Data to 7 Oct 2026

E(n) Equivariant Graph Neural Networks

arXiv 2102.09844 ↗First posted 19 Feb 2021cs.LG stat.MLcited by 951

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Cited by 131 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

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 scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

Key facts. Cited by 951 papers in the map (data through 7 Oct 2026). Builds on 32 of its 42 references that are in the map. First posted on arXiv 19 Feb 2021.

Builds on

32 of 42 references.

References · 32

2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
2017Neural Message Passing for Quantum Chemistrycited by 3,460
2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
2016Variational Graph Auto-Encoderscited by 1,373
2016Group Equivariant Convolutional Networkscited by 1,154
2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
2020Directional Message Passing for Molecular Graphscited by 556
2019Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Datacited by 532

20 more

2019General E(2)-Equivariant Steerable CNNscited by 441
2018GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Modelscited by 406
2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 375
2018Neural Relational Inference for Interacting Systemscited by 339
2016Steerable CNNscited by 298
2017Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuningcited by 288
2019Cormorant: Covariant Molecular Neural Networkscited by 262
2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
2018Graphite: Iterative Generative Modeling of Graphscited by 112
2019Graph Normalizing Flowscited by 103
2017Visual Interaction Networkscited by 94
2020Group Equivariant Stand-Alone Self-Attention For Visioncited by 63
2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
2018Covariant Compositional Networks For Learning Graphscited by 54
2020Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Propertiescited by 51
2019Equivariant Hamiltonian Flowscited by 39
2020Isometric Transformation Invariant and Equivariant Graph Convolutional Networkscited by 17
2020Set2Graph: Learning Graphs From Setscited by 16

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 44; 2022: 124; 2023: 196; 2024: 207; 2025: 220; 2026: 160.

951 papers.

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2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
2022Message Passing Neural PDE Solverscited by 368
2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
2024A Survey on Vision-Language-Action Models for Embodied AIcited by 274
2022Torsional Diffusion for Molecular Conformer Generationcited by 262
2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
2021Pre-training Molecular Graph Representation with 3D Geometrycited by 248
2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229

38 more

2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 182
2022Graph neural networks for materials science and chemistrycited by 181
2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 176
2022e3nn: Euclidean Neural Networkscited by 171
2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
2021E(n) Equivariant Normalizing Flowscited by 165
2022Multi-modal Molecule Structure-text Model for Text-based Retrieval and Editingcited by 165
2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
2022Protein Representation Learning by Geometric Structure Pretrainingcited by 161
20213D Infomax improves GNNs for Molecular Property Predictioncited by 146
2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
2022EquiBind: Geometric Deep Learning for Drug Binding Structure Predictioncited by 143
2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
2023Equivariant flow matchingcited by 131
2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
2022Pre-training via Denoising for Molecular Property Predictioncited by 124
2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
2021Geometric Deep Learning on Molecular Representationscited by 113
2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
2022Equivariance with Learned Canonicalization Functionscited by 106
2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
2024TFG: Unified Training-Free Guidance for Diffusion Modelscited by 103
2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
2024DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Designcited by 87
2023Everything is Connected: Graph Neural Networkscited by 85

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