mlsanityData to 7 Oct 2026

Universally Invariant Learning in Equivariant GNNs

arXiv 2510.13169 ↗First posted 15 Oct 2025cs.LGcited by 3

Not on the map. Why?

Abstract (arXiv)

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must effectively capture the intricate multi-body interactions among different nodes. Prior methods attain this via deeper architectures, augmented body orders, or increased degrees of steerable features, often at high computational cost and without polynomial-time solutions. In this work, we present a theoretically grounded framework for constructing complete equivariant GNNs that is both efficient and practical. We prove that a complete equivariant GNN can be achieved through two key components: 1) a complete scalar function, referred to as the canonical form of the geometric graph; and 2) a full-rank steerable basis set. Leveraging this finding, we propose an efficient algorithm for constructing complete equivariant GNNs based on two common models: EGNN and TFN. Empirical results demonstrate that our model demonstrates superior completeness and excellent performance with only a few layers, thereby significantly reducing computational overhead while maintaining strong practical efficacy.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 61 of its 108 references that are in the map. First posted on arXiv 15 Oct 2025.

Builds on

61 of 108 references.

References · 61

  1. 2017Deep Setscited by 1,394
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  4. 2020Directional Message Passing for Molecular Graphscited by 556
  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  6. 2018Spherical CNNscited by 452
  7. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  8. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  9. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  10. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  11. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  12. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
38 more
  1. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  2. 2022e3nn: Euclidean Neural Networkscited by 171
  3. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  4. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  5. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  6. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  7. 2022Equivariance with Learned Canonicalization Functionscited by 106
  8. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  9. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  10. 2022Conditional Antibody Design as 3D Equivariant Graph Translationcited by 75
  11. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  12. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  13. 2022Equivariant Graph Mechanics Networks with Constraintscited by 67
  14. 2021Molecule Generation by Principal Subgraph Mining and Assemblingcited by 53
  15. 2023End-to-End Full-Atom Antibody Designcited by 48
  16. 2022Energy-Motivated Equivariant Pretraining for 3D Molecular Graphscited by 37
  17. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  18. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  19. 2021Roto-translated Local Coordinate Frames For Interacting Dynamical Systemscited by 24
  20. 2023E(n) Equivariant Message Passing Simplicial Networkscited by 23
  21. 2023Is Distance Matrix Enough for Geometric Deep Learning?cited by 22
  22. 2024E(n) Equivariant Topological Neural Networkscited by 22
  23. 2023Generalist Equivariant Transformer Towards 3D Molecular Interaction Learningcited by 18
  24. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  25. 2023EquiPocket: an E(3)-Equivariant Geometric Graph Neural Network for Ligand Binding Site Predictioncited by 15
  26. 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 14
  27. 2024Geometric Representation Condition Improves Equivariant Molecule Generationcited by 13
  28. 2024Geometric Trajectory Diffusion Modelscited by 13
  29. 2024MMPolymer: A Multimodal Multitask Pretraining Framework for Polymer Property Predictioncited by 12
  30. 2025E2Former: An Efficient and Equivariant Transformer with Linear-Scaling Tensor Productscited by 12
  31. 2025A Survey of Graph Transformers: Architectures, Theories and Applicationscited by 12
  32. 2024On the Completeness of Invariant Geometric Deep Learning Modelscited by 11
  33. 2024Weisfeiler Leman for Euclidean Equivariant Machine Learningcited by 10
  34. 2025Large Language-Geometry Model: When LLM meets Equivariancecited by 10
  35. 2025ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generationcited by 10
  36. 2023Three iterations of (d-1)-WL test distinguish non isometric clouds of d-dimensional pointscited by 9
  37. 2025Siamese Foundation Models for Crystal Structure Predictioncited by 8
  38. 2023Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positivescited by 7

50 most cited of 61 All 61 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2026Identifiable Equivariant Networks are Layerwise Equivariantcited by 7
  2. 2025Geometric Mixture Models for Electrolyte Conductivity Predictioncited by 2
  3. 2026Reducing Symmetry Increase in Equivariant Neural Networkscited by 0