mlsanityData to 7 Oct 2026

Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency

arXiv 2406.07598 ↗First posted 11 Jun 2024cs.LGcited by 18

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Abstract (arXiv)

We consider achieving equivariance in machine learning systems via frame averaging. Current frame averaging methods involve a costly sum over large frames or rely on sampling-based approaches that only yield approximate equivariance. Here, we propose Minimal Frame Averaging (MFA), a mathematical framework for constructing provably minimal frames that are exactly equivariant. The general foundations of MFA also allow us to extend frame averaging to more groups than previously considered, including the Lorentz group for describing symmetries in space-time, and the unitary group for complex-valued domains. Results demonstrate the efficiency and effectiveness of encoding symmetries via MFA across a diverse range of tasks, including n-body simulation, top tagging in collider physics, and relaxed energy prediction. Our code is available at https://github.com/divelab/MFA.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 71 of its 89 references that are in the map. First posted on arXiv 11 Jun 2024.

Builds on

71 of 89 references.

References · 71

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
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  3. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
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38 more
  1. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  2. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  3. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  4. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
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  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  7. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  8. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  9. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  10. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  11. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  12. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  13. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  14. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  15. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  16. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
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  20. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
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  22. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
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  24. 2019Deep Scale-spaces: Equivariance Over Scalecited by 113
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  26. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  27. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
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  38. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41

50 most cited of 71 All 71 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 9; 2026: 5.

18 papers.

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  1. 2024Probing the effects of broken symmetries in machine learningcited by 13
  2. 2024Relaxed Equivariance via Multitask Learningcited by 13
  3. 2025Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariantcited by 12
  4. 2025Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetrycited by 6
  5. 2025Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Framescited by 5
  6. 2025Learning Inter-Atomic Potentials without Explicit Equivariancecited by 5
  7. 2025Equivariant Neural Networks for General Linear Symmetries on Lie Algebrascited by 4
  8. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  9. 2024A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoilscited by 2
  10. 2026Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentialscited by 2
  11. 2026Adaptive Symmetry Discovery for Dynamical System Identificationcited by 2
  12. 2025Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computationscited by 1
6 more
  1. 2026Quantitative Approximation Rates for Group Equivariant Learningcited by 1
  2. 2024Adaptive Sampling for Continuous Group Equivariant Neural Networkscited by 0
  3. 2025CrystalFramer: Rethinking the Role of Frames for SE(3)-Invariant Crystal Structure Modelingcited by 0
  4. 2025NeurIPS 2024 ML4CFD Competition: Results and Retrospective Analysiscited by 0
  5. 2026When and How to Canonize: A Generalization Perspectivecited by 0
  6. 2026Sparse Data Augmentation for Optimization with Provable Guaranteescited by 0