# Value-Guided KV Compression for LLMs via Approximated CUR Decomposition

arXiv: https://arxiv.org/abs/2509.15038 · HTML: https://mlsanity.com/paper/2509.15038/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 24 of 24)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [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)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [The NarrativeQA Reading Comprehension Challenge](https://mlsanity.com/paper/1712.07040/) (2017)
- [SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization](https://mlsanity.com/paper/1911.12237/) (2019)
- [A Dataset of Information-Seeking Questions and Answers Anchored in Research Papers](https://mlsanity.com/paper/2105.03011/) (2021)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [QMSum: A New Benchmark for Query-based Multi-domain Meeting Summarization](https://mlsanity.com/paper/2104.05938/) (2021)
- [RepoBench: Benchmarking Repository-Level Code Auto-Completion Systems](https://mlsanity.com/paper/2306.03091/) (2023)
- [Efficient Attentions for Long Document Summarization](https://mlsanity.com/paper/2104.02112/) (2021)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [LongCoder: A Long-Range Pre-trained Language Model for Code Completion](https://mlsanity.com/paper/2306.14893/) (2023)
- [ChunkKV: Semantic-Preserving KV Cache Compression for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2502.00299/) (2025)

## Built on by (most cited first, 7 of 7)

- [KV Packet: Recomputation-Free Context-Independent KV Caching for LLMs](https://mlsanity.com/paper/2604.13226/) (2026)
- [Value-Aware Stochastic KV Cache Eviction for Reasoning Models](https://mlsanity.com/paper/2606.03928/) (2026)
- [Revisiting Multimodal KV Cache Compression: A Frequency-Domain-Guided Outlier-KV-Aware Approach](https://mlsanity.com/paper/2511.16786/) (2025)
- [SPHERICAL KV: Angle-Domain Attention and Rate-Distortion Retention for Efficient Long-Context Inference](https://mlsanity.com/paper/2605.18856/) (2026)
- [TaskPress: Query-Agnostic KV Cache Compression via Task-Guided Pruning](https://mlsanity.com/paper/2608.03276/) (2026)
- [KV2: A Self-Refining KV Cache](https://mlsanity.com/paper/2610.03198/) (2026)
- [Spend Bytes on Breadth: Precision-Count Trade-offs for Decode-Time KV Compression in Long Chain-of-Thought Reasoning](https://mlsanity.com/paper/2610.05685/) (2026)

## Abstract (arXiv)

Key-value (KV) cache compression has emerged as a critical technique for reducing the memory and latency overhead of autoregressive language models during inference. Prior approaches predominantly rely on query-key attention scores to rank and evict cached tokens, assuming that attention intensity correlates with semantic importance. However, this heuristic overlooks the contribution of value vectors, which directly influence the attention output. In this paper, we propose CurDKV, a novel, value-centric KV compression method that selects keys and values based on leverage scores computed from CUR matrix decomposition. Our approach approximates the dominant subspace of the attention output softmax(QKT)V, ensuring that the retained tokens best preserve the model's predictive behavior. Theoretically, we show that attention score approximation does not guarantee output preservation, and demonstrate that CUR-based selection minimizes end-to-end attention reconstruction loss. Empirically, CurDKV achieves up to 9.6% higher accuracy than state-of-the-art methods like SnapKV and ChunkKV under aggressive compression budgets on LLaMA and Mistral, while maintaining compatibility with FlashAttention and Grouped Query Attention. In addition to improved accuracy, CurDKV reduces generation latency by up to 40% at high compression, offering a practical speed-accuracy tradeoff.