# Don't Read Everything: A Curvature-Conditioned Query for Linear Attention

arXiv: https://arxiv.org/abs/2606.01294 · HTML: https://mlsanity.com/paper/2606.01294/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 31 May 2026.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Hopfield Networks is All You Need](https://mlsanity.com/paper/2008.02217/) (2020)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Simple linear attention language models balance the recall-throughput tradeoff](https://mlsanity.com/paper/2402.18668/) (2024)
- [Zoology: Measuring and Improving Recall in Efficient Language Models](https://mlsanity.com/paper/2312.04927/) (2023)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)
- [Finetuning Pretrained Transformers into RNNs](https://mlsanity.com/paper/2103.13076/) (2021)
- [On the Expressiveness of Softmax Attention: A Recurrent Neural Network Perspective](https://mlsanity.com/paper/2507.23632/) (2025)
- [2Mamba2Furious: Linear in Complexity, Competitive in Accuracy](https://mlsanity.com/paper/2602.17363/) (2026)

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

- [COBS: Cumulant Order Block Sparse Attention](https://mlsanity.com/paper/2607.09052/) (2026)
- [Power law graph attention: exact generalization of scaled dot-product attention, empirical collapse at inference](https://mlsanity.com/paper/2608.10288/) (2026)

## Abstract (arXiv)

Linear attention reduces the quadratic cost of softmax attention by maintaining a recurrent fast-weight state, but it consistently lags on in-context retrieval and long-context tasks. Existing remedies act on the write side of memory through gating, delta updates, or kernel feature maps, but the read step is left unchanged: every past key contributes additively to the output, so useful targets are diluted by the bulk of stored vectors. We borrow one specific piece of softmax's geometry to construct a cheap read-time contraction of the query. A second-order Taylor expansion of the softmax log-partition at the isotropic-attention point gives a local quadratic model whose curvature coincides with the running key covariance, a quantity that can be maintained with the same recurrent/chunkwise mechanism as the linear-attention state. The associated linear operator contracts the query along the high-variance directions of memory before it reads the state. We call this mechanism Curvature-Conditioned Query (CCQ). CCQ modifies only the read step and is composable with any linear-attention backbone. Attached to GLA and Gated DeltaNet, it improves perplexity, zero-shot downstream accuracy, S-NIAH retrieval at and beyond the training context, length-extrapolation perplexity from 4K to 20K, and LongBench accuracy.