# Equivariant Graph Neural Networks for 3D Macromolecular Structure

arXiv: https://arxiv.org/abs/2106.03843 · HTML: https://mlsanity.com/paper/2106.03843/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [ATOM3D: Tasks On Molecules in Three Dimensions](https://mlsanity.com/paper/2012.04035/) (2020)
- [N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials](https://mlsanity.com/paper/1803.01588/) (2018)
- [Protein model quality assessment using rotation-equivariant, hierarchical neural networks](https://mlsanity.com/paper/2011.13557/) (2020)
- [Protein sequence-to-structure learning: Is this the end(-to-end revolution)?](https://mlsanity.com/paper/2105.07407/) (2021)

## Built on by (most cited first, 30 of 53)

- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [DiffBP: Generative Diffusion of 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2211.11214/) (2022)
- [Learning Hierarchical Protein Representations via Complete 3D Graph Networks](https://mlsanity.com/paper/2207.12600/) (2022)
- [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024)
- [Functional-Group-Based Diffusion for Pocket-Specific Molecule Generation and Elaboration](https://mlsanity.com/paper/2306.13769/) (2023)
- [Learning Subpocket Prototypes for Generalizable Structure-based Drug Design](https://mlsanity.com/paper/2305.13997/) (2023)
- [Over-Squashing in Graph Neural Networks: A Comprehensive survey](https://mlsanity.com/paper/2308.15568/) (2023)
- [Uncovering Neural Scaling Laws in Molecular Representation Learning](https://mlsanity.com/paper/2309.15123/) (2023)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [Equivariant Graph Attention Networks for Molecular Property Prediction](https://mlsanity.com/paper/2202.09891/) (2022)
- [Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning](https://mlsanity.com/paper/2306.01474/) (2023)
- [FABind: Fast and Accurate Protein-Ligand Binding](https://mlsanity.com/paper/2310.06763/) (2023)
- [Geometry-Complete Perceptron Networks for 3D Molecular Graphs](https://mlsanity.com/paper/2211.02504/) (2022)
- [Diffusion Models in Bioinformatics: A New Wave of Deep Learning Revolution in Action](https://mlsanity.com/paper/2302.10907/) (2023)
- [Multi-domain Distribution Learning for De Novo Drug Design](https://mlsanity.com/paper/2508.17815/) (2025)
- [Integration of Pre-trained Protein Language Models into Geometric Deep Learning Networks](https://mlsanity.com/paper/2212.03447/) (2022)
- [Pre-Training Protein Encoder via Siamese Sequence-Structure Diffusion Trajectory Prediction](https://mlsanity.com/paper/2301.12068/) (2023)
- [Generation of 3D Molecules in Pockets via Language Model](https://mlsanity.com/paper/2305.10133/) (2023)
- [RNAFlow: RNA Structure & Sequence Design via Inverse Folding-Based Flow Matching](https://mlsanity.com/paper/2405.18768/) (2024)
- [Equivariant Neural Operator Learning with Graphon Convolution](https://mlsanity.com/paper/2311.10908/) (2023)
- [Exploring Discrete Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2411.16644/) (2024)
- [SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representation](https://mlsanity.com/paper/2209.05924/) (2022)
- [UniSim: A Unified Simulator for Time-Coarsened Dynamics of Biomolecules](https://mlsanity.com/paper/2506.03157/) (2025)
- [BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation](https://mlsanity.com/paper/2507.00846/) (2025)
- [SE(3)-Hyena Operator for Scalable Equivariant Learning](https://mlsanity.com/paper/2407.01049/) (2024)
- [AtomSurf : Surface Representation for Learning on Protein Structures](https://mlsanity.com/paper/2309.16519/) (2023)
- [An Equivariant Pretrained Transformer for Unified 3D Molecular Representation Learning](https://mlsanity.com/paper/2402.12714/) (2024)
- [Improving Inverse Folding for Peptide Design with Diversity-regularized Direct Preference Optimization](https://mlsanity.com/paper/2410.19471/) (2024)
- [Accelerating Inference in Molecular Diffusion Models with Latent Representations of Protein Structure](https://mlsanity.com/paper/2311.13466/) (2023)
- [Rigid Protein-Protein Docking via Equivariant Elliptic-Paraboloid Interface Prediction](https://mlsanity.com/paper/2401.08986/) (2024)

## Abstract (arXiv)

Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide range of tasks from structural biology. Our method outperforms all reference architectures on three out of eight tasks in the ATOM3D benchmark, is tied for first on two others, and is competitive with equivariant networks using higher-order representations and spherical harmonic convolutions. In addition, we demonstrate that transfer learning can further improve performance on certain downstream tasks. Code is available at https://github.com/drorlab/gvp-pytorch.