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Reconstructing short-lived particles using hypergraph representation learning

Callum Birch-Sykes, Brian Le, Yvonne Peters, Ethan Simpson, Zihan Zhang

arXiv:2402.10149v3hep-ph

TL;DR

Reconstructing short-lived particles from their decay products is challenging in events with many jets. HyPER combines graph message passing with hypergraph representations to reconstruct parent particles. In the all-hadronic t¯t benchmark, it performs favorably against existing methods, with fewer model parameters.

  • Problem

    High jet multiplicity and combinatorics make it challenging to infer short-lived parent particles from the kinematics of their decay products.

    Source: §I · p. 1

  • Method

    HyPER combines graph message passing with hyperedges representing candidate parent particles to classify higher-order relations among final-state objects.

    Source: §II · p. 2

  • Results

    HyPER’s inclusive event reconstruction efficiency εt¯t is 67.0%, compared with 65.1% for SPANet and 64.5% for Topograph, and it has the highest efficiency across the considered t¯t mass spectrum.

    Source: §VI · p. 6

  • Takeaways & Limitations

    Hyperedges can represent candidate particles with arbitrary numbers of final states, so the approach is in principle applicable to a wide variety of physics processes.

    Source: §VII · p. 8

    The reported benchmark focuses on simulated all-hadronic t¯t events; applications to other collider processes are described as potential rather than demonstrated evaluations.

    Source: §VII · p. 8

Abstract

from arXiv · show

In collider experiments, the kinematic reconstruction of heavy, short-lived particles is vital for precision tests of the Standard Model and in searches for physics beyond it. Performing kinematic reconstruction in collider events with many final-state jets, such as the all-hadronic decay of top-antitop quark pairs, is challenging. We present HyPER: Hypergraph for Particle Event Reconstruction, a novel architecture based on graph neural networks that uses hypergraph representation learning to build more powerful and efficient representations of collider events. HyPER is used to reconstruct parent particles from sets of final-state objects. Trained and tested on simulation, the HyPER model is shown to perform favorably when compared to existing state-of-the-art reconstruction techniques, while demonstrating superior parameter efficiency. The novel hypergraph approach allows the method to be applied to particle reconstruction in a multitude of different physics processes.

I. INTRODUCTION

Reconstructing short-lived particles matters for precision tests of the Standard Model and searches for new physics, but inferring them from decay products is difficult in high-multiplicity events. The all-hadronic top-pair channel offers a useful benchmark whose methods may extend to more complex processes.

I. INTRODUCTION

  • Accurate reconstruction of short-lived particles is critical for measuring their properties and defining observables sensitive to new physics.The introduction also identifies rare topologies such as t¯tH as a motivation for flexible reconstruction methods.Source: §I · p. 1
  • High-multiplicity final states create large combinatorics, making it difficult to identify which decay products belong to each parent particle.The particles’ kinematics must be inferred from the recorded kinematics of their decay products.Source: §I · p. 1
  • Jets from particle decays, partonic splittings, and concurrent proton-proton interactions increase jet multiplicity and complicate jet assignment.The all-hadronic channel lacks undetected final-state neutrinos, although their kinematics in other channels can only be partly inferred from transverse momentum conservation.Source: §I · p. 1
  • The all-hadronic t¯t decay is a useful reconstruction benchmark, and techniques validated there can be generalized to processes with more complex final states.In this channel, both W bosons decay hadronically.Source: §I · pp. 1–2

II. STATE OF THE ART

Existing methods reconstruct parent particles using jet-combination classification or direct kinematic regression. HyPER applies hypergraph representation learning to higher-order relations and is evaluated in the all-hadronic t¯t channel against established methods.

II. STATE OF THE ART

  • SPANet and Topograph classify jet combinations, whereas the Covariant Particle Transformer directly regresses top-quark kinematics from final-state objects.SPANet uses attention to assign jets to parent particles; Topograph uses edge classification to identify decay chains.Source: §II · p. 2
  • HyPER uses hypergraph representation learning to model higher-order relations among final-state jets by constructing and classifying hyperedges for short-lived particles.A hypergraph generalizes a graph by representing correlations among an arbitrary number of objects.Source: §II · p. 2
  • The study benchmarks HyPER against SPANet and Topograph in all-hadronic t¯t reconstruction, while applications to other collider processes remain future work.The stated aims include reconstruction performance, reduced model size, and flexibility for parents with arbitrary numbers of decay products.Source: §II · p. 2
  • To the authors’ knowledge, this is the first use of hypergraph learning to reconstruct resonances in high-energy particle collisions.Other cited applications concern low-level jet reconstruction and jet substructure.Source: §II · p. 2

III. GRAPH AND HYPERGRAPH REPRESENTATIONS

HyPER represents final-state objects and their pairwise relations in a graph, then uses hyperedges to represent candidate top quarks. This blended representation uses message-passing information to classify particle candidates.

III. GRAPH AND HYPERGRAPH REPRESENTATIONS

  • HyPER represents each final-state object as a node and pairwise links between final states as directed edges in a fully connected digraph.Event-level information not naturally captured by node or edge features is included in a global embedding.Source: §III · pp. 2–3
  • W-boson candidates are represented by directed edges between their two daughter jets, making reconstruction a two-body edge-classification task.For each true W candidate, the graph contains two edges when edge direction is considered.Source: §III · p. 3
  • Because graph edges encode only pairs of nodes, HyPER represents each top-quark candidate as a three-node hyperedge and classifies its embedding.The method uses pairwise relational information learned during message passing to construct hyperedge embeddings; this combination is called blended graph-hypergraph representation learning.Source: §III · p. 3
  • Six jets yield 20 possible three-jet top candidates, and HyPER imposes no b-tag requirement on hyperedge constituents.Avoiding that restriction avoids dependence on b-tagging algorithm accuracy.Source: §III · p. 3

IV. THE HyPER NETWORK

HyPER first embeds event kinematics in a graph and processes it with message-passing layers. The resulting graph attributes support separate reconstruction stages for top quarks and W bosons.

IV. THE HyPER NETWORK

  • HyPER feeds feature-embedded event graphs into a multilayer message-passing neural network.Each layer exchanges information between neighboring nodes and updates node, edge, and global feature vectors using relational information in the graph.Source: §IV · p. 3
  • After message passing, updated node and global attributes are carried into top-quark reconstruction, while edge attributes are used to reconstruct W bosons.These reconstruction stages use the outputs of the shared graph-processing network.Source: §IV · pp. 3–4
  • The architecture combines graph-processing components with hypergraph-processing components.The architecture diagram distinguishes graph components with a purple dotted boundary and hypergraph components with an orange dashed boundary.Source: Figure 3 · p. 4

A. Hypergraph: Reconstruction of the top quarks

HyPER embeds predefined candidate hyperedges from features inherited through message passing, then scores them as possible top-quark decays. It selects the two independent highest-scoring candidates to reconstruct the top-quark pair.

A. Hypergraph: Reconstruction of the top quarks

  • Each predefined hyperedge aggregates node and global attributes inherited from message passing into a D-dimensional hyperedge embedding.The aggregation maps incoming features to the embedding used for subsequent scoring.Source: A. Hypergraph: Reconstruction of the… · p. 4
  • A hyperedge layer transforms candidate embeddings and derives a feature-importance vector from the incoming features of all hyperedges.A learnable weight matrix and ReLU transform the hyperedge features; the importance vector weights features before classification.Source: A. Hypergraph: Reconstruction of the… · p. 4
  • HyPER assigns each hyperedge a soft probability of containing the true top-quark decay products and selects the two independent highest-scoring hyperedges.The probability is produced by applying a sigmoid after dimensionality reduction; the selected hyperedges reconstruct the top-quark pair.Source: A. Hypergraph: Reconstruction of the… · p. 4

B. Graph: Identification of the W boson

HyPER assigns probabilities to graph edges as W-boson candidates and combines edges with the same endpoints using a permutation-invariant function. Within each selected top-quark hyperedge, the highest-scoring permissible edge is reconstructed as the W boson.

B. Graph: Identification of the W boson

  • HyPER applies a sigmoid to message-passed graph edge attributes to obtain probabilities that edges correspond to actual W bosons.Edges with the same endpoints are combined using a permutation-invariant function because decay ordering is invariant in reconstruction.Source: B. Graph: Identification of the W boson · p. 4
  • The reconstructed W boson is the highest-scoring permissible edge whose nodes lie within the selected top-quark hyperedge.Only edges contained in that selected hyperedge are considered as W-boson candidates.Source: B. Graph: Identification of the W boson · p. 4
  • W-boson reconstruction follows top-quark reconstruction by restricting candidate edges to the nodes in the selected top-quark hyperedge.The highest-scoring edge satisfying this containment condition is chosen.Source: B. Graph: Identification of the W boson · p. 4

C. Training

Training combines graph-edge and hyperedge classification losses, averages event losses across batches, and uses Adam. The stated hyperparameters were tuned, with individual tuning recommended for each HyPER use case.

C. Training

  • HyPER’s per-graph loss combines binary cross-entropy losses for hyperedge scores and graph-edge scores, weighted by α.The hyperparameter α adjusts the training importance of the graph and hypergraph components.Source: C. Training · pp. 4–5
  • Batches contain 4096 graphs, and each batch loss is the average of the per-event losses.The paper computes loss for each event to maximize event reconstruction efficiency.Source: C. Training · p. 5
  • Training uses Adam with message-passing dimension S = 64, hyperedge-embedding dimension D = 128, and α = 0.8; individual tuning is recommended for each use case.The paper reports that these hyperparameters were chosen through tuning.Source: C. Training · p. 5

V. SIMULATION

The study evaluates HyPER on simulated all-hadronic top-antitop events, applying jet selections and truth matching to define training and evaluation samples. The event selection requires at least six jets, including at least two b-tagged jets, and the test set includes both fully and partially matched events.

V. SIMULATION

  • The simulation starts with 6 × 10^7 all-hadronic t¯t events at 13 TeV, with detector response modeled using an ATLAS parametrization.Matrix elements are generated at next-to-leading order in QCD, then events are showered and hadronized; selected jets require pT ≥ 25 GeV and |η| < 2.5.Source: §V · p. 5
  • Jets are truth-matched to hard particles when ΔR < 0.4, with only the closest jet assigned to each particle.The matching procedure uses generator history to identify outgoing hard particles before calculating angular distances to clustered jets.Source: §V · p. 5
  • The dataset is split 90% for training, 5% for validation, and 5% for performance evaluation; partially matched events may have one or more missing jet labels.The highest jet multiplicity in an event is 20.Source: §V · p. 5
  • After preselection, the training, validation, and test samples contain 7,921,299, 439,692, and 440,069 events, respectively.Preselection requires at least six jets, at least two b-tagged jets, and at least one identifiable W boson; requiring both top quarks identifiable leaves 2,116,231, 117,487, and 116,960 fully matched events.Source: §V · p. 5

VI. RESULTS

HyPER achieves higher inclusive event reconstruction efficiency than SPANet and Topograph with far fewer trainable parameters. It also performs best across the reported truth-mass regions and training-set sizes.

VI. RESULTS

  • HyPER’s inclusive event efficiency is 67.0%, versus 65.1% for SPANet and 64.5% for Topograph, despite having only 3.45 × 10^3 network parameters.SPANet and Topograph have 1.7 × 10^7 and 6.5 × 10^6 parameters, respectively.Source: §VI · p. 6, Table I · p. 6
  • HyPER’s inclusive top-quark efficiency is 64.4%, and its W-boson efficiency is marginally improved, though SPANet slightly exceeds it for top quarks at the lowest jet multiplicity.Across all jet-multiplicity regions, HyPER has moderately larger event efficiency than its counterparts.Source: §VI · pp. 5–6, Table II · p. 6
  • Reconstructed top-quark and W-boson invariant-mass distributions recover the truth peaks and generally retain the truth-kinematic shapes.Undetermined candidates have no truth counterpart, but their mass distributions have shapes that agree with the combined correct and incorrect categories.Source: §VI · p. 6, Figure 4 · p. 7
  • HyPER has the highest event efficiencies across truth t-tbar mass regions, especially around and above the production threshold.All three methods’ event efficiency increases for harder top-quark pairs; Topograph does better in lower-mass bins, while SPANet overtakes it in higher-mass bins.Source: §VI · p. 6, Figure 5 · p. 7
  • HyPER is the best-performing technique at every considered training-dataset size, while all three models generally lose reconstruction performance as datasets shrink.SPANet showed some instability below 10^6 training events; those runs were repeated and the highest event efficiency was used.Source: §VI · p. 7, Figure 6 · p. 7
  • HyPER has a far smaller GPU-memory footprint than the other networks during the reported training comparison, attributed to its fewer learnable parameters.Memory was measured on one Nvidia A100 GPU over 20 epochs, with batch sizes set to 2048 for this comparison.Source: §VI · pp. 7–8, Figure 7 · p. 8

VII. CONCLUSIONS

HyPER combines hypergraph representation learning with a parameter-efficient architecture for all-hadronic t-tbar reconstruction, and the paper describes how its representation could extend to other collider processes.

VII. CONCLUSIONS

  • 67% of fully matched events were reconstructed by HyPER, versus 65.1% by SPANet and 64.5% by Topograph, with 20 times fewer parameters.HyPER also performed comparatively better across t-tbar invariant-mass regions and training-dataset sizes.Source: §VII · p. 8
  • Hyperedges represent candidates decaying to arbitrary numbers of final states, and the paper proposes applying this representation to processes such as t-tbar-Higgs production.The authors also describe ongoing work on simultaneous reconstruction of final-state neutrino kinematics for four-top events.Source: §VII · p. 8
  • HyPER's edge and hyperedge outputs could support downstream event classification, or event classification could be added using global graph attributes without introducing additional MLPs.The paper presents these as possible extensions, not evaluated results.Source: §VII · p. 8

1. Graph input kinematics

  • Jet-level inputs include kinematics, b-tag indicators, pairwise invariant masses and angular separations, plus global jet and b-tag counts.Transverse momentum, energy and pairwise invariant mass are log-normalized before network input.Source: §1 · pp. 8–9

2. Message passing

  • Each message-passing layer updates edge, node and global attributes; HyPER repeats this process for three layers.Messages are aggregated from neighboring nodes to update node states, while the global attribute is updated from nodes.Source: §2 · p. 9

3. MLP design

  • HyPER's MLPs each have two fully connected hidden layers, with ReLU nonlinearity and dropout regularization.The MLPs share an architecture but vary in input and output dimensionalities.Source: §3 · p. 9

4. Hyperparameters

  • Hyperparameters were tuned across 100 HyPER models trained for ten epochs each, with pruning used to terminate unpromising trials early.The learning rate was reduced by a factor of 0.8 after ten epochs without improved validation hyperedge accuracy, and training stopped after 50 epochs without improvement.Source: §4 · p. 9

APPENDIX B: FULLY MATCHED EFFICIENCIES

  • HyPER had the highest per-top and per-W efficiencies across jet-multiplicity categories in fully matched events, and each network's metrics exceeded those for combined fully and partially matched events.The appendix reports these comparisons in Table IV.Source: Appendix B · pp. 9–10, Table IV · p. 10

APPENDIX C: PARTIAL EVENT TRAINING

With partially matched events included in training, all three models had higher per-top efficiency, while HyPER remained the best in that category. Supplementary plots describe HyPER scores and compare model efficiencies across jet multiplicities.

APPENDIX C: PARTIAL EVENT TRAINING

  • All three models had increased per-top efficiency when trained with partially matched events, but HyPER and Topograph had minor reductions in per-event performance; fully matched-trained HyPER retained the best per-event result.The authors attribute the per-top increase to the expanded training set, which provides more identifiable top quarks.Source: Appendix C · p. 10, Table V · p. 10

APPENDIX D: HyPER OUTPUTS

  • HyPER's reconstructed-particle scores show reasonable separation among correct, incorrect and undetermined categories.The paper proposes using the scores as discriminants, but says this use was not investigated.Source: Figure 8 · p. 10, Appendix D · p. 11
  • A selection requiring the top-quark and W-boson scores to exceed 0.8 covers 46.1% of fully matched events and has inclusive event efficiency εt¯t = 0.923.The authors note that fine-tuning the confidence requirements can optimize performance and statistics.Source: Appendix D · p. 11

APPENDIX E: SUPPLEMENTARY PLOTS

  • Confusion matrices show HyPER has the highest percentage of correctly matched jets; supplementary efficiency plots compare per-event and per-top efficiencies across jet multiplicities.The plots include HyPER, SPANet and Topograph.Source: Figure 9 · p. 11, Appendix E · p. 11, Figure 10 · p. 12
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