# Explainable Equivariant Neural Networks for Particle Physics: PELICAN

arXiv: https://arxiv.org/abs/2307.16506 · HTML: https://mlsanity.com/paper/2307.16506/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 67 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 22 of 22)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [On the Universality of Invariant Networks](https://mlsanity.com/paper/1901.09342/) (2019)
- [Fast inference of deep neural networks in FPGAs for particle physics](https://mlsanity.com/paper/1804.06913/) (2018)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Expressive Power of Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/2006.15646/) (2020)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [On the Universality of Rotation Equivariant Point Cloud Networks](https://mlsanity.com/paper/2010.02449/) (2020)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [Universal approximations of permutation invariant/equivariant functions by deep neural networks](https://mlsanity.com/paper/1903.01939/) (2019)
- [Point Cloud Transformers applied to Collider Physics](https://mlsanity.com/paper/2102.05073/) (2021)
- [Symmetry Group Equivariant Architectures for Physics](https://mlsanity.com/paper/2203.06153/) (2022)
- [Deep learning in color: towards automated quark/gluon jet discrimination](https://mlsanity.com/paper/1612.01551/) (2016)
- [Jet Constituents for Deep Neural Network Based Top Quark Tagging](https://mlsanity.com/paper/1704.02124/) (2017)
- [BIP: Boost Invariant Polynomials for Efficient Jet Tagging](https://mlsanity.com/paper/2207.08272/) (2022)

## Built on by (most cited first, 24 of 24)

- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Ultrafast jet classification on FPGAs for the HL-LHC](https://mlsanity.com/paper/2402.01876/) (2024)
- [Neural Scaling Laws for Boosted Jet Tagging](https://mlsanity.com/paper/2602.15781/) (2026)
- [EveNet: A Foundation Model for Particle Collision Data Analysis](https://mlsanity.com/paper/2601.17126/) (2026)
- [Reconstruction of Unstable Heavy Particles Using Deep Symmetry-Preserving Attention Networks](https://mlsanity.com/paper/2309.01886/) (2023)
- [Scaling Laws in Jet Classification](https://mlsanity.com/paper/2312.02264/) (2023)
- [RINO: Renormalization Group Invariance with No Labels](https://mlsanity.com/paper/2509.07486/) (2025)
- [Sub-microsecond Transformers for Jet Tagging on FPGAs](https://mlsanity.com/paper/2510.24784/) (2025)
- [Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoods](https://mlsanity.com/paper/2410.18553/) (2024)
- [SURFing to the Fundamental Limit of Jet Tagging](https://mlsanity.com/paper/2511.15779/) (2025)
- [ColliderML: The First Release of an OpenDataDetector High-Luminosity Physics Benchmark Dataset](https://mlsanity.com/paper/2512.15230/) (2025)
- [Explainable AI for Jet Tagging: A Comparative Study of GNNExplainer, GNNShap, and GradCAM for Jet Tagging in the Lund Jet Plane](https://mlsanity.com/paper/2604.25885/) (2026)
- [Any-Subgroup Equivariant Networks via Symmetry Breaking](https://mlsanity.com/paper/2603.19486/) (2026)
- [Optimal Symmetries in Binary Classification](https://mlsanity.com/paper/2408.08823/) (2024)
- [SEAL - A Symmetry EncourAging Loss for High Energy Physics](https://mlsanity.com/paper/2511.01982/) (2025)
- [19 Parameters Is All You Need: Tiny Neural Networks for Particle Physics](https://mlsanity.com/paper/2310.16121/) (2023)
- [Moments of Clarity: Streamlining Latent Spaces in Machine Learning using Moment Pooling](https://mlsanity.com/paper/2403.08854/) (2024)
- [Enhancing generalization in high energy physics using white-box adversarial attacks](https://mlsanity.com/paper/2411.09296/) (2024)
- [Tagging fully hadronic exotic decays of the vectorlike B quark using a graph neural network](https://mlsanity.com/paper/2505.07769/) (2025)
- [Generative models on phase space](https://mlsanity.com/paper/2604.02415/) (2026)
- [Group-Equivariant Poincar'e Convolutional Networks](https://mlsanity.com/paper/2607.00556/) (2026)
- [Local Diagnostics of Learned Event Representations for Anomaly Detection at the HL-LHC](https://mlsanity.com/paper/2610.13437/) (2026)
- [RINO: Renormalization Group Distillation with No Labels](https://mlsanity.com/paper/2610.15919/) (2026)

## Abstract (arXiv)

PELICAN is a novel permutation equivariant and Lorentz invariant or covariant aggregator network designed to overcome common limitations found in architectures applied to particle physics problems. Compared to many approaches that use non-specialized architectures that neglect underlying physics principles and require very large numbers of parameters, PELICAN employs a fundamentally symmetry group-based architecture that demonstrates benefits in terms of reduced complexity, increased interpretability, and raw performance. We present a comprehensive study of the PELICAN algorithm architecture in the context of both tagging (classification) and reconstructing (regression) Lorentz-boosted top quarks, including the difficult task of specifically identifying and measuring the W-boson inside the dense environment of the Lorentz-boosted top-quark hadronic final state. We also extend the application of PELICAN to the tasks of identifying quark-initiated vs.~gluon-initiated jets, and a multi-class identification across five separate target categories of jets. When tested on the standard task of Lorentz-boosted top-quark tagging, PELICAN outperforms existing competitors with much lower model complexity and high sample efficiency. On the less common and more complex task of 4-momentum regression, PELICAN also outperforms hand-crafted, non-machine learning algorithms. We discuss the implications of symmetry-restricted architectures for the wider field of machine learning for physics.