# COBS: Cumulant Order Block Sparse Attention

arXiv: https://arxiv.org/abs/2607.09052 · HTML: https://mlsanity.com/paper/2607.09052/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 29 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Native Sparse Attention: Hardware-Aligned and Natively Trainable Sparse Attention](https://mlsanity.com/paper/2502.11089/) (2025)
- [Loki: Low-rank Keys for Efficient Sparse Attention](https://mlsanity.com/paper/2406.02542/) (2024)
- [Don't Read Everything: A Curvature-Conditioned Query for Linear Attention](https://mlsanity.com/paper/2606.01294/) (2026)

## Built on by (most cited first, 2 of 2)

- [LOCKS: Page-Local Compact Key Summaries for Efficient Long-Context Decoding](https://mlsanity.com/paper/2607.24555/) (2026)
- [The Evolution of Attention in Large Language Models: Mechanisms, Trade-offs, and Emerging Trends](https://mlsanity.com/paper/2609.39661/) (2026)

## Abstract (arXiv)

Block sparse attention is a hardware friendly way to alleviate the key-value (KV) cache read bottleneck in large language models (LLMs). However, it is not prevalent among leading open-weight LLMs, which rely instead on dense attention or fine-grained selection, thereby motivating our analysis. We study DeepSeek's Native Sparse Attention (NSA) as a representative method, whose three-branch design lets us isolate block selection, the most challenging and consequential stage. We formalize selection and reduce it to ranking blocks by a single quantity, the attention mass: the sum of a block's attention scores. We show that if selection retrieves the blocks with the largest attention mass, block sparse attention can match the quality of dense attention. However, computing the exact attention mass requires reading every key, so the problem of block selection ultimately reduces to approximating this mass from a compact summary instead of the full keys. Via a cumulant expansion, we show why existing methods falter: their selection strategies attempt to estimate the attention mass, but are confined to a first-order approximation. Therefore, we propose COBS (Cumulant Order Block Sparse Attention), an attention method that builds on NSA, incorporating a novel selector that stores a compressed second-order statistic per block. On the 32k RULER long-context retrieval benchmark, COBS raises the NSA baseline's mean score from 0.2999 to 0.8195, approaching dense attention at 0.9040 and closing about 86% of the gap, while using only 1.21x the KV cache read traffic of the NSA baseline and 15.15x less read traffic than dense. The same model preserves short-context behavior and attains lower position-wise negative log-likelihood (NLL) than dense attention in our comparison.