# SE(3)-Hyena Operator for Scalable Equivariant Learning

arXiv: https://arxiv.org/abs/2407.01049 · HTML: https://mlsanity.com/paper/2407.01049/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 61 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 30 of 47)

- [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)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [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)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)

## Built on by (most cited first, 6 of 6)

- [HELM: Hierarchical Encoding for mRNA Language Modeling](https://mlsanity.com/paper/2410.12459/) (2024)
- [Beyond Sequence: Impact of Geometric Context for RNA Property Prediction](https://mlsanity.com/paper/2410.11933/) (2024)
- [DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules](https://mlsanity.com/paper/2506.19862/) (2025)
- [Clebsch-Gordan Transformer: Fast and Global Equivariant Attention](https://mlsanity.com/paper/2509.24093/) (2025)
- [HyperHELM: Hyperbolic Hierarchy Encoding for mRNA Language Modeling](https://mlsanity.com/paper/2509.24655/) (2025)
- [Breaking the Bottlenecks: Scalable Diffusion Models for 3D Molecular Generation](https://mlsanity.com/paper/2601.08963/) (2026)

## Abstract (arXiv)

Modeling global geometric context while maintaining equivariance is crucial for accurate predictions in many fields such as biology, chemistry, or vision. Yet, this is challenging due to the computational demands of processing high-dimensional data at scale. Existing approaches such as equivariant self-attention or distance-based message passing, suffer from quadratic complexity with respect to sequence length, while localized methods sacrifice global information. Inspired by the recent success of state-space and long-convolutional models, in this work, we introduce SE(3)-Hyena operator, an equivariant long-convolutional model based on the Hyena operator. The SE(3)-Hyena captures global geometric context at sub-quadratic complexity while maintaining equivariance to rotations and translations. Evaluated on equivariant associative recall and n-body modeling, SE(3)-Hyena matches or outperforms equivariant self-attention while requiring significantly less memory and computational resources for long sequences. Our model processes the geometric context of 20k tokens x3.5 times faster than the equivariant transformer and allows x175 longer a context within the same memory budget.