# Lorentz Group Equivariant Neural Network for Particle Physics

arXiv: https://arxiv.org/abs/2006.04780 · HTML: https://mlsanity.com/paper/2006.04780/

## Key facts

- Cited by 121 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 30 of 121)

- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Low Dimensional Invariant Embeddings for Universal Geometric Learning](https://mlsanity.com/paper/2205.02956/) (2022)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atze](https://mlsanity.com/paper/2112.07611/) (2021)
- [Interpretable Geometric Deep Learning via Learnable Randomness Injection](https://mlsanity.com/paper/2210.16966/) (2022)
- [PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics](https://mlsanity.com/paper/2211.00454/) (2022)
- [Clifford-Steerable Convolutional Neural Networks](https://mlsanity.com/paper/2402.14730/) (2024)
- [Explainable Equivariant Neural Networks for Particle Physics: PELICAN](https://mlsanity.com/paper/2307.16506/) (2023)
- [Symmetry Group Equivariant Architectures for Physics](https://mlsanity.com/paper/2203.06153/) (2022)
- [Improving Equivariant Model Training via Constraint Relaxation](https://mlsanity.com/paper/2408.13242/) (2024)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Models](https://mlsanity.com/paper/2410.04207/) (2024)
- [What is an equivariant neural network?](https://mlsanity.com/paper/2205.07362/) (2022)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)

## Abstract (arXiv)

We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the finite-dimensional representations of the Lorentz group and the equivariant nonlinearity involves the tensor product. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters and are much more physically interpretable than leading approaches that use CNNs and point cloud approaches. The competitive performance of the network is demonstrated on a public classification dataset [27] for tagging top quark decays given energy-momenta of jet constituents produced in proton-proton collisions.