# PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics

arXiv: https://arxiv.org/abs/2211.00454 · HTML: https://mlsanity.com/paper/2211.00454/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [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)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [Automatic heterogeneous quantization of deep neural networks for low-latency inference on the edge for particle detectors](https://mlsanity.com/paper/2006.10159/) (2020)
- [Only Train Once: A One-Shot Neural Network Training And Pruning Framework](https://mlsanity.com/paper/2107.07467/) (2021)
- [Distance-Weighted Graph Neural Networks on FPGAs for Real-Time Particle Reconstruction in High Energy Physics](https://mlsanity.com/paper/2008.03601/) (2020)
- [Exponential Separations in Symmetric Neural Networks](https://mlsanity.com/paper/2206.01266/) (2022)
- [Nanosecond machine learning event classification with boosted decision trees in FPGA for high energy physics](https://mlsanity.com/paper/2104.03408/) (2021)

## Built on by (most cited first, 26 of 26)

- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)
- [Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics](https://mlsanity.com/paper/2405.14806/) (2024)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [Ultrafast jet classification on FPGAs for the HL-LHC](https://mlsanity.com/paper/2402.01876/) (2024)
- [Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant](https://mlsanity.com/paper/2505.20280/) (2025)
- [Anomalies, Representations, and Self-Supervision](https://mlsanity.com/paper/2301.04660/) (2023)
- [Reconstruction of Unstable Heavy Particles Using Deep Symmetry-Preserving Attention Networks](https://mlsanity.com/paper/2309.01886/) (2023)
- [Equivariance Is Not All You Need: Characterizing the Utility of Equivariant Graph Neural Networks for Particle Physics Tasks](https://mlsanity.com/paper/2311.03094/) (2023)
- [mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks](https://mlsanity.com/paper/2311.18744/) (2023)
- [Equivariant Neural Networks for General Linear Symmetries on Lie Algebras](https://mlsanity.com/paper/2510.22984/) (2025)
- [Feature Selection with Distance Correlation](https://mlsanity.com/paper/2212.00046/) (2022)
- [PCN: A Deep Learning Approach to Jet Tagging Utilizing Novel Graph Construction Methods and Chebyshev Graph Convolutions](https://mlsanity.com/paper/2309.08630/) (2023)
- [Rotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds](https://mlsanity.com/paper/2308.06271/) (2023)
- [Prompting Particle Physics: Tokenized Multi-modal Foundation Models for Combinatorially Many Tasks](https://mlsanity.com/paper/2609.31862/) (2026)
- [Image and Point-cloud Classification for Jet Analysis in High-Energy Physics: A survey](https://mlsanity.com/paper/2403.11934/) (2024)
- [Learning symmetries in datasets](https://mlsanity.com/paper/2504.05174/) (2025)
- [Latent Representation Learning in Heavy-Ion Collisions with MaskPoint Transformer](https://mlsanity.com/paper/2510.06691/) (2025)
- [KIGNet: Physics-Motivated Multi-Graph Representation Learning for Explainable Jet Tagging](https://mlsanity.com/paper/2512.07420/) (2025)
- [How unconstrained machine-learning models learn physical symmetries](https://mlsanity.com/paper/2603.24638/) (2026)
- [Unknown Unknowns: Model Misspecification in Machine Learning for Physics](https://mlsanity.com/paper/2608.13633/) (2026)
- [A Geometric Insight into Equivariant Message Passing Neural Networks on Riemannian Manifolds](https://mlsanity.com/paper/2310.10448/) (2023)
- [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)
- [Generative models on phase space](https://mlsanity.com/paper/2604.02415/) (2026)
- [Predict before you train: Scaling Laws for particle physics foundation models](https://mlsanity.com/paper/2607.23377/) (2026)

## Abstract (arXiv)

Many current approaches to machine learning in particle physics use generic architectures that require large numbers of parameters and disregard underlying physics principles, limiting their applicability as scientific modeling tools. In this work, we present a machine learning architecture that uses a set of inputs maximally reduced with respect to the full 6-dimensional Lorentz symmetry, and is fully permutation-equivariant throughout. We study the application of this network architecture to the standard task of top quark tagging and show that the resulting network outperforms all existing competitors despite much lower model complexity. In addition, we present a Lorentz-covariant variant of the same network applied to a 4-momentum regression task.