Divergence Timing and Cumulative Disagreement under KV-Cache Eviction

Autoregressive decoding in Transformer-based language models relies on the KV cache, whose memory footprint grows linearly with sequence length and becomes the primary bottleneck for long-context inference. KV cache eviction addresses this by retaining a fixed-size subset of key-value pairs and discarding the rest. We identify that a primary source of output degradation is not the residual attention mass on evicted tokens, which existing methods already minimize, but a directional mismatch between the retained and evicted token sets. Specifically, the evicted tokens in practice are often near-orthogonal to the retained ones. Thus, even a small evicted mass could have an oversized impact on the resulting direction distribution and amplify into substantial output error. This reveals a fundamental limit in existing strategies. To address this, we propose MomentKV, which maintains compact, small-size moment statistics over the evicted token set, including a count, key mean, value mean, and value-key covariance. During eviction, the moment statistics is leveraged to identify tokens already well aligned with and captured by the accumulated summary, keeping the evicted set geometrically regular. During inference, they yield a closed-form first-order approximation of the evicted attention output, forming a mutually reinforcing loop between selective eviction and accurate correction. On LongBench and RULER with LLaMA-3.1-8B-Instruct and Qwen3-4B-Instruct, MomentKV outperforms all baselines at every cache budget, with the largest gains under aggressive compression.

Long-context inference is bottlenecked by the memory footprint of the key-value (KV) cache, especially for small models under tight resource budgets. Existing KV cache eviction methods score tokens using the model's attention distribution or, in attention-free variants, each key's distance from a global reference point. Using a controlled leave-one-out probe, we find that attention magnitude is unrelated to a token's causal contribution to the answer (Spearman $ρ=-0.004$), challenging the premise behind dominant eviction methods. We introduce TwinKV, a training-free, attention-free redundancy signal that detects whether a token's key has a near-duplicate elsewhere in context. Rather than replacing existing policies, TwinKV acts as a composable repair pass: given a policy's fixed retained set, it identifies evicted tokens with no surviving duplicate (\emph{orphans}) and retained tokens whose information is duplicated elsewhere (\emph{redundant donors}), then swaps them while preserving the original budget and scoring rule. We compose TwinKV with four recent eviction policies across LongBench, LooGLE, RULER, and a short-context MMLU-Pro no-harm control at compression ratios ${0.3,0.5,0.7}$. On Qwen3-4B, TwinKV improves a majority of configurations for two policies, is near-even for a third, and helps only a minority for a fourth adaptive baseline already near a performance ceiling; gains across the three non-ceiling policies are smallest at the loosest ratio. On RULER with Llama-3.2-1B, however, that fourth policy improves in every evaluated cell because its Alone score leaves substantial room to improve. More broadly, Llama-3.2-1B shows a smaller average LongBench gain but a higher fraction of improved cells on LongBench and LooGLE than Qwen3-4B, plus a clean RULER win. We also identify few-shot classification exemplars as a task structure where TwinKV does not help on either model.

The key-value (KV) cache is a major bottleneck in long-context inference, where memory and computation grow with sequence length. Existing KV eviction methods reduce this cost but typically degrade performance relative to full-cache inference. Our key insight is that full-cache attention is not always optimal: in long contexts, irrelevant tokens can dilute attention away from useful evidence, so selective, learnable eviction can improve generation rather than merely approximate the full cache. We introduce a global retention-based KV eviction method that learns each token's future utility under a unified memory budget. Lightweight retention gates assign utility scores to cached KV entries, and a shared final scoring projection calibrates these scores across all layers and heads. This enables a single global eviction policy in which tokens from different layers, heads, and modalities compete directly for cache capacity. We further provide theoretical analysis showing that preferentially retaining useful tokens reduces attention dilution, and we justify geometric retention as a query-agnostic proxy for future utility. Across diverse long-context language and vision-language reasoning, and multi-turn dialogue benchmarks, our method substantially reduces KV memory while matching or surpassing full-cache inference. These results suggest that learned, globally calibrated KV eviction is not only a compression technique, but also a mechanism for improving long-context reasoning.