mlsanityData to 7 Oct 2026

Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties

arXiv 2008.08461 ↗First posted 19 Aug 2020cs.LG physics.chem-ph physics.comp-phcited by 51

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Abstract (arXiv)

Equivariant neural networks (ENNs) are graph neural networks embedded in ℝ3 and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on distances between points, or also on angular features, making them rotationally invariant, or equivariant, respectively. This paper studies the practical value of including angular dependencies for molecular property prediction directly via an ablation study with texttte3nn and the QM9 data set. We find that, for fixed network depth and parameter count, adding angular features decreased test error by an average of 23%. Meanwhile, increasing network depth decreased test error by only 4% on average, implying that rotationally equivariant layers are comparatively parameter efficient. We present an explanation of the accuracy improvement on the dipole moment, the target which benefited most from the introduction of angular features.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Aug 2020.

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Citing papers per year: 2021: 11; 2022: 16; 2023: 11; 2024: 6; 2025: 5; 2026: 2.

51 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  3. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  4. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  5. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  6. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  7. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  8. 2022e3nn: Euclidean Neural Networkscited by 171
  9. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  10. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  11. 2021Geometric Deep Learning on Molecular Representationscited by 113
  12. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 105
38 more
  1. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  2. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  3. 2024FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributionscited by 52
  4. 2022Unsupervised Learning of Group Invariant and Equivariant Representationscited by 38
  5. 2023Geometric Clifford Algebra Networkscited by 37
  6. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 28
  7. 2022INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservationcited by 28
  8. 2021Relative Molecule Self-Attention Transformercited by 21
  9. 2022Graph Neural Networks for Moleculescited by 21
  10. 2021Federated Learning of Molecular Properties with Graph Neural Networks in a Heterogeneous Settingcited by 19
  11. 2022Equivariant Graph Attention Networks for Molecular Property Predictioncited by 19
  12. 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
  13. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 15
  14. 2021Applying Machine Learning to Study Fluid Mechanicscited by 13
  15. 2022Machine learning and invariant theorycited by 13
  16. 2023Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networkscited by 10
  17. 2022Implicit Convolutional Kernels for Steerable CNNscited by 9
  18. 2023Task-Equivariant Graph Few-shot Learningcited by 8
  19. 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Spacecited by 7
  20. 2026EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformerscited by 7
  21. 2021Optimal radial basis for density-based atomic representationscited by 4
  22. 2023Symmetry-enforcing neural networks with applications to constitutive modelingcited by 4
  23. 2026Explainable AI: Learning from the Learnerscited by 4
  24. 2023Geometric Deep Learning for Molecular Crystal Structure Predictioncited by 3
  25. 2023StrainTensorNet: Predicting crystal structure elastic properties using SE(3)-equivariant graph neural networkscited by 3
  26. 2023Ophiuchus: Scalable Modeling of Protein Structures through Hierarchical Coarse-graining SO(3)-Equivariant Autoencoderscited by 3
  27. 2024Molecule Graph Networks with Many-body Equivariant Interactionscited by 3
  28. 2025Equivariant Spherical Transformer for Efficient Molecular Modelingcited by 3
  29. 2023Molecular Conformation Generation via Shifting Scorescited by 2
  30. 2024Accelerating superconductor discovery through tempered deep learning of the electron-phonon spectral functioncited by 2
  31. 2022Machine learning frontier orbital energies of nanodiamondscited by 1
  32. 2022Learning Regularized Positional Encoding for Molecular Predictioncited by 1
  33. 2021Flexible dual-branched message passing neural network for quantum mechanical property prediction with molecular conformationcited by 0
  34. 2022Transferring Chemical and Energetic Knowledge Between Molecular Systems with Machine Learningcited by 0
  35. 2022Hierarchical Learning in Euclidean Neural Networkscited by 0
  36. 2023On Accelerating Diffusion-based Molecular Conformation Generation in SE(3)-invariant Spacecited by 0
  37. 2023Diffusion-Driven Generative Framework for Molecular Conformation Predictioncited by 0
  38. 2025Permutation Equivariant Neural Networks for Symmetric Tensorscited by 0

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