# MARA: Continuous SE(3)-Equivariant Attention for Molecular Force Fields

arXiv: https://arxiv.org/abs/2602.02671 · HTML: https://mlsanity.com/paper/2602.02671/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 49 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [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)
- [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)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [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)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [SphereUFormer: A U-Shaped Transformer for Spherical 360 Perception](https://mlsanity.com/paper/2412.06968/) (2024)
- [Spherical Transformer](https://mlsanity.com/paper/2202.04942/) (2022)
- [Attention on the Sphere](https://mlsanity.com/paper/2505.11157/) (2025)
- [Equivariant Spherical Transformer for Efficient Molecular Modeling](https://mlsanity.com/paper/2505.23086/) (2025)
- [Beyond Force Metrics: Pre-Training MLFFs for Stable MD Simulations](https://mlsanity.com/paper/2506.14850/) (2025)

## Built on by (most cited first, 1 of 1)

- [A library for differentiable signal processing and machine learning on the sphere](https://mlsanity.com/paper/2609.39737/) (2026)

## Abstract (arXiv)

Machine learning force fields (MLFFs) have become essential for accurate and efficient atomistic modeling. Despite their high accuracy, most existing approaches rely on fixed angular expansions, limiting flexibility in weighting local geometric interactions. We introduce Modular Angular-Radial Attention (MARA), a module that extends spherical attention -- originally developed for SO(3) tasks -- to the molecular domain and SE(3), providing an efficient approximation of equivariant interactions. MARA operates directly on the angular and radial coordinates of neighboring atoms, enabling flexible, geometrically informed, and modular weighting of local environments. Unlike existing attention mechanisms in SE(3)-equivariant architectures, MARA can be integrated in a plug-and-play manner into models such as MACE without architectural modifications. Across molecular benchmarks, MARA improves energy and force predictions, reduces high-error events, and enhances robustness. These results demonstrate that continuous spherical attention is an effective and generalizable geometric operator that increases the expressiveness, stability, and reliability of atomistic models.