@inproceedings{li-etal-2026-expected,
title = "Expected Contribution Matching: Optimal Value Merging for {KV} Cache Compression",
author = "Li, Pengzhan and
Wang, Yixuan and
Che, Wanxiang",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.921/",
doi = "10.18653/2026.findings-emnlp.921",
pages = "19446--19458",
ISBN = "979-8-89176-462-0",
abstract = "Large Language Models (LLMs) use KV cache for efficient auto-regressive generation, but its linearly growing memory footprint bottlenecks long-context inference. Existing compression methods typically merge evicted information into retained tokens by additively combining both key and value vectors, despite their distinct roles in the attention mechanism. However, this uniform treatment overlooks the distinct roles of keys and values in attention: perturbations to keys are amplified through the Softmax exponential, whereas perturbations to values remain bounded and linear after Softmax. Based on this observation, we propose a differentiated strategy that evicts keys while merging values. Specifically, we formulate value merging as an MSE minimization problem and derive Expected Contribution Matching (ECM), a closed-form scheme that redistributes evicted values by their historical attention contributions. We further preserve semantic coherence by routing evicted information to semantically similar retained tokens via global semantic matching. Experiments on LongBench and LongBenchV2 demonstrate the effectiveness of our method, which achieves consistent improvements over existing training-free merging-based and eviction-based approaches under the same cache budget. Our code is available at https://github.com/Lpzhan931/ECM."
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<abstract>Large Language Models (LLMs) use KV cache for efficient auto-regressive generation, but its linearly growing memory footprint bottlenecks long-context inference. Existing compression methods typically merge evicted information into retained tokens by additively combining both key and value vectors, despite their distinct roles in the attention mechanism. However, this uniform treatment overlooks the distinct roles of keys and values in attention: perturbations to keys are amplified through the Softmax exponential, whereas perturbations to values remain bounded and linear after Softmax. Based on this observation, we propose a differentiated strategy that evicts keys while merging values. Specifically, we formulate value merging as an MSE minimization problem and derive Expected Contribution Matching (ECM), a closed-form scheme that redistributes evicted values by their historical attention contributions. We further preserve semantic coherence by routing evicted information to semantically similar retained tokens via global semantic matching. Experiments on LongBench and LongBenchV2 demonstrate the effectiveness of our method, which achieves consistent improvements over existing training-free merging-based and eviction-based approaches under the same cache budget. Our code is available at https://github.com/Lpzhan931/ECM.</abstract>
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%0 Conference Proceedings
%T Expected Contribution Matching: Optimal Value Merging for KV Cache Compression
%A Li, Pengzhan
%A Wang, Yixuan
%A Che, Wanxiang
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F li-etal-2026-expected
%X Large Language Models (LLMs) use KV cache for efficient auto-regressive generation, but its linearly growing memory footprint bottlenecks long-context inference. Existing compression methods typically merge evicted information into retained tokens by additively combining both key and value vectors, despite their distinct roles in the attention mechanism. However, this uniform treatment overlooks the distinct roles of keys and values in attention: perturbations to keys are amplified through the Softmax exponential, whereas perturbations to values remain bounded and linear after Softmax. Based on this observation, we propose a differentiated strategy that evicts keys while merging values. Specifically, we formulate value merging as an MSE minimization problem and derive Expected Contribution Matching (ECM), a closed-form scheme that redistributes evicted values by their historical attention contributions. We further preserve semantic coherence by routing evicted information to semantically similar retained tokens via global semantic matching. Experiments on LongBench and LongBenchV2 demonstrate the effectiveness of our method, which achieves consistent improvements over existing training-free merging-based and eviction-based approaches under the same cache budget. Our code is available at https://github.com/Lpzhan931/ECM.
%R 10.18653/2026.findings-emnlp.921
%U https://aclanthology.org/2026.findings-emnlp.921/
%U https://doi.org/10.18653/2026.findings-emnlp.921
%P 19446-19458
Markdown (Informal)
[Expected Contribution Matching: Optimal Value Merging for KV Cache Compression](https://aclanthology.org/2026.findings-emnlp.921/) (Li et al., Findings 2026)
ACL