# Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties

arXiv: https://arxiv.org/abs/2008.08461 · HTML: https://mlsanity.com/paper/2008.08461/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2020.

## Built on by (most cited first, 30 of 51)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Pre-training via Denoising for Molecular Property Prediction](https://mlsanity.com/paper/2206.00133/) (2022)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [INO: Invariant Neural Operators for Learning Complex Physical Systems with Momentum Conservation](https://mlsanity.com/paper/2212.14365/) (2022)
- [Relative Molecule Self-Attention Transformer](https://mlsanity.com/paper/2110.05841/) (2021)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Equivariant Graph Attention Networks for Molecular Property Prediction](https://mlsanity.com/paper/2202.09891/) (2022)
- [Federated Learning of Molecular Properties with Graph Neural Networks in a Heterogeneous Setting](https://mlsanity.com/paper/2109.07258/) (2021)
- [Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fields](https://mlsanity.com/paper/2403.09549/) (2024)
- [EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants](https://mlsanity.com/paper/2410.09667/) (2024)
- [Applying Machine Learning to Study Fluid Mechanics](https://mlsanity.com/paper/2110.02083/) (2021)
- [Machine learning and invariant theory](https://mlsanity.com/paper/2209.14991/) (2022)
- [EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers](https://mlsanity.com/paper/2604.09130/) (2026)
- [Using Multiple Vector Channels Improves E(n)-Equivariant Graph Neural Networks](https://mlsanity.com/paper/2309.03139/) (2023)
- [Implicit Convolutional Kernels for Steerable CNNs](https://mlsanity.com/paper/2212.06096/) (2022)

## Abstract (arXiv)

Equivariant neural networks (ENNs) are graph neural networks embedded in ℝ3 and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on distances between points, or also on angular features, making them rotationally invariant, or equivariant, respectively. This paper studies the practical value of including angular dependencies for molecular property prediction directly via an ablation study with texttte3nn and the QM9 data set. We find that, for fixed network depth and parameter count, adding angular features decreased test error by an average of 23%. Meanwhile, increasing network depth decreased test error by only 4% on average, implying that rotationally equivariant layers are comparatively parameter efficient. We present an explanation of the accuracy improvement on the dipole moment, the target which benefited most from the introduction of angular features.