Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs
Not on the map. Why?
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
- 2017Attention Is All You Needcited by 59,932
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
- 2020Language Models are Few-Shot Learnerscited by 32,199
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2017Graph Attention Networkscited by 8,854
- 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
- 2020End-to-End Object Detection with Transformerscited by 7,384
- 2017Inductive Representation Learning on Large Graphscited by 6,284
- 2016Layer Normalizationcited by 5,579
- 2020Training data-efficient image transformers & distillation through attentioncited by 4,560
38 more
- 2018How Powerful are Graph Neural Networks?cited by 4,355
- 2020wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representationscited by 3,853
- 2017MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applicationscited by 3,827
- 2017Neural Message Passing for Quantum Chemistrycited by 3,460
- 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
- 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
- 2016Group Equivariant Convolutional Networkscited by 1,154
- 2021Transformers in Vision: A Surveycited by 1,009
- 2021E(n) Equivariant Graph Neural Networkscited by 951
- 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
- 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
- 2021How Attentive are Graph Attention Networks?cited by 818
- 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
- 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
- 2020A Generalization of Transformer Networks to Graphscited by 653
- 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
- 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
- 2020Directional Message Passing for Molecular Graphscited by 556
- 2020Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classificationcited by 500
- 2021Rethinking Graph Transformers with Spectral Attentioncited by 468
- 2018Spherical CNNscited by 452
- 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
- 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
- 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
- 2021OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphscited by 328
- 2021Do Transformers Really Perform Bad for Graph Representation?cited by 318
- 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
- 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
- 2019Cormorant: Covariant Molecular Neural Networkscited by 262
- 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
- 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
- 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
- 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
- 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
- 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 213
- 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
- 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 168
- 2021Spherical Message Passing for 3D Graph Networkscited by 166
50 most cited of 69 All 69 (JSON)
Built on by
Citing papers per year: 2022: 5; 2023: 47; 2024: 67; 2025: 81; 2026: 58.
258 papers.
Sort:
By area:
- 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
- 2023SGFormer: Simplifying and Empowering Transformers for Large-Graph Representationscited by 131
- 2023Equivariant flow matchingcited by 131
- 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
- 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
- 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
- 2023Attending to Graph Transformerscited by 81
- 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
- 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
- 2024Orb: A Fast, Scalable Neural Network Potentialcited by 63
- 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 51
- 2024Does equivariance matter at scale?cited by 49
38 more
- 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
- 2023Geometric Algebra Transformercited by 46
- 2024Transferable Boltzmann Generatorscited by 43
- 2024SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matchingcited by 40
- 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
- 2023From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Predictioncited by 39
- 20233D molecule generation by denoising voxel gridscited by 38
- 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
- 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
- 2023Matbench Discovery -- A framework to evaluate machine learning crystal stability predictionscited by 34
- 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
- 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
- 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
- 2023Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencecited by 25
- 2024ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policycited by 24
- 2023Uncovering Neural Scaling Laws in Molecular Representation Learningcited by 23
- 2023Highly Accurate Quantum Chemical Property Prediction with Uni-Mol+cited by 22
- 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
- 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
- 2023Scaling Spherical CNNscited by 21
- 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
- 2025An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networkscited by 19
- 2023Generalist Equivariant Transformer Towards 3D Molecular Interaction Learningcited by 18
- 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
- 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
- 2024Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policiescited by 18
- 2025Scalable Generation of Spatial Transcriptomics from Histology Images via Whole-Slide Flow Matchingcited by 18
- 2022Protein Language Models and Structure Prediction: Connection and Progressioncited by 17
- 2024LieRE: Lie Rotational Positional Encodingscited by 16
- 2022DPA-1: Pretraining of Attention-based Deep Potential Model for Molecular Simulationcited by 15
- 2023EGraFFBench: Evaluation of Equivariant Graph Neural Network Force Fields for Atomistic Simulationscited by 15
- 2023Learning to design protein-protein interactions with enhanced generalizationcited by 15
- 2024TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulationscited by 15
- 2024Crystalformer: Infinitely Connected Attention for Periodic Structure Encodingcited by 15
- 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 15
- 2025Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometriescited by 15
- 2023MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modelingcited by 14
- 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 14
50 most cited of 258 All 258 (JSON)
- 2026ASPIRE: Saddle-Point Discovery through Set Prediction and Physical Refinement7 Oct 2026
- 2026NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning7 Oct 2026
- 2026Clifford Sheaf Neural Networks1 Oct 2026
- 2026Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction30 Sep 2026
- 2026E3J: An Efficient and Open-Source Backend for Euclidean Equivariant Operations on GPU and TPU28 Sep 2026
- 2026SphMind: Towards Robust, Training-Free VLM-based Spatial Reasoning with a 360 Camera27 Sep 2026
- 2026QSV: Quat-Sphere-Vision for Coupled Quaternion Attention on Spherical Lattices24 Sep 2026
- 2026EquiSELD: Efficient training of equivariant sound event localization and detection networks19 Sep 2026
- 2026Learning Materials Properties from Scarce Labels and Unlabeled Crystals31 Aug 2026
- 2026PhysECD: A Physics-Constrained E(3)-Equivariant Framework for Electronic Circular Dichroism Spectrum Prediction22 Aug 2026
- 2026Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations31 Jul 2026
- 2026Generator-Aligned Representation Interfaces for Diagnostic Soft Equivariance28 Jul 2026
38 more
- 2026EnsembleEGNN: Set-Based Graph Learning for Thermodynamic Ensembles of Cyclic Peptides23 Jul 2026
- 2026Sobek: Streaming Equivariant Tensor Product Convolutions20 Jul 2026
- 2026Pix2Act: Image-Space Manipulation Policies with Equivariant Augmentation13 Jul 2026
- 2026EAGOR: Embodied Reasoning in Omni-direction7 Jul 2026
- 2026Beyond Adam: SOAP and Muon for Faster, Label-Efficient Training of Machine Learning Interatomic Potentials2 Jul 2026
- 2026Spin-Weighted Spherical Harmonics Enable Complete and Scalable E(3)-Equivariant Networks1 Jul 2026
- 2026Mirror-Fusion Attention for Reflection-Aware Self-Supervised Representation Learning1 Jul 2026
- 2026ElemeNet: Multiscale Molecular Machine Learning with Uncertainty Quantification Across the Periodic Table29 Jun 2026
- 2026REViT: Roto-reflection Equivariant Convolutional Vision Transformer24 Jun 2026
- 2026Scalable Peptide Design via Memory-Efficient Equivariant Transformer23 Jun 2026
- 2026The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups18 Jun 2026
- 2026Equivariant Graph Neural Networks Improve Optical Spectra Prediction for Materials Screening17 Jun 2026
- 2026Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning17 Jun 2026
- 2026A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction12 Jun 2026
- 2026ProHiFlo: Hierarchical Flow Matching with Functional Guidance for De Novo Protein Generation3 Jun 2026
- 2026EpiFormer: Learning Antigen-Antibody Interactions for Epitope Prediction via Geometric Deep Learning2 Jun 2026
- 2026Benchmark Dataset for Catalysis on 2D MXenes30 May 2026
- 2026Latent Diffusion Pretraining for Crystal Property Prediction30 May 2026
- 2026TriSearch: Learning to Optimize Triangulations via Bistellar Flips28 May 2026
- 2026Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction20 May 2026
- 2026CatalyticMLLM: A Graph-Text Multimodal Large Language Model for Catalytic Materials17 May 2026
- 2026From Single-Step Edit Response to Multi-Step Molecular Optimization11 May 2026
- 2026Diagnosing Spectral Ceilings in Equivariant Neural Force Fields8 May 2026
- 2026h-MINT: Modeling Pocket-Ligand Binding with Hierarchical Molecular Interaction Network25 Apr 2026
- 2026A Systematic Survey and Benchmark of Deep Learning for Molecular Property Prediction in the Foundation Model Era17 Apr 2026
- 2026Exascale Multi-Task Graph Foundation Models for Imbalanced, Multi-Fidelity Atomistic Data15 Apr 2026
- 2026EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers10 Apr 2026
- 2026Tunable Soft Equivariance with Guarantees27 Mar 2026
- 2026Efficient Hybrid SE(3)-Equivariant Visuomotor Flow Policy via Spherical Harmonics for Robot Manipulation24 Mar 2026
- 2026GDEGAN: Gaussian Dynamic Equivariant Graph Attention Network for Ligand Binding Site Prediction20 Mar 2026
- 2026The Convergence Frontier: Integrating Machine Learning and High Performance Quantum Computing for Next-Generation Drug Discovery18 Mar 2026
- 2026Self-Conditioned Denoising for Atomistic Representation Learning17 Mar 2026
- 2026Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation10 Mar 2026
- 2026A recipe for scalable attention-based MLIPs: unlocking long-range accuracy with all-to-all node attention6 Mar 2026
- 2026MatRIS: Toward Reliable and Efficient Pretrained Machine Learning Interatomic Potentials2 Mar 2026
- 2026Enhancing Molecular Property Predictions by Learning from Bond Modelling and Interactions28 Feb 2026
- 2026Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materials24 Feb 2026
- 2026UBio-MolFM: A Universal Molecular Foundation Model for Bio-Systems13 Feb 2026
50 newest of 258 All 258 (JSON)
- 2023Equivariant flow matchingcited by 131
- 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
- 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 51
- 2024ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policycited by 24
- 2025Scalable Generation of Spatial Transcriptomics from Histology Images via Whole-Slide Flow Matchingcited by 18
- 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Spacecited by 7
- 2025A Practical Guide for Incorporating Symmetry in Diffusion Policycited by 4
- 20253D Equivariant Visuomotor Policy Learning via Spherical Projectioncited by 4
- 2025Guiding Diffusion Models with Reinforcement Learning for Stable Molecule Generationcited by 4
- 2023Ophiuchus: Scalable Modeling of Protein Structures through Hierarchical Coarse-graining SO(3)-Equivariant Autoencoderscited by 3
- 2024EquiFlow: Equivariant Conditional Flow Matching with Optimal Transport for 3D Molecular Conformation Predictioncited by 3
- 2026Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learning Force Fieldscited by 3
12 most cited of 19 All 19 (JSON)
- 2026ProHiFlo: Hierarchical Flow Matching with Functional Guidance for De Novo Protein Generation3 Jun 2026
- 2026Latent Diffusion Pretraining for Crystal Property Prediction30 May 2026
- 2026Efficient Hybrid SE(3)-Equivariant Visuomotor Flow Policy via Spherical Harmonics for Robot Manipulation24 Mar 2026
- 2026Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation10 Mar 2026
- 2026Elign: Equivariant Diffusion Model Alignment from Foundational Machine Learning Force Fields29 Jan 2026
- 2025VEDA: 3D Molecular Generation via Variance-Exploding Diffusion with Annealing11 Nov 2025
- 2025Guiding Diffusion Models with Reinforcement Learning for Stable Molecule Generation22 Aug 2025
- 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space2 Jul 2025
- 2025Generative Modeling of Full-Atom Protein Conformations using Latent Diffusion on Graph Embeddings20 Jun 2025
- 2025Scalable Generation of Spatial Transcriptomics from Histology Images via Whole-Slide Flow Matching25 May 2025
- 2025Equivariant Flow Matching for Point Cloud Assembly24 May 2025
- 20253D Equivariant Visuomotor Policy Learning via Spherical Projection22 May 2025
12 newest of 19 All 19 (JSON)
- 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
- 2023SGFormer: Simplifying and Empowering Transformers for Large-Graph Representationscited by 131
- 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
- 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
- 2023Attending to Graph Transformerscited by 81
- 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
- 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
- 2024Orb: A Fast, Scalable Neural Network Potentialcited by 63
- 2024Does equivariance matter at scale?cited by 49
- 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
- 2023Geometric Algebra Transformercited by 46
- 2024Transferable Boltzmann Generatorscited by 43
12 most cited of 234 All 234 (JSON)
- 2026ASPIRE: Saddle-Point Discovery through Set Prediction and Physical Refinement7 Oct 2026
- 2026NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning7 Oct 2026
- 2026Clifford Sheaf Neural Networks1 Oct 2026
- 2026Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction30 Sep 2026
- 2026E3J: An Efficient and Open-Source Backend for Euclidean Equivariant Operations on GPU and TPU28 Sep 2026
- 2026QSV: Quat-Sphere-Vision for Coupled Quaternion Attention on Spherical Lattices24 Sep 2026
- 2026EquiSELD: Efficient training of equivariant sound event localization and detection networks19 Sep 2026
- 2026Learning Materials Properties from Scarce Labels and Unlabeled Crystals31 Aug 2026
- 2026PhysECD: A Physics-Constrained E(3)-Equivariant Framework for Electronic Circular Dichroism Spectrum Prediction22 Aug 2026
- 2026Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations31 Jul 2026
- 2026Generator-Aligned Representation Interfaces for Diagnostic Soft Equivariance28 Jul 2026
- 2026EnsembleEGNN: Set-Based Graph Learning for Thermodynamic Ensembles of Cyclic Peptides23 Jul 2026
12 newest of 234 All 234 (JSON)