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

Dong Le, Thong Thanh Nguyen, Cong-Duy T Nguyen, Anh Tuan Luu


Abstract
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.
Anthology ID:
2026.emnlp-main.1153
Volume:
Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
Month:
October
Year:
2026
Address:
Budapest, Hungary
Editors:
Hung-Yi Lee, Sunipa Dev, Jessy Li, Desmond Elliott
Venue:
EMNLP
SIG:
SIGDAT
Publisher:
Association for Computational Linguistics
Note:
Pages:
26439–26458
Language:
URL:
https://aclanthology.org/2026.emnlp-main.1153/
DOI:
Bibkey:
Cite (ACL):
Dong Le, Thong Thanh Nguyen, Cong-Duy T Nguyen, and Anh Tuan Luu. 2026. Don’t Read Everything: A Curvature-Conditioned Query for Linear Attention. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 26439–26458, Budapest, Hungary. Association for Computational Linguistics.
Cite (Informal):
Don’t Read Everything: A Curvature-Conditioned Query for Linear Attention (Le et al., EMNLP 2026)
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PDF:
https://aclanthology.org/2026.emnlp-main.1153.pdf