# Equivariant Spherical Transformer for Efficient Molecular Modeling

arXiv: https://arxiv.org/abs/2505.23086 · HTML: https://mlsanity.com/paper/2505.23086/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 43 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [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)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Position Information in Transformers: An Overview](https://mlsanity.com/paper/2102.11090/) (2021)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [On the Universality of Rotation Equivariant Point Cloud Networks](https://mlsanity.com/paper/2010.02449/) (2020)
- [GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasets](https://mlsanity.com/paper/2204.02782/) (2022)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [Spherical Channels for Modeling Atomic Interactions](https://mlsanity.com/paper/2206.14331/) (2022)

## Built on by (most cited first, 3 of 3)

- [Universally Invariant Learning in Equivariant GNNs](https://mlsanity.com/paper/2510.13169/) (2025)
- [MARA: Continuous SE(3)-Equivariant Attention for Molecular Force Fields](https://mlsanity.com/paper/2602.02671/) (2026)
- [Suiren-1.0 Technical Report: A Family of Molecular Foundation Models](https://mlsanity.com/paper/2603.21942/) (2026)

## Abstract (arXiv)

Equivariant Graph Neural Networks (GNNs) have significantly advanced the modeling of 3D molecular structure by leveraging group representations. However, their message passing, heavily relying on Clebsch-Gordan tensor product convolutions, suffers from restricted expressiveness due to the limited non-linearity and low degree of group representations. To overcome this, we introduce the Equivariant Spherical Transformer (EST), a novel plug-and-play framework that applies a Transformer-like architecture to the Fourier spatial domain of group representations. EST achieves higher expressiveness than conventional models while preserving the crucial equivariant inductive bias through a uniform sampling strategy of spherical Fourier transforms. As demonstrated by our experiments on challenging benchmarks like OC20 and QM9, EST-based models achieve state-of-the-art performance. For the complex molecular systems within OC20, small models empowered by EST can outperform some larger models and those using additional data. In addition to demonstrating such strong expressiveness,we provide both theoretical and experimental validation of EST's equivariance as well, paving the way for new research in this area.