# Symmetry-driven graph neural networks

arXiv: https://arxiv.org/abs/2105.14058 · HTML: https://mlsanity.com/paper/2105.14058/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 28 May 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [B-Spline CNNs on Lie Groups](https://mlsanity.com/paper/1909.12057/) (2019)
- [Learning with invariances in random features and kernel models](https://mlsanity.com/paper/2102.13219/) (2021)
- [Causal Discovery in Physical Systems from Videos](https://mlsanity.com/paper/2007.00631/) (2020)
- [Group Equivariant Stand-Alone Self-Attention For Vision](https://mlsanity.com/paper/2010.00977/) (2020)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)
- [Jet tagging in the Lund plane with graph networks](https://mlsanity.com/paper/2012.08526/) (2020)
- [Isometric Transformation Invariant and Equivariant Graph Convolutional Networks](https://mlsanity.com/paper/2005.06316/) (2020)
- [Symmetry meets AI](https://mlsanity.com/paper/2103.06115/) (2021)
- [Beyond permutation equivariance in graph networks](https://mlsanity.com/paper/2103.14066/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Continuous Rotation Canonicalization with Radial Beam Sampling](https://mlsanity.com/paper/2206.10690/) (2022)

## Abstract (arXiv)

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several types of transformations affecting the node coordinates. First, we build equivariance to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes, allowing for equivariance to the Euclidean group. Then, we introduce angle attributes to build equivariance to any angle preserving transformation - thus, to the conformal group. Thanks to their equivariance properties, the proposed models can be vastly more data efficient with respect to classical graph architectures, intrinsically equipped with a better inductive bias and better at generalising. We demonstrate these capabilities on a synthetic dataset composed of n-dimensional geometric objects. Additionally, we provide examples of their limitations when (the right) symmetries are not present in the data.