mlsanityData to 14 Oct 2026

e3nn: Euclidean Neural Networks

arXiv 2207.09453 ↗First posted 18 Jul 2022cs.LG cs.AI cs.NEcited by 174

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Abstract (arXiv)

We present e3nn, a generalized framework for creating E(3) equivariant trainable functions, also known as Euclidean neural networks. e3nn naturally operates on geometry and geometric tensors that describe systems in 3D and transform predictably under a change of coordinate system. The core of e3nn are equivariant operations such as the TensorProduct class or the spherical harmonics functions that can be composed to create more complex modules such as convolutions and attention mechanisms. These core operations of e3nn can be used to efficiently articulate Tensor Field Networks, 3D Steerable CNNs, Clebsch-Gordan Networks, SE(3) Transformers and other E(3) equivariant networks.

Key facts. Cited by 174 papers in the map (data through 14 Oct 2026). Builds on 19 of its 40 references that are in the map. First posted on arXiv 18 Jul 2022.

Builds on

19 of 40 references.

References · 19

  1. 2021E(n) Equivariant Graph Neural Networkscited by 965
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  4. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  5. 2020Directional Message Passing for Molecular Graphscited by 561
  6. 2018Spherical CNNscited by 456
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  8. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  9. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 256
  10. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  11. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  12. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 171
7 more
  1. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  2. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  3. 2020Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Propertiescited by 51
  4. 2020Finding Symmetry Breaking Order Parameters with Euclidean Neural Networkscited by 30
  5. 2022Generative Coarse-Graining of Molecular Conformationscited by 21
  6. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20
  7. 2021Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graphcited by 11

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 10; 2023: 39; 2024: 46; 2025: 39; 2026: 40.

174 papers.

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  1. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 313
  2. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 117
  3. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 109
  4. 2022Clifford Neural Layers for PDE Modelingcited by 92
  5. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  6. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  7. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 84
  8. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 68
  9. 2023EigenFold: Generative Protein Structure Prediction with Diffusion Modelscited by 63
  10. 2022Theory for Equivariant Quantum Neural Networkscited by 62
  11. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 53
  12. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 52
38 more
  1. 20233D molecule generation by denoising voxel gridscited by 40
  2. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  3. 2023Geometric Clifford Algebra Networkscited by 38
  4. 2023Aligned Diffusion Schr"odinger Bridgescited by 38
  5. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  6. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 36
  7. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  8. 2023Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic sizecited by 33
  9. 2024Cartesian atomic cluster expansion for machine learning interatomic potentialscited by 31
  10. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 29
  11. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  12. 2025A practical guide to machine learning interatomic potentials -- Status and futurecited by 26
  13. 2023Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencecited by 25
  14. 2023Uncovering Neural Scaling Laws in Molecular Representation Learningcited by 23
  15. 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
  16. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 20
  17. 2024DisCo-Diff: Enhancing Continuous Diffusion Models with Discrete Latentscited by 20
  18. 2024Structure-based drug design by denoising voxel gridscited by 19
  19. 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
  20. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  21. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 17
  22. 2023A General Framework for Equivariant Neural Networks on Reductive Lie Groupscited by 16
  23. 2023Approximately Equivariant Graph Networkscited by 16
  24. 2024Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridgecited by 16
  25. 2024Evaluating representation learning on the protein structure universecited by 16
  26. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 16
  27. 2022Lorentz group equivariant autoencoderscited by 15
  28. 2024TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulationscited by 15
  29. 2025Towards Fast, Specialized Machine Learning Force Fields: Distilling Foundation Models via Energy Hessianscited by 15
  30. 2025Force-Free Molecular Dynamics Through Autoregressive Equivariant Networkscited by 15
  31. 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 15
  32. 2022Machine learning and invariant theorycited by 13
  33. 2023CHGNet: Pretrained universal neural network potential for charge-informed atomistic modelingcited by 13
  34. 2023Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materialscited by 13
  35. 2023Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networkscited by 12
  36. 2025HIP: Hessian Interatomic Potentials without derivativescited by 12
  37. 2023SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasetscited by 11
  38. 2025High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Predictioncited by 11

50 most cited of 174 All 174 (JSON)