Clebsch-Gordan Transformer: Fast and Global Equivariant Attention

• URL: http://arxiv.org/abs/2509.24093v1
• Date: Sun, 28 Sep 2025 22:09:36 GMT
• Title: Clebsch-Gordan Transformer: Fast and Global Equivariant Attention
• Authors: Owen Lewis Howell, Linfeng Zhao, Xupeng Zhu, Yaoyao Qian, Haojie Huang, Lingfeng Sun, Wil Thomason, Robert Platt, Robin Walters,
• Abstract summary: We propose Clebsch-Gordan Transformer, achieving efficient global attention by a novel Clebsch-Gordon Convolution on $SO(3)$ irreducible representations.<n>Our method enables equivariant modeling of features at all orders while achieving $O(N log N)$ input token complexity.<n>We benchmark our method on a diverse set of benchmarks including n-body simulation, QM9, ModelNet point cloud classification and a robotic grasping dataset.
• Score: 19.720202550140325
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The global attention mechanism is one of the keys to the success of transformer architecture, but it incurs quadratic computational costs in relation to the number of tokens. On the other hand, equivariant models, which leverage the underlying geometric structures of problem instance, often achieve superior accuracy in physical, biochemical, computer vision, and robotic tasks, at the cost of additional compute requirements. As a result, existing equivariant transformers only support low-order equivariant features and local context windows, limiting their expressiveness and performance. This work proposes Clebsch-Gordan Transformer, achieving efficient global attention by a novel Clebsch-Gordon Convolution on $\SO(3)$ irreducible representations. Our method enables equivariant modeling of features at all orders while achieving ${O}(N \log N)$ input token complexity. Additionally, the proposed method scales well with high-order irreducible features, by exploiting the sparsity of the Clebsch-Gordon matrix. Lastly, we also incorporate optional token permutation equivariance through either weight sharing or data augmentation. We benchmark our method on a diverse set of benchmarks including n-body simulation, QM9, ModelNet point cloud classification and a robotic grasping dataset, showing clear gains over existing equivariant transformers in GPU memory size, speed, and accuracy.

Related papers

• A Hybrid Transformer Architecture with a Quantized Self-Attention Mechanism Applied to Molecular Generation [0.0]
  We propose a hybrid quantum-classical self-attention mechanism as part of a transformer decoder.<n>We show that the time complexity of the query-key dot product is reduced from $mathcalO(n2 d)$ in a classical model to $mathcalO(n2 d)$ in our quantum model.<n>This work provides a promising avenue for quantum-enhanced natural language processing (NLP)
  arXiv  Detail & Related papers  (2025-02-26T15:15:01Z)
• Token Statistics Transformer: Linear-Time Attention via Variational Rate Reduction [29.12836710966048]
  We propose a novel transformer attention operator whose computational complexity scales linearly with the number of tokens.<n>Our results call into question the conventional wisdom that pairwise similarity style attention mechanisms are critical to the success of transformer architectures.
  arXiv  Detail & Related papers  (2024-12-23T18:59:21Z)
• Transformers as Support Vector Machines [54.642793677472724]
  We establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem. We characterize the implicit bias of 1-layer transformers optimized with gradient descent. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.
  arXiv  Detail & Related papers  (2023-08-31T17:57:50Z)
• ClusTR: Exploring Efficient Self-attention via Clustering for Vision Transformers [70.76313507550684]
  We propose a content-based sparse attention method, as an alternative to dense self-attention. Specifically, we cluster and then aggregate key and value tokens, as a content-based method of reducing the total token count. The resulting clustered-token sequence retains the semantic diversity of the original signal, but can be processed at a lower computational cost.
  arXiv  Detail & Related papers  (2022-08-28T04:18:27Z)
• CloudAttention: Efficient Multi-Scale Attention Scheme For 3D Point Cloud Learning [81.85951026033787]
  We set transformers in this work and incorporate them into a hierarchical framework for shape classification and part and scene segmentation. We also compute efficient and dynamic global cross attentions by leveraging sampling and grouping at each iteration. The proposed hierarchical model achieves state-of-the-art shape classification in mean accuracy and yields results on par with the previous segmentation methods.
  arXiv  Detail & Related papers  (2022-07-31T21:39:15Z)
• Frame Averaging for Invariant and Equivariant Network Design [50.87023773850824]
  We introduce Frame Averaging (FA), a framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. We show that FA-based models have maximal expressive power in a broad setting. We propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs.
  arXiv  Detail & Related papers  (2021-10-07T11:05:23Z)
• Combiner: Full Attention Transformer with Sparse Computation Cost [142.10203598824964]
  We propose Combiner, which provides full attention capability in each attention head while maintaining low computation complexity. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach.
  arXiv  Detail & Related papers  (2021-07-12T22:43:11Z)
• $O(n)$ Connections are Expressive Enough: Universal Approximability of Sparse Transformers [71.31712741938837]
  We show that sparse Transformers with only $O(n)$ connections per attention layer can approximate the same function class as the dense model with $n2$ connections. We also present experiments comparing different patterns/levels of sparsity on standard NLP tasks.
  arXiv  Detail & Related papers  (2020-06-08T18:30:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.