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arxiv.org: arXiv:2607.24555v2 Announce Type: replace-cross Abstract: Serving large language models at long context is bottlenecked by the key-value (KV) cache, which is read in full at every decode step. Attention keys are locally low-rank though globally high-rank: a fixed low-rank sketch shared across pages is provably blind to page-specific directions, while at the same summary size a page's own basis ranks pages and keeps carriers far better. LOCKS gives every page its own rank-$r$ spectral summary (resident, a tenth of the cache at $r{=}8$ and a twenty-fifth at $r{=}2$), reconstructs within-page logits, estimates each page's attention mass by log-sum-exp, and attends only the top pages; selection itself reads no candidate keys or values. Selecting on this summary alone stays within about a point of the full cache on long-document QA (LongBench-v1; Llama-3.1-8B), tracks the read-every-key exact-LSE oracle on retrieval-dense RULER down to the smallest budgets, and holds quality furthest into the small-budget regime on long-form reasoning (AIME26, MATH-500; Qwen3-4B), where selectors and eviction-based reasoning compressors both fall away. At a $2048$-token budget LOCKS matches FullKV aggregate quality at $100$K$+$ context (GLM-4-9B-Chat-1M) while attending about $2\%$ of the tokens; since the summary is scanned in full each step, the per-step KV read falls by about $10$--$25\times$ across that rank range, and this halves per-token decode latency ($2.0\times$ at $1$M tokens on one H200 NVL, measured at $r{=}8$) against dense attention. LOCKS ships as a drop-in plugin for unmodified vLLM, with batched decode running in full CUDA graphs.