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  • Technical Review
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Graph neural networks at the Large Hadron Collider

Nature Reviews Physics volume 5, pages 281–303 (2023)Cite this article

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Abstract

From raw detector activations to reconstructed particles, data at the Large Hadron Collider (LHC) are sparse, irregular, heterogeneous and highly relational in nature. Graph neural networks (GNNs), a class of algorithms belonging to the rapidly growing field of geometric deep learning (GDL), are well suited to tackling such data because GNNs are equipped with relational inductive biases that explicitly make use of localized information encoded in graphs. Furthermore, graphs offer a flexible and efficient alternative to rectilinear structures when representing sparse or irregular data, and can naturally encode heterogeneous information. For these reasons, GNNs have been applied to a number of LHC physics tasks including reconstructing particles from detector readouts and discriminating physics signals against background processes. We introduce and categorize these applications in a manner accessible to both physicists and non-physicists. Our explicit goal is to bridge the gap between the particle physics and GDL communities. After an accessible description of LHC physics, including theory, measurement, simulation and analysis, we overview applications of GNNs at the LHC. We conclude by highlighting technical challenges and future directions that may inspire further collaboration between the physics and GDL communities.

Key points

  • The LHC will face unprecedented technical challenges in processing and analysing large volumes of data during its high-luminosity (HL-LHC) phase; physicists are exploring various learning algorithms to maintain and improve physics performance at the HL-LHC.

  • Graphs are a flexible and efficient way to represent LHC data, which are sparse, irregular and heterogeneous in nature.

  • GNNs are well suited to making use of the highly relational nature of LHC data through mechanisms such as neural message passing.

  • GNNs have been applied to various LHC physics tasks including reconstruction (clustering), identification (classification), calibration (regression), anomaly detection and simulation (generative modelling).

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Fig. 1: Elementary particles and their production and observation at the LHC.
Fig. 2: Detectors and signatures specific to a given particle.
Fig. 3: Graph structure and the message-passing paradigm.
Fig. 4: A particle tracking pipeline based on edge classification.
Fig. 5: Edge representation and object condensation in multilayer calorimetry.
Fig. 6: Jet measurements, types, and representations.
Fig. 7: Event observables and representations.

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Acknowledgements

J.-R.V. is partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 772369) and by the US DOE, Office of Science, Office of High Energy Physics under award nos. DE-SC0011925, DE-SC0019227 and DE-AC02-07CH11359.

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Authors and Affiliations

  1. Princeton University, Princeton, NJ, USA

    Gage DeZoort

  2. DeepMind, London, UK

    Peter W. Battaglia

  3. Laboratoire des 2 Infinis — Toulouse (L2IT-IN2P3), Université de Toulouse, CNRS, UPS, Toulouse, France

    Catherine Biscarat

  4. California Institute of Technology, Pasadena, CA, USA

    Jean-Roch Vlimant

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  1. Gage DeZoort
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The authors contributed equally to all aspects of the article.

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Correspondence to Gage DeZoort.

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Official public site of the ALICE experiment: https://home.cern/science/experiments/alice

Official public site of the ATLAS experiment: https://home.cern/science/experiments/atlas

Official public site of the CMS experiment: https://home.cern/science/experiments/cms

Official public site of the LHCb experiment: https://home.cern/science/experiments/lhcb

Official public site of the Large Hadron Collier: https://home.cern/science/accelerators/large-hadron-collider

Official public site of the HH cross-section recommendations of the LHC Higgs Working Group: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHWGHH

Official public site of the High Luminosity LHC project: https://hilumilhc.web.cern.ch/content/hl-lhc-project

Supplementary information

Glossary

Attributed graphs

Graphs endowed with node features (X), edge features (E) or global features (P) are called attributed graphs.

Bidirected graphs

Graphs containing directed edges, where for every (u,v) ∈ E there is a corresponding (v,u) ∈ E, also appear in the literature122.

Directed edges

Edges that have an associated directionality, where the ordered tuple (u,v) implies that node u sends the edge and node v receives.

Heterogeneous graphs

Graphs are considered to be heterogeneous if they have different types of nodes/edges.

Hypergraphs

Hypergraphs generalize graphs by allowing for k-edge connectivity, where k-edges are edges that connect sets of k nodes. Standard graphs comprise 2-edges encoding only pairwise relations between nodes.

IRC-safe observables

Infrared and collinear-safe observables that do not change under the addition of low-energy particles (soft emissions) or the collinear division of a particle’s momentum.

Loss functions

Often referred to as objective functions, these are the functions that are minimized during the training of machine-learning (ML) algorithms.

Point clouds

Sets of data points arranged in space.

Trees

Trees are a special case of connected graphs in which nodes are connected by exactly one path; in this case, edges are called branches.

Truth information

Labels attached to data; frequently this refers to the target quantities that ML algorithms are trained to predict, and it is often used in high-energy physics jargon to describe simulation labels (for example kinematics, particle identities, particle origins).

Undirected edges

Edges that have no associated directionality so that (u,v) = (v,u).

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DeZoort, G., Battaglia, P.W., Biscarat, C. et al. Graph neural networks at the Large Hadron Collider. Nat Rev Phys 5, 281–303 (2023). https://doi.org/10.1038/s42254-023-00569-0

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