mlsanityData to 7 Oct 2026

Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

arXiv 1802.08219 ↗First posted 22 Feb 2018cs.LG cs.AI cs.CVcited by 735

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Cited by 46 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in arbitrary orientations. Our network uses filters built from spherical harmonics; due to the mathematical consequences of this filter choice, each layer accepts as input (and guarantees as output) scalars, vectors, and higher-order tensors, in the geometric sense of these terms. We demonstrate the capabilities of tensor field networks with tasks in geometry, physics, and chemistry.

Key facts. Cited by 735 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Feb 2018.

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Citing papers per year: 2021: 81; 2022: 121; 2023: 152; 2024: 143; 2025: 133; 2026: 105.

735 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  4. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  5. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  6. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  8. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  9. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  10. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  11. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  12. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
38 more
  1. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  2. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  3. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  4. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  5. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  6. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  7. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  8. 2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 182
  9. 2022Graph neural networks for materials science and chemistrycited by 181
  10. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 176
  11. 2022e3nn: Euclidean Neural Networkscited by 171
  12. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  13. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  14. 2021E(n) Equivariant Normalizing Flowscited by 165
  15. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  16. 2022EquiBind: Geometric Deep Learning for Drug Binding Structure Predictioncited by 143
  17. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  18. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  19. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  20. 2021CKConv: Continuous Kernel Convolution For Sequential Datacited by 117
  21. 2021Geometric Deep Learning on Molecular Representationscited by 113
  22. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  23. 2022Equivariance with Learned Canonicalization Functionscited by 106
  24. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  25. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
  26. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  27. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  28. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  29. 2024A Review of Large Language Models and Autonomous Agents in Chemistrycited by 96
  30. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  31. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
  32. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  33. 2024DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Designcited by 87
  34. 2023Everything is Connected: Graph Neural Networkscited by 85
  35. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 85
  36. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  37. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  38. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79

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