# E(n) Equivariant Graph Neural Networks

@inproceedings{Satorras2021EnEG, title={E(n) Equivariant Graph Neural Networks}, author={Victor Garcia Satorras and Emiel Hoogeboom and Max Welling}, booktitle={International Conference on Machine Learning}, year={2021} }

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reﬂections and permutations called E( n ) Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily…

## 247 Citations

### Beyond permutation equivariance in graph networks

- Computer Science, MathematicsArXiv
- 2021

We introduce a novel architecture for graph networks which is equivariant to the Euclidean group in n-dimensions, and is additionally able to deal with affine transformations. Our model is designed…

### E(n) Equivariant Normalizing Flows

- Computer Science, MathematicsNeurIPS
- 2021

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs), the first flow that jointly generates molecule features and positions in 3D.

### Data efficiency in graph networks through equivariance

- Computer ScienceArXiv
- 2021

It is shown that, learning on a minimal amount of data, the architecture proposed can perfectly generalise to unseen data in a synthetic problem, while much more training data are required from a standard model to reach comparable performance.

### Symmetry-driven graph neural networks

- Computer ScienceArXiv
- 2021

Two graph network architectures that are equivariant to several types of transformations affecting the node coordinates are introduced that can be vastly more data efficient with respect to classical graph architectures, intrinsically equipped with a better inductive bias and better at generalising.

### E(n) Equivariant Normalizing Flows for Molecule Generation in 3D

- Computer ScienceArXiv
- 2021

It is demonstrated that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood.

### UNiTE: Unitary N-body Tensor Equivariant Network with Applications to Quantum Chemistry

- Computer ScienceArXiv
- 2021

This work proposes unitary N -body tensor equivariant neural network (UNiTE), an architecture for a general class of symmetric tensors called N - body tensors, and introduces a normalization method, viz., Equivariant Normalization, to improve generalization of the neural network while preserving symmetry.

### Equivariant Graph Neural Networks for 3D Macromolecular Structure

- Computer ScienceArXiv
- 2021

This work extends recent work on geometric vector perceptrons and applies equivariant graph neural networks to a wide range of tasks from structural biology and demonstrates that transfer learning can improve performance in learning from macromolecular structure.

### ChebLieNet: Invariant Spectral Graph NNs Turned Equivariant by Riemannian Geometry on Lie Groups

- Mathematics, Computer ScienceArXiv
- 2021

The existence of (data-dependent) sweet spots for anisotropic parameters on CIFAR10 is empirically proved, and ChebLieNet, a group-equivariant method on (anisotropic) manifolds is introduced, opening the doors to a better understanding of anisotropies.

### Frame Averaging for Invariant and Equivariant Network Design

- Computer Science, MathematicsArXiv
- 2021

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network…

### Self-Supervised Graph Representation Learning via Topology Transformations

- Computer ScienceIEEE Transactions on Knowledge and Data Engineering
- 2021

We present the Topology Transformation Equivariant Representation learning, a general paradigm of self-supervised learning for node representations of graph data to enable the wide applicability of…

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