mlsanityData to 7 Oct 2026

Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs

arXiv 2206.11990 ↗First posted 23 Jun 2022cs.LG cs.AI physics.comp-phcited by 258

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Abstract (arXiv)

Despite their widespread success in various domains, Transformer networks have yet to perform well across datasets in the domain of 3D atomistic graphs such as molecules even when 3D-related inductive biases like translational invariance and rotational equivariance are considered. In this paper, we demonstrate that Transformers can generalize well to 3D atomistic graphs and present Equiformer, a graph neural network leveraging the strength of Transformer architectures and incorporating SE(3)/E(3)-equivariant features based on irreducible representations (irreps). First, we propose a simple and effective architecture by only replacing original operations in Transformers with their equivariant counterparts and including tensor products. Using equivariant operations enables encoding equivariant information in channels of irreps features without complicating graph structures. With minimal modifications to Transformers, this architecture has already achieved strong empirical results. Second, we propose a novel attention mechanism called equivariant graph attention, which improves upon typical attention in Transformers through replacing dot product attention with multi-layer perceptron attention and including non-linear message passing. With these two innovations, Equiformer achieves competitive results to previous models on QM9, MD17 and OC20 datasets.

Key facts. Cited by 258 papers in the map (data through 7 Oct 2026). Builds on 69 of its 92 references that are in the map. First posted on arXiv 23 Jun 2022.

Builds on

69 of 92 references.

References · 69

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38 more
  1. 2018How Powerful are Graph Neural Networks?cited by 4,355
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50 most cited of 69 All 69 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 47; 2024: 67; 2025: 81; 2026: 58.

258 papers.

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  1. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  2. 2023SGFormer: Simplifying and Empowering Transformers for Large-Graph Representationscited by 131
  3. 2023Equivariant flow matchingcited by 131
  4. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  5. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  6. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
  7. 2023Attending to Graph Transformerscited by 81
  8. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
  9. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  10. 2024Orb: A Fast, Scalable Neural Network Potentialcited by 63
  11. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 51
  12. 2024Does equivariance matter at scale?cited by 49
38 more
  1. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  2. 2023Geometric Algebra Transformercited by 46
  3. 2024Transferable Boltzmann Generatorscited by 43
  4. 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 40
  5. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  6. 2023From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Predictioncited by 39
  7. 20233D molecule generation by denoising voxel gridscited by 38
  8. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  9. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
  10. 2023Matbench Discovery -- A framework to evaluate machine learning crystal stability predictionscited by 34
  11. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  12. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  13. 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
  14. 2023Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencecited by 25
  15. 2024ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policycited by 24
  16. 2023Uncovering Neural Scaling Laws in Molecular Representation Learningcited by 23
  17. 2023Highly Accurate Quantum Chemical Property Prediction with Uni-Mol+cited by 22
  18. 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
  19. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  20. 2023Scaling Spherical CNNscited by 21
  21. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
  22. 2025An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networkscited by 19
  23. 2023Generalist Equivariant Transformer Towards 3D Molecular Interaction Learningcited by 18
  24. 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
  25. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  26. 2024Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policiescited by 18
  27. 2025Scalable Generation of Spatial Transcriptomics from Histology Images via Whole-Slide Flow Matchingcited by 18
  28. 2022Protein Language Models and Structure Prediction: Connection and Progressioncited by 17
  29. 2024LieRE: Lie Rotational Positional Encodingscited by 16
  30. 2022DPA-1: Pretraining of Attention-based Deep Potential Model for Molecular Simulationcited by 15
  31. 2023EGraFFBench: Evaluation of Equivariant Graph Neural Network Force Fields for Atomistic Simulationscited by 15
  32. 2023Learning to design protein-protein interactions with enhanced generalizationcited by 15
  33. 2024TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulationscited by 15
  34. 2024Crystalformer: Infinitely Connected Attention for Periodic Structure Encodingcited by 15
  35. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 15
  36. 2025Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometriescited by 15
  37. 2023MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modelingcited by 14
  38. 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 14

50 most cited of 258 All 258 (JSON)