---
title: "S2O: Early Stopping for Sparse Attention via Online Permutation"
description: "The authors argue that fixed-size blocks impose a sparsity ceiling. 32 references. Among them: 0."
authors: ["Yu Zhang", "Songwei Liu", "Chenqian Yan", "Linsheng", "Beichen Ning", "Fangmin Chen", "Xing Wang"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.351/"
doi: "10.18653/v1/2026.acl-long.351"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhang-2026-s2o-early-stopping-sparse-attention/"
---
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# S2O: Early Stopping for Sparse Attention via Online Permutation

**Authors:** [Yu Zhang](https://md.research.elamur.ai/free/en/authors/yu-zhang/), Songwei Liu, Chenqian Yan, Linsheng, Beichen Ning, Fangmin Chen and [Xing Wang](https://md.research.elamur.ai/free/en/authors/xing-wang/) · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.351/) · [PDF](https://aclanthology.org/2026.acl-long.351.pdf) · [DOI 10.18653/v1/2026.acl-long.351](https://doi.org/10.18653/v1/2026.acl-long.351) · [OpenAlex](https://openalex.org/W7166832430)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
Long-context LLM inference is held back by attention, whose cost grows quadratically with sequence length. Block-sparse attention built on FlashAttention reduces this cost. The authors argue that fixed-size blocks impose a sparsity ceiling. Real attention maps are made of thin vertical, horizontal and diagonal stripes, so even well-chosen blocks contain many near-zero entries.

S2O tackles this without physically moving tensors. Borrowing the idea of logical-to-physical address mapping, it builds lightweight index arrays: a segment-local query ordering and a global key/value ordering ranked by stripe-level mean pooling. The kernel uses these indices to fetch scattered tokens into SRAM. Blocks are then processed from most to least important. Computation stops once a block's score falls under a threshold τ, skipping the low-value tail within a controlled error budget. The authors report indexing overhead typically below 10%.

On Llama-3.1-8B at 128K tokens, S2O achieves lower operator error at equal sparsity, preserves end-to-end accuracy, and accelerates both attention and full inference. This suggests that reorder-aware, fine-grained sparsity can move past block-granularity limits.

## Key points
- At 128K context on Llama-3.1-8B, S2O gives the following results versus FlashAttention-based baselines:
  - 3.82× lower single-operator MSE at matched sparsity.
  - 3.31× lower prefill compute density at matched MSE.
  - Up to 7.51× attention speedup and 3.81× end-to-end speedup.
- In the 128K latency comparison, S2O reaches sparsity 0.933 with MSE 9.50e-05. This beats XAttn (2.74×), PBS-Attn (3.00×) and FlexPrefill (3.43×) in end-to-end speedup.
- Hyperparameter ablations were run on Qwen3-8B at 128K.
  - The threshold τ dominates the speed–accuracy trade-off. With S=2048, raising τ from 0.001 to 0.020 lifts sparsity from 0.721 to 0.944 and MSE from 0.00058 to 0.00876.
  - Segment length S (1024–4096) has little effect on error.
- In the component ablation, query permutation (Q perm) raises sparsity from 0.796 to 0.852 at similar error. Keeping only the dense local window produces much higher MSE (about 1.84×10⁻³).
- Limitations include:
  - Extra hyperparameters that may need re-tuning.
  - Evaluation only on the prefill stage of decoder-only LLMs.
  - Experiments on a single GPU and software stack.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Yu Zhang, Songwei Liu, Chenqian Yan, Linsheng, Beichen Ning, Fangmin Chen and Xing Wang. 2026. S2O: Early Stopping for Sparse Attention via Online Permutation. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{zhang2026s2o,
  title = {{S2O: Early Stopping for Sparse Attention via Online Permutation}},
  author = {Yu Zhang, Songwei Liu, Chenqian Yan, Linsheng, Beichen Ning, Fangmin Chen and Xing Wang},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.351},
  url = {https://doi.org/10.18653/v1/2026.acl-long.351}
}
```

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*Updated 2 November 2026*