# Equivariance Is Not All You Need: Characterizing the Utility of Equivariant Graph Neural Networks for Particle Physics Tasks

arXiv: https://arxiv.org/abs/2311.03094 · HTML: https://mlsanity.com/paper/2311.03094/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 28 of 28)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Energy Flow Networks: Deep Sets for Particle Jets](https://mlsanity.com/paper/1810.05165/) (2018)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Jet-Images -- Deep Learning Edition](https://mlsanity.com/paper/1511.05190/) (2015)
- [Accelerating Large Scale Real-Time GNN Inference using Channel Pruning](https://mlsanity.com/paper/2105.04528/) (2021)
- [Relaxing Equivariance Constraints with Non-stationary Continuous Filters](https://mlsanity.com/paper/2204.07178/) (2022)
- [Constraint-based graph network simulator](https://mlsanity.com/paper/2112.09161/) (2021)
- [PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics](https://mlsanity.com/paper/2211.00454/) (2022)
- [Symmetry Group Equivariant Architectures for Physics](https://mlsanity.com/paper/2203.06153/) (2022)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Graph Neural Networks for Charged Particle Tracking on FPGAs](https://mlsanity.com/paper/2112.02048/) (2021)
- [Semi-Equivariant GNN Architectures for Jet Tagging](https://mlsanity.com/paper/2202.06941/) (2022)
- [Equivariant Graph Neural Networks for Charged Particle Tracking](https://mlsanity.com/paper/2304.05293/) (2023)

## Built on by (most cited first, 5 of 5)

- [Locality-Sensitive Hashing-Based Efficient Point Transformer with Applications in High-Energy Physics](https://mlsanity.com/paper/2402.12535/) (2024)
- [Probing Equivariance and Symmetry Breaking in Convolutional Networks](https://mlsanity.com/paper/2501.01999/) (2025)
- [Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoods](https://mlsanity.com/paper/2410.18553/) (2024)
- [On the design space between molecular mechanics and machine learning force fields](https://mlsanity.com/paper/2409.01931/) (2024)
- [ColliderML: The First Release of an OpenDataDetector High-Luminosity Physics Benchmark Dataset](https://mlsanity.com/paper/2512.15230/) (2025)

## Abstract (arXiv)

Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for learning from physics data because they directly incorporate the symmetries of the underlying physical system. Drawing from the relevant literature around group equivariant networks, this paper presents a comprehensive evaluation of the proposed benefits of equivariant GNNs by using real-world particle physics reconstruction tasks as an evaluation test-bed. We demonstrate that many of the theoretical benefits generally associated with equivariant networks may not hold for realistic systems and introduce compelling directions for future research that will benefit both the scientific theory of ML and physics applications.