet-image sparsity through pixel occupancy measures. Background images generally have higher average occupancy because their radiation pattern is more diffuse.
- Pixel occupancy is the fraction of image pixels with nonzero intensity.
- A second occupancy measure counts pixels containing at least 1% of the total scalar pixel-intensity sum.
- Background jet images generally have higher average occupancy because their radiation pattern is more diffuse.
B Joint and Marginal Distributions
The appendix presents marginal network-output distributions and joint distributions relating network outputs to jet-mass and substructure observables. These plots expose a non-smooth MaxOut feature near the signal-background likelihood-ratio crossing.
- Near output 0.5, the MaxOut distribution becomes wavy where the likelihood ratio is unity.
- At that likelihood-ratio regime, the MaxOut network cannot differentiate signal from background.
- Figures 20–22 show joint network-output distributions with jet mass, τ21, and subjet separation ΔR.
- Figures 23–24 show joint distributions among jet mass, subjet separation ΔR, and τ21.
- Figure 19 compares marginal ConvNet and MaxOut outputs for signal and background jet images.