# Multipole Semantic Attention: A Fast Approximation of Softmax Attention for Pretraining

arXiv: https://arxiv.org/abs/2509.10406 · HTML: https://mlsanity.com/paper/2509.10406/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Builds on (most cited first, 22 of 22)

- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [FlashInfer: Efficient and Customizable Attention Engine for LLM Inference Serving](https://mlsanity.com/paper/2501.01005/) (2025)
- [MoBA: Mixture of Block Attention for Long-Context LLMs](https://mlsanity.com/paper/2502.13189/) (2025)
- [Luna: Linear Unified Nested Attention](https://mlsanity.com/paper/2106.01540/) (2021)
- [Squeezed Attention: Accelerating Long Context Length LLM Inference](https://mlsanity.com/paper/2411.09688/) (2024)
- [H-Transformer-1D: Fast One-Dimensional Hierarchical Attention for Sequences](https://mlsanity.com/paper/2107.11906/) (2021)
- [Tactic: Adaptive Sparse Attention with Clustering and Distribution Fitting for Long-Context LLMs](https://mlsanity.com/paper/2502.12216/) (2025)
- [Multipole Attention for Efficient Long Context Reasoning](https://mlsanity.com/paper/2506.13059/) (2025)
- [A2ATS: Retrieval-Based KV Cache Reduction via Windowed Rotary Position Embedding and Query-Aware Vector Quantization](https://mlsanity.com/paper/2502.12665/) (2025)
- [Fast Multipole Attention: A Scalable Multilevel Attention Mechanism for Text and Images](https://mlsanity.com/paper/2310.11960/) (2023)

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

- [ClusterAttention: A training-free speedup of bidirectional attention](https://mlsanity.com/paper/2608.26965/) (2026)

## Abstract (arXiv)

Pretraining transformers on long sequences (entire code repositories, collections of related documents) is bottlenecked by quadratic attention costs. We present Multipole Semantic Attention (MuSe), which accelerates 64k-context pretraining by 36% while matching baseline loss, requiring no architectural changes. MuSe clusters queries and keys separately in representation space. This yields query-specific summaries that substantially outperform spatial blocking at matched sparsity, while also enabling drop-in compatibility with existing pretrained models; we validate on Llama 3.1-8B and 3.2-1B without retraining. We pretrain language models up to 1B parameters at 64k context on code and scientific documents, confirming that MuSe preserves quality and long-context utilization during training.