GRKV: Global Regression for Training-Free KV Cache Compression in Long-Context LLMs

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 this https URL.

Computation and Language (cs.CL)

arXiv:2605.31105 [cs.CL]

(or arXiv:2605.31105v2 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2605.31105 Focus to learn more arXiv-issued DOI via DataCite

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