ParticleNet: Jet Tagging via Particle Clouds

• Jets are collimated sprays of particles produced in proton-proton collisions at the LHC.Source: §I · p. 1
• Jet tagging identifies the elementary particle initiating a jet, whose characteristics can reveal the collision process.Source: §I · p. 1
• Machine-learning methods have represented jets as images, sequences, trees, graphs, or particle sets for tagging.Source: §I · p. 1
• ParticleNet treats constituent particles as an unordered set, analogous to a point cloud, and operates directly on this particle-cloud representation.Source: §I · p. 1
• The paper evaluates ParticleNet on two jet-tagging benchmarks and reports significant improvements over existing methods.Source: §I · p. 1

Image representation

• Calorimeter energy deposits naturally form jet images, while particle-flow jets can be mapped onto calorimeter cells.Source: A. Image-based representation · p. 1
• Image-based CNNs have achieved sizable improvements over traditional QCD-motivated multivariate methods on several tagging tasks.Source: A. Image-based representation · p. 2
• More than 90% of typical 32 × 32 jet-image pixels are blank because jets contain O(10) to O(100) particles, making image CNNs computationally inefficient.Source: A. Image-based representation · p. 2

Particle-based representation

• Particle collections can include arbitrary per-particle features and are more compact than images, but their lengths vary across jets.Source: B. Particle-based representation · p. 2
• Sequences and binary trees organize particles using imposed orderings, supporting RNNs, 1D CNNs, physics-oriented networks, or recursive networks.Source: B. Particle-based representation · p. 2
• Because jet constituents have no intrinsic order, manually imposed ordering may be suboptimal and impair performance.Source: B. Particle-based representation · p. 2

• A particle cloud is an unordered, permutation-invariant set of a jet’s constituent particles.Source: C. Jet as a particle cloud · p. 2
• Particle clouds retain flexible per-particle features while representing jets as irregularly distributed, internally correlated entities.Source: C. Jet as a particle cloud · p. 2
• The representation is analogous to 3D point clouds, allowing point-cloud deep-learning algorithms to inform jet models.Source: C. Jet as a particle cloud · p. 2
• Deep Sets processes particle clouds globally, whereas the DGCNN approach used here explicitly exploits local spatial structure.Source: C. Jet as a particle cloud · p. 2
• ParticleNet is a CNN-like deep neural network designed for jet tagging with particle-cloud data.Source: §III · p. 2

• CNN success reflects shared kernels that exploit symmetry and hierarchical feature learning across scales.Source: A. Edge convolution · p. 3
• Regular convolution cannot directly handle irregular point clouds because their local patches and permutation-invariant operation are not naturally defined.Source: A. Edge convolution · p. 3
• EdgeConv constructs a graph by connecting each point to its k nearest neighbors, defining a local convolutional patch.Source: A. Edge convolution · p. 3
• Shared edge-function parameters and symmetric aggregation make EdgeConv permutation-symmetric.Source: A. Edge convolution · p. 3
• The paper uses neighbor-feature differences, a shared MLP edge function, and mean aggregation in its specialized EdgeConv form.Source: A. Edge convolution · p. 3
• EdgeConv outputs another point cloud with the same number of points, allowing operations to stack and learn hierarchical features.Source: A. Edge convolution · p. 3
• DGCNN recomputes nearest-neighbor proximity in a learned latent space, allowing the graph structure to change dynamically.Source: A. Edge convolution · p. 3

ParticleNet

• ParticleNet uses customized EdgeConv blocks and dynamic graph updates to suit jet tagging.Its design choices include the neighbor count, EdgeConv MLP configuration, and shortcut connections.Source: B. ParticleNet · p. 3
• Each EdgeConv block finds k nearest particles from coordinates, constructs edge features, and processes them with a three-layer MLP.The layers apply linear transformations, batch normalization, and rectified linear units.Source: B. ParticleNet · p. 3
• ParticleNet stacks three EdgeConv blocks, using pseudorapidity-azimuth coordinates first and learned feature vectors thereafter.The blocks use k = 16 and channel configurations (64, 64, 64), (128, 128, 128), and (256, 256, 256), followed by global average pooling.Source: B. ParticleNet · p. 4

ParticleNet-Lite

• ParticleNet-Lite uses two smaller EdgeConv blocks and reduces arithmetic operations by almost an order of magnitude.It is designed to be more suitable when computational resources are limited.Source: B. ParticleNet · p. 4

Training

• The networks are implemented in Apache MXNet and trained with AdamW, cross-entropy loss, and a one-cycle learning-rate schedule.ParticleNet and ParticleNet-Lite use different batch sizes and learning-rate settings because of their differing resource requirements.Source: B. ParticleNet · p. 4

IV. RESULTS

• ParticleNet is evaluated on top tagging and quark-gluon tagging benchmark tasks.The section presents benchmark results for both tasks.Source: §IV · p. 4

Dataset and task

• Top tagging identifies jets originating from hadronically decaying top quarks and is commonly used in searches for new physics at the LHC.The benchmark uses a dataset generated with Pythia8 and processed through Delphes.Source: A. Top tagging · p. 4
• The simulated top-tagging jets exclude multiple parton interactions and pileup and are restricted to pT ∈[550, 650] and |η| < 2.Signal jets are matched to hadronically decaying top quarks and their three decay quarks within ∆R = 0.8 of the jet axis.Source: A. Top tagging · p. 5

Inputs

• ParticleNet uses up to 100 highest-pT constituents and seven variables derived from each particle’s four-momentum.The (∆η, ∆φ) variables provide coordinates for distances in the first EdgeConv block.Source: A. Top tagging · p. 5

Baselines

• The comparison includes ResNeXt-50 image inputs, P-CNN particle sequences, and PFN unordered particle sets.PFN uses global symmetric functions but does not explicitly exploit local neighborhood information as EdgeConv does.Source: A. Top tagging · p. 5

Metrics

• The evaluation reports accuracy, AUC, and background rejection 1/εb at signal efficiencies of 50% and 30%.Background rejection is emphasized because it is directly related to expected background contributions in LHC analyses.Source: A. Top tagging · p. 5

Results

• 1.8 (2.1) times as good as PFN (P-CNN), and about 40% better than ResNeXt-50, ParticleNet’s background rejection is strongest at 30% signal efficiency.ParticleNet-Lite also outperforms all previous models, improving about 10% over ResNeXt-50.Source: A. Top tagging · p. 6

Dataset and task

• Quark-gluon tagging discriminates jets initiated by quarks from those initiated by gluons using a simulated dataset without detector simulation.The signal and background samples are generated with Pythia8 from Z(→νν) + (u, d, s) and Z(→νν) + g processes.Source: B. Quark-gluon tagging · p. 6

Inputs

• The dataset includes particle types in addition to four-momentum, enabling ParticleNet variants with and without particle-identification inputs.PID is incorporated in an experimentally realistic way using only five particle-type categories.Source: B. Quark-gluon tagging · p. 6

Comparison

• Table III compares ParticleNet, ParticleNet-Lite, P-CNN, and ResNeXt-50, including model variants with and without PID.ResNeXt-50 is shown only without PID because jet images cannot straightforwardly incorporate that information.Source: B. Quark-gluon tagging · p. 6, Table III · p. 7

Results

• 10%–15% higher background rejection results from adding PID inputs compared with the same model without PID.The comparison demonstrates that particle-based representations can integrate additional per-particle information.Source: B. Quark-gluon tagging · p. 7
• Almost 15% improvement in background rejection over PFN-Ex and P-CNN is achieved by ParticleNet with PID inputs.ParticleNet-Lite achieves the second-best performance, improving about 7% over PFN-Ex and P-CNN.Source: B. Quark-gluon tagging · p. 7

• ParticleNet achieves the best classification performance but is more than an order of magnitude slower than PFN and P-CNN.The comparison uses inference time per object, measured separately on CPU and GPU.Source: §V · p. 7
• ParticleNet-Lite improves performance by more than 40% while running only a few times slower than PFN and P-CNN.Source: §V · p. 8
• ParticleNet-Lite is the most economical model, with 26k parameters, while outperforming all previous approaches.Its performance is attributed to effective exploitation of particle-cloud permutation symmetry.Source: §V · p. 8
• PFN is the fastest model on both CPU and GPU, making it suitable for extremely time-critical tasks.Source: §V · p. 8

• ParticleNet treats jets as unordered particle clouds and uses this representation in a network architecture tailored to jet tagging.Source: §VI · p. 8
• ParticleNet achieves state-of-the-art performance on both top-tagging and quark–gluon-tagging benchmarks.Source: §VI · p. 8
• ParticleNet significantly improves over image-based ResNeXt-50, sequence-based P-CNN, and set-based PFN architectures.Source: §VI · p. 8

Implementation details of ResNeXt-50

• ResNeXt-50 represents each jet as a 64 × 64 image whose pixel intensities contain rescaled summed particle pT.Pixels correspond to 0.025 rad granularity in pseudorapidity–azimuth space.Source: Appendix A · p. 11
• ResNeXt-50 adapts the original architecture by reducing channels in most convolutional layers and adding dropout with probability 0.5.Source: Appendix A · p. 11
• ResNeXt-50 is trained for 30 epochs with Adam, minibatches of 256, and learning-rate reductions at epochs 10 and 20.The final model is selected using validation accuracy.Source: Appendix A · p. 11

Implementation details of P-CNN

• P-CNN represents each jet as a sequence of 100 particles sorted by descending pT, padding shorter jets and truncating longer ones.Source: Appendix B · p. 11
• P-CNN uses 14 one-dimensional convolutional layers followed by global pooling, a 512-unit fully connected layer, dropout, and classification output.Source: Appendix B · p. 11
• P-CNN is trained for 30 epochs with Adam, minibatches of 1024, and learning-rate reductions at epochs 10 and 20.The final model is selected using validation accuracy.Source: Appendix B · p. 11