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Jet Substructure Classification in High-Energy Physics with Deep Neural Networks
Pierre Baldi, Kevin Bauer, Clara Eng, Peter Sadowski, Daniel Whiteson
TL;DR
The paper addresses how to distinguish single-particle jets from overlapping jets produced by boosted massive-particle decays when expert features may omit information. It trains deep neural networks on simulated detector-level jet images, finding performance that matches or modestly exceeds expert-feature classifiers, including with pileup. The results also retain a role for expert features because simulation accuracy limits the networks and expert variables can provide diagnostic insight.
Problem
Jet tagging must distinguish single hadronic-particle jets from overlapping decay jets, while expert features may not capture all information in high-dimensional detector data.
Method
Deep neural networks with locally-connected and fully-connected layers classify simulated detector-response jet images directly, using expert features as a benchmark.
Results
Deep networks match or modestly outperform shallow classifiers combining expert features, and the performance advantage persists under pileup.
Takeaways & Limitations
Deep networks can automatically extract classification knowledge from high-dimensional jet images, while expert features remain useful for evaluating simulation models.
Takeaways & Limitations
Network performance is limited by simulation-model accuracy, and expert features may be more robust across existing simulation models.
Abstract
from arXiv · showhide
At the extreme energies of the Large Hadron Collider, massive particles can be produced at such high velocities that their hadronic decays are collimated and the resulting jets overlap. Deducing whether the substructure of an observed jet is due to a low-mass single particle or due to multiple decay objects of a massive particle is an important problem in the analysis of collider data. Traditional approaches have relied on expert features designed to detect energy deposition patterns in the calorimeter, but the complexity of the data make this task an excellent candidate for the application of machine learning tools. The data collected by the detector can be treated as a two-dimensional image, lending itself to the natural application of image classification techniques. In this work, we apply deep neural networks with a mixture of locally-connected and fully-connected nodes. Our experiments demonstrate that without the aid of expert features, such networks match or modestly outperform the current state-of-the-art approach for discriminating between jets from single hadronic particles and overlapping jets from pairs of collimated hadronic particles, and that such performance gains persist in the presence of pileup interactions.
INTRODUCTION
Boosted-particle decays can produce overlapping jets whose detector substructure must be tagged as single-particle or multi-particle origin. Because expert features may omit information in high-dimensional detector data, the paper applies deep networks directly to jet images and finds performance matching or exceeding shallow expert-feature classifiers.
- INTRODUCTION: Boosted W decays produce overlapping quark jets that appear as a single merged detector jet requiring substructure-based tagging.The task distinguishes single hadronic particles from massive particles decaying into multiple hadronic particles.
- INTRODUCTION: Expert-designed features reduce dimensionality but may not capture all information in high-dimensional jet data.The paper motivates learning from lower-level detector information instead.
- INTRODUCTION: Detector measurements can be represented as two-dimensional images, enabling computer-vision methods for jet classification.The paper notes prior encouraging results with shallow models and identifies detector response and pileup as important realistic effects.
- INTRODUCTION: Deep networks using locally-connected and fully-connected layers classify detector clusters without domain knowledge, matching or exceeding shallow classifiers combining expert features.This is the paper’s central contribution and reported comparison.
THEORY
The target is to distinguish single quark or gluon jets from two overlapping jets produced by boosted W decay. The paper learns this classification from simulated samples because the likelihood ratio is difficult to formulate and estimate directly, while simulation accuracy remains a constraint.
- THEORY: The representative task separates single quark or gluon jets from two overlapping jets generated by boosted W →qq′ decay.The classifier is intended to learn the corresponding classification function.
- THEORY: A fundamental-QCD likelihood-ratio formulation is unavailable, and estimating it from high-dimensional simulated samples is difficult.Expert features reduce dimensionality but may omit information.
- THEORY: Simulation accuracy limits learned classification, so expert features remain useful for assessing model success and failure.The paper presents deep networks as potentially complementary to, rather than replacements for, expert features.
DATA
The study builds simulated calorimeter jet images for boosted W decays and single quark or gluon jets, including pileup conditions. It compares direct image information with conventional high-level substructure variables.
- DATA: Training samples use realistic particle-physics simulation for both single-jet and overlapping W-decay classes.The samples represent the two classification categories used throughout the study.
- DATA: Samples use √s = 14 TeV and jets with pT ∈[300, 400] GeV for both production scenarios.Boosted W →qq′ samples come from pp →W +W −→qqqq, while single jets come from pp →qq, qg, gg.
- DATA: Pileup is simulated at ⟨µ⟩= 50 interactions per event, followed by anti-kT reconstruction with R = 1.2 and jet trimming.Trimming is intended to remove pileup while preserving two-pronged boson-decay structure.
- DATA: The benchmark uses six high-level jet variables, with their distributions examined for samples with and without pileup.These variables provide the expert-feature comparison to direct image classification.
- DATA: The image strategy uses lower-level calorimeter data directly, after centering and rotating each jet into a canonical orientation.This avoids the dimensional reduction supplied by the high-level variables.
- DATA: Images are centered and cropped to a 3.0 × 3.0 radian window, then binned into 32 × 32 pixels with coincident-cell energies summed.Individual and averaged class images are shown in Figures 2 and 3.
TRAINING
Deep networks and expert-feature BDTs are trained and tuned on large balanced datasets, with locally-connected layers learning localized detector patterns before fully-connected aggregation.
- TRAINING: Classifiers use 10 million balanced training examples, 500 thousand validation examples, and a separate 5 million-example test set.Hyperparameters are selected with Bayesian optimization before testing.
- TRAINING: Typical and averaged preprocessed images show the single-QCD and overlapping-W classes side by side.These visualizations illustrate the inputs supplied to the neural networks.
- TRAINING: The neural networks use tanh hidden units, a logistic output, cross-entropy loss, and ADAM optimization.Training uses minibatches and a decaying learning rate.
- TRAINING: Locally-connected layers learn spatially localized features without assuming convolutional translational invariance.Each neuron connects to a distinct 4-by-4 pixel region.
- TRAINING: Fully-connected layers aggregate information across detector regions after local feature extraction.The architecture is optimized over layer counts and fully-connected widths.
- TRAINING: BDTs provide the comparison baseline using six expert-designed high-level variables.Their hyperparameters are separately optimized for datasets with and without pileup.
RESULTS
Deep networks with locally-connected layers performed best, modestly outperforming expert-variable methods without pile-up and showing a more pronounced advantage with many pile-up interactions.
- Network performance: Locally-connected deep networks outperformed five-layer fully-connected networks, using two locally-connected layers followed by three fully-connected layers of 300 units each.The comparison involved a five-layer network with fully-connected layers of 500 units each.
- Pile-up dependence: Without pile-up, the deep network modestly outperformed physics-domain variables, indicating classification without expert-designed features.The authors also report some information loss from reducing the data to expert features.
- Pile-up dependence: With many pile-up interactions, deep-network performance held up and the gap over expert variables became more pronounced.The authors attribute this likely difference to physics-inspired variables being motivated by idealized pictures.
- Evaluation: Table III reports signal efficiency at background rejection of 10 and AUC, with neural-network results averaged over three random initializations.AUC is calculated from signal efficiency versus background efficiency, and larger AUC indicates better performance.
- Evaluation: Figure 4 compares signal efficiency against inverse background efficiency for image-trained deep networks and expert-feature-trained BDTs with and without pile-up.It also includes jet mass alone and two expert variables combined with a mass window; typical application efficiencies are 0.5-0.7.
INTERPRETATION
The deep network matched or slightly exceeded the combined state-of-the-art expert-variable benchmark. Event-distribution comparisons suggest it identifies the same signal-rich regions while also optimizing classification in some background-dominated regions.
- Benchmark: A BDT combining all six high-level variables provided a stronger benchmark than typical combinations of jet mass with τ21 or an energy-correlation variable.The benchmark was used to assess the power of deep learning.
- Benchmark: The deep network matched or slightly exceeded the performance of the combined state-of-the-art expert variables.This is the paper’s central comparison between image-based deep learning and expert-feature classification.
- Interpretation: The authors raise whether the deep network learned a novel classification strategy or rediscovered and optimized existing expert features.Event-distribution comparisons are used to investigate how the classifiers accomplish their separation.
- Interpretation: At equivalent background rejection, the DNN had modestly higher efficiency and sometimes retained more jets away from the signal-dominated feature region.The authors suggest it found the same signal-rich region as the BDT while additionally optimizing into background-dominated regions.
DISCUSSION
The discussion finds that deep networks can learn useful jet-substructure information without exclusive reliance on expert features, while expert features remain valuable for interpreting simulation validity. These conclusions extend to pileup conditions and suggest broader applications, but robustness to modeling uncertainties remains an open direction.
- DISCUSSION: Deep networks can automatically extract classification knowledge, in principle reducing exclusive reliance on expert features.The paper does not claim that expert features are obsolete.
- DISCUSSION: A slight improvement over combined expert features likely reflects small network optimizations accounting for detector and pileup effects.The comparison concerns simulated samples including detector and pileup effects.
- DISCUSSION: Expert features remain useful for assessing simulation validity, while deep-network performance is limited by the accuracy of the simulation models.Expert features may also be more robust to variation among existing simulation models.
- DISCUSSION: Combined expert features appear to capture nearly all relevant information in the jet image’s high-dimensional low-level features.This conclusion applies to the current feature set used with a BDT or another shallow multivariate approach.
- DISCUSSION: The representative single-jet versus W-jet task may generalize to three-constituent jets and other massive-particle decays, although future work must test systematic and showering-model robustness.Examples include top-quark and Higgs-boson decays; future studies should examine systematic uncertainties and changes in hadronization and showering models.