# Learning 3D Representations of Molecular Chirality with Invariance to Bond Rotations

arXiv: https://arxiv.org/abs/2110.04383 · HTML: https://mlsanity.com/paper/2110.04383/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 58 references that are in the map.
- First posted on arXiv 8 Oct 2021.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [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)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [A Generative Model for Molecular Distance Geometry](https://mlsanity.com/paper/1909.11459/) (2019)
- [Deep learning for molecular design - a review of the state of the art](https://mlsanity.com/paper/1903.04388/) (2019)
- [Chirality Nets for Human Pose Regression](https://mlsanity.com/paper/1911.00029/) (2019)
- [Molecular machine learning with conformer ensembles](https://mlsanity.com/paper/2012.08452/) (2020)
- [Neural Message Passing on High Order Paths](https://mlsanity.com/paper/2002.10413/) (2020)
- [Visual Chirality](https://mlsanity.com/paper/2006.09512/) (2020)

## Built on by (most cited first, 29 of 29)

- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Graph Positional and Structural Encoder](https://mlsanity.com/paper/2307.07107/) (2023)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Geometry-Complete Perceptron Networks for 3D Molecular Graphs](https://mlsanity.com/paper/2211.02504/) (2022)
- [On the Completeness of Invariant Geometric Deep Learning Models](https://mlsanity.com/paper/2402.04836/) (2024)
- [3D Graph Contrastive Learning for Molecular Property Prediction](https://mlsanity.com/paper/2208.06360/) (2022)
- [Learning Over Molecular Conformer Ensembles: Datasets and Benchmarks](https://mlsanity.com/paper/2310.00115/) (2023)
- [PhAST: Physics-Aware, Scalable, and Task-specific GNNs for Accelerated Catalyst Design](https://mlsanity.com/paper/2211.12020/) (2022)
- [Knowledge-augmented Graph Machine Learning for Drug Discovery: A Survey](https://mlsanity.com/paper/2302.08261/) (2023)
- [ChiENN: Embracing Molecular Chirality with Graph Neural Networks](https://mlsanity.com/paper/2307.02198/) (2023)
- [E(3)-equivariant models cannot learn chirality: Field-based molecular generation](https://mlsanity.com/paper/2402.15864/) (2024)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [MolNet: A Chemically Intuitive Graph Neural Network for Prediction of Molecular Properties](https://mlsanity.com/paper/2203.09456/) (2022)
- [A 3D-Shape Similarity-based Contrastive Approach to Molecular Representation Learning](https://mlsanity.com/paper/2211.02130/) (2022)
- [Geometric Deep Learning for Structure-Based Drug Design: A Survey](https://mlsanity.com/paper/2306.11768/) (2023)
- [Learning Molecular Chirality via Chiral Determinant Kernels](https://mlsanity.com/paper/2602.07415/) (2026)
- [SE(3)-Invariant Multiparameter Persistent Homology for Chiral-Sensitive Molecular Property Prediction](https://mlsanity.com/paper/2312.07633/) (2023)
- [Predicting the Temperature Dependence of Surfactant CMCs Using Graph Neural Networks](https://mlsanity.com/paper/2403.03767/) (2024)
- [Predicting Protein-Ligand Binding Affinity with Equivariant Line Graph Network](https://mlsanity.com/paper/2210.16098/) (2022)
- [Urban delineation through the lens of commute networks: Leveraging graph embeddings to distinguish socioeconomic groups in cities](https://mlsanity.com/paper/2507.11057/) (2025)
- [Chi-Geometry: A Library for Benchmarking Chirality Prediction of GNNs](https://mlsanity.com/paper/2508.09097/) (2025)
- [Cross-Chirality Generalization by Axial Vectors for Hetero-Chiral Protein-Peptide Interaction Design](https://mlsanity.com/paper/2602.20176/) (2026)
- [h-MINT: Modeling Pocket-Ligand Binding with Hierarchical Molecular Interaction Network](https://mlsanity.com/paper/2604.23134/) (2026)
- [PhysECD: A Physics-Constrained E(3)-Equivariant Framework for Electronic Circular Dichroism Spectrum Prediction](https://mlsanity.com/paper/2608.21892/) (2026)
- [GSF-chi: Global Stereochemical Fields for Chiral Graph Transformers](https://mlsanity.com/paper/2609.12532/) (2026)

## Abstract (arXiv)

Molecular chirality, a form of stereochemistry most often describing relative spatial arrangements of bonded neighbors around tetrahedral carbon centers, influences the set of 3D conformers accessible to the molecule without changing its 2D graph connectivity. Chirality can strongly alter (bio)chemical interactions, particularly protein-drug binding. Most 2D graph neural networks (GNNs) designed for molecular property prediction at best use atomic labels to na"ively treat chirality, while E(3)-invariant 3D GNNs are invariant to chirality altogether. To enable representation learning on molecules with defined stereochemistry, we design an SE(3)-invariant model that processes torsion angles of a 3D molecular conformer. We explicitly model conformational flexibility by integrating a novel type of invariance to rotations about internal molecular bonds into the architecture, mitigating the need for multi-conformer data augmentation. We test our model on four benchmarks: contrastive learning to distinguish conformers of different stereoisomers in a learned latent space, classification of chiral centers as R/S, prediction of how enantiomers rotate circularly polarized light, and ranking enantiomers by their docking scores in an enantiosensitive protein pocket. We compare our model, Chiral InterRoto-Invariant Neural Network (ChIRo), with 2D and 3D GNNs to demonstrate that our model achieves state of the art performance when learning chiral-sensitive functions from molecular structures.