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Divergence Timing and Cumulative Disagreement under KV-Cache Eviction

KV-cache eviction perturbs the conditional token distributions governing autoregressive generation. We investigate how first-divergence timing and subsequent token mismatch determine cumulative disagreement. We derive an exact decomposition under a specified stepwise maximal coupling: the expected mismatch fraction equals a first-mismatch contribution plus post-divergence exposure multiplied by its mismatch rate. An explicit construction over unrestricted autoregressive kernel pairs realizes the sharp interval of risks compatible with a finite divergence-aligned observation window. Residual-branch conditional Monte Carlo provides unbiased joint estimates of occurrence, occupation, and window/tail contributions, with per-replicate variance dominance for total token loss. Complete trajectories from Meta-Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct show that SnapKV at 50% retention enters divergence later and less often than SnapKV-512 or recent-token retention with the same 50% prompt-cache budget, while post-divergence total variation (TV) remains high. In an exploratory analysis of 288 documents, post-divergence exposure accounts for 85-90% of four aggregate mismatch gaps. On 288 independent documents at 90% retention, prespecified comparisons show higher branch-aligned TV in the late than in the early window in both models.

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