Cross-Model KV Cache Transfer in LLM Families: A Closed-Form Linear Mapping for Prefill Reuse — part 4/4

Cleaned-text code points [46117, 48975). Bibliography omitted here; source.md includes it.

For each pair we sweep k ∈ { 1 , 2 , 4 , 6 , 8 , 10 , 12 , 16 , 20 , 24 , all } k\in\{1,2,4,6,8,10,12,16,20,24,\text{all}\} and take the k k maximizing the arithmetic mean of the log-likelihood benchmark accuracies. The criterion nominally covers ARC-Challenge, HellaSwag, WinoGrande and MMLU, but WinoGrande is absent at most k k for these six pairs, so in practice the argmax is over ARC-Challenge, HellaSwag and MMLU. Near-ties break toward larger k k for evaluation coverage: five pairs take the argmax outright, and Ministral 3B → \to 8B takes k = all k{=}\text{all} over the argmax at k = 20 k{=}20 , which it trails by 0.38 0.38 pp (Appendix D ). GSM8K, CoQA and prefill latency never enter selection: the argmax is computed over the three benchmarks above, so they are holdouts by construction.

#### Leave-one-benchmark-out re-selection.

We drop one selection benchmark, re-select k k by argmax on the remaining two, and read the dropped benchmark at both the full-selection k k and the leave-one-out k k . This isolates how much a benchmark’s own inclusion raises its reported accuracy. The Ministral 3B → \to 8B rows use the data-driven argmax ( k = 20 k{=}20 ), not its manual override to k = all k{=}\text{all} .

The largest shift, 2.49 2.49 pp, occurs on Ministral 8B → \to 14B, a Tier 2 pair. Across the four Tier 1 pairs it is at most 1.45 1.45 pp.

#### Held-out benchmarks.

We evaluate each pair’s selected mapper on three benchmarks that played no part in selection (Table 18 ). Neither the fit nor k k is changed, so this measures the reported configuration out of sample.

Retention is at or above in-sample retention for every pair, and the tier structure of § 4.2 reappears: the four Tier 1 pairs stay above 96% and the two Tier 2 pairs below 64%. PIQA and ARC-Easy are easier than the selection benchmarks, so absolute levels are not comparable across the two sets.

## Instructions for reporting errors

We are continuing to improve HTML versions of papers, and your feedback helps enhance accessibility and mobile support. To report errors in the HTML that will help us improve conversion and rendering, choose any of the methods listed below:

Click the "Report Issue" ( ) button, located in the page header.

Tip: You can select the relevant text first, to include it in your report.

Our team has already identified the following issues . We appreciate your time reviewing and reporting rendering errors we may not have found yet. Your efforts will help us improve the HTML versions for all readers, because disability should not be a barrier to accessing research. Thank you for your continued support in championing open access for all.

Have a free development cycle? Help support accessibility at arXiv! Our collaborators at LaTeXML maintain a list of packages that need conversion , and welcome developer contributions .