# Rotation Invariant Graph Neural Networks using Spin Convolutions

arXiv: https://arxiv.org/abs/2106.09575 · HTML: https://mlsanity.com/paper/2106.09575/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (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)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://mlsanity.com/paper/2103.01436/) (2021)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storage](https://mlsanity.com/paper/2010.09435/) (2020)
- [Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials](https://mlsanity.com/paper/1806.03146/) (2018)

## Built on by (most cited first, 30 of 52)

- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (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)
- [Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matching](https://mlsanity.com/paper/2206.13602/) (2022)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Benchmarking Graphormer on Large-Scale Molecular Modeling Datasets](https://mlsanity.com/paper/2203.04810/) (2022)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)
- [AlphaDesign: A graph protein design method and benchmark on AlphaFoldDB](https://mlsanity.com/paper/2202.01079/) (2022)
- [Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products](https://mlsanity.com/paper/2401.10216/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [AdsorbML: A Leap in Efficiency for Adsorption Energy Calculations using Generalizable Machine Learning Potentials](https://mlsanity.com/paper/2211.16486/) (2022)
- [Towards Training Billion Parameter Graph Neural Networks for Atomic Simulations](https://mlsanity.com/paper/2203.09697/) (2022)
- [The Open DAC 2023 Dataset and Challenges for Sorbent Discovery in Direct Air Capture](https://mlsanity.com/paper/2311.00341/) (2023)
- [DPA-1: Pretraining of Attention-based Deep Potential Model for Molecular Simulation](https://mlsanity.com/paper/2208.08236/) (2022)
- [SToFM: a Multi-scale Foundation Model for Spatial Transcriptomics](https://mlsanity.com/paper/2507.11588/) (2025)
- [MolBind: Multimodal Alignment of Language, Molecules, and Proteins](https://mlsanity.com/paper/2403.08167/) (2024)
- [Baking Symmetry into GFlowNets](https://mlsanity.com/paper/2406.05426/) (2024)
- [PhAST: Physics-Aware, Scalable, and Task-specific GNNs for Accelerated Catalyst Design](https://mlsanity.com/paper/2211.12020/) (2022)
- [Impact of Domain Knowledge and Multi-Modality on Intelligent Molecular Property Prediction: A Systematic Survey](https://mlsanity.com/paper/2402.07249/) (2024)
- [GeoMFormer: A General Architecture for Geometric Molecular Representation Learning](https://mlsanity.com/paper/2406.16853/) (2024)
- [Towards Combinatorial Generalization for Catalysts: A Kohn-Sham Charge-Density Approach](https://mlsanity.com/paper/2310.18702/) (2023)

## Abstract (arXiv)

Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional Theory (DFT), are limited in their practical use due to their high computational expense. Machine learning approaches have the potential to approximate DFT in a computationally efficient manner, which could dramatically increase the impact of computational simulations on real-world problems. Approximating DFT poses several challenges. These include accurately modeling the subtle changes in the relative positions and angles between atoms, and enforcing constraints such as rotation invariance or energy conservation. We introduce a novel approach to modeling angular information between sets of neighboring atoms in a graph neural network. Rotation invariance is achieved for the network's edge messages through the use of a per-edge local coordinate frame and a novel spin convolution over the remaining degree of freedom. Two model variants are proposed for the applications of structure relaxation and molecular dynamics. State-of-the-art results are demonstrated on the large-scale Open Catalyst 2020 dataset. Comparisons are also performed on the MD17 and QM9 datasets.