GRKV: Global Regression for Training-Free KV Cache Compression in Long-Context LLMs
Authors: Junjie Peng, You Wu, Haoyi Wu, Jialong Han, Xiaohua Xie, Kewei Tu, Jianhuang Lai
Organizations: 1Sun Yat-sen University · 2ShanghaiTech University · 3Guangdong Province Key Laboratory of Information Security Technology
Abstract
Large language models (LLMs) with extended context lengths rely on the key-value (KV) cache to support attention over prior tokens. However, maintaining the KV cache incurs substantial memory overhead, motivating KV-cache compression methods that enforce a fixed budget through eviction and merging. Modern eviction methods increasingly adopt span-based retention because preserving contiguous spans is empirically effective and better preserves semantic coherence. Yet, when combined with post-eviction merging, span-based retention concentrates merges onto a small set of span-boundary carrier tokens, producing a highly imbalanced merge pattern that exacerbates over-merging and increases information loss. To address this imbalance, we propose GRKV (Global Regression for KV Cache), a training-free KV-cache merging method that directly minimizes the discrepancy between compressed-cache and full-cache attention outputs. GRKV uses ridge-regression-based merge steps to distribute information from evicted tokens across retained tokens, while regularizing the updates to prevent over-smoothing. Across the LongBench and RULER long-context benchmarks, GRKV is the only merging method that improves overall performance with minimal overhead. Our code is available at https://github.com/pjunjie/GRKV.
Long-context large language model (LLM) inference is increasingly constrained by the memory footprint and decoding cost of key-value (KV) caches, limiting sustainable deployment on resource-constrained hardware. Existing KV cache eviction methods typically apply heuristic token scoring over all heads in GQA-based LLMs. These methods ignore the different functionalities of attention heads, leading to the eviction of critical tokens and thus degrading the performance of LLMs. To address this issue, we propose CompressKV, a resource-efficient KV-cache compression framework for GQA-based LLMs. Instead of aggregating attention scores from all heads, CompressKV identifies Semantic Retrieval Heads (SRHs) that capture both the initial and final tokens of a prompt and semantically important mid-context evidence, and uses them to select tokens whose KV pairs should be retained. Furthermore, CompressKV allocates cache budgets across layers according to offline estimates of layer-wise eviction error. Experiments on LongBench and Needle-in-a-Haystack show that CompressKV consistently outperforms existing KV-cache eviction methods across memory budgets. Notably, it preserves over 97% of full-cache performance using only 3% of the KV cache on LongBench question-answering tasks and achieves 90% accuracy with just 0.7% KV storage on Needle-in-a-Haystack. These results demonstrate an improved resource--performance trade-off for long-context LLM inference. Our code is publicly available at: https://github.com/TUDa-HWAI/CompressKV
Long-context inference in Large Language Models (LLMs) is bottlenecked by the linear growth of Key-Value (KV) cache memory. Existing KV cache compression paradigms are fundamentally limited by heuristics: heuristic budgeting relies on statistical priors rather than task objectives, causing resource misallocation, while heuristic selection relies on coupled query-key interactions or static inductive biases (e.g., attention sinks). To address this limitation, we introduce LKV (Learned KV Eviction), which formulates KV compression as an end-to-end differentiable optimization problem. LKV integrates LKV-H to learn task-optimized global budgets, and LKV-T to derive intrinsic KV importance without materializing attention matrices. This design bypasses heuristic proxies, strictly aligning compression with task objectives. Extensive evaluations demonstrate that LKV achieves state-of-the-art performance on both LongBench and RULER benchmarks at high compression rates. In particular, on LongBench, LKV achieves near-lossless performance with only 15% KV cache retention. Crucially, our analysis identifies learned budgeting as the dominant driver of fidelity, demonstrating that data-driven allocation is essential to overcome the limitations of hand-crafted heuristics.
Large language models (LLMs) face severe memory bottlenecks in long-context inference due to the linearly growing size of key-value (KV) caches. Existing KV cache compression techniques typically rely on simple heuristics, overlooking the distinct functional roles of different attention heads. We present SGD-KV (Summarization-Guided KV Cache Compression), a head-aware framework that leverages a novel chunk-summarization diagnostic task to systematically identify and prioritize attention heads specialized in hierarchical information aggregation. Experiments on Qwen2.5-7B-1M and Qwen3-32B across diverse long-context benchmarks demonstrate that SGD-KV achieves state-of-the-art performance with contexts up to 1M tokens, while reducing KV cache memory usage by up to 75%. Our findings show that strategically allocating the KV cache budget based on the summarization score distribution of attention heads yields a superior efficiency-accuracy trade-off for long-context inference.