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

Bita Darvish Rouhani; Makesh Tarun Chandran; Maximilian Golub; Mohammad Mahdi Kamani; Pantea Zardoshti; Rasoul Shafipour; Ritchie Zhao; Ritika Borkar; Taekyung Heo

REVIEW 3 major objections 6 minor 12 references

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

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Cross-model KV cache transfer via closed-form per-head ridge mapping can skip receiver prefill in model-family swaps, retaining 73-98% of standalone accuracy on four of six matched-KV pairs.

desk verdict A solid, honestly-scoped empirical paper on cross-model KV transfer; the central claim holds for its four successful pairs, but the calibration-to-eval distribution shift is an unresolved deployment risk. read the letter →

arxiv 2608.03893 v1 pith:ZLHEVXOV submitted 2026-08-04 cs.LG

Taekyung Heo , Rasoul Shafipour , Ritchie Zhao , Maximilian Golub , Mohammad Mahdi Kamani , Ritika Borkar , Makesh Tarun Chandran , Pantea Zardoshti

show 1 more author

Bita Darvish Rouhani

This is my paper

classification cs.LG

keywords KVcachereusecross-modeltransferprefillaccelerationlinearmappingridgeregressionrotarypositionembeddingLLMservingmodelfamilies

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Production settings often swap between different-sized models in the same family, and each swap forces the receiving model to recompute prefill from scratch, which is costly for long contexts. This paper tries to establish that the first model's KV cache can be linearly transformed into the second model's format, allowing the receiver to skip prefill entirely. The central claim is that, when source and target share KV head count and per-head dimension, a closed-form per-head ridge regression fitted on just 500 calibration sequences retains 73-98% of standalone accuracy on four of six tested pairs and runs 2.7-25x faster than re-prefill. Two Ministral pairs degrade sharply, and a nonlinear MLP recovers most of the gap. If this holds, multi-model serving can reuse prefill work across model swaps without gradient-based adapters.

What carries the argument

The central object is a per-head closed-form ridge mapper. For each target layer and head, it concatenates key and value features from the top-k most predictive source layers and solves a Tikhonov-regularized least-squares problem, W* = (X^T X + lambda I)^-1 X^T Y, to project them into the target's KV space. Keys are mapped after stripping RoPE and re-encoded with target RoPE, making the fit position-free and reusable across context lengths. Cross-layer source selection, not reconstruction quality alone, carries most of the transfer performance.

What would settle it

Apply the paper's exact protocol to a matched-KV pair from an unseen fourth family, fitting on 500 FineWeb-Edu sequences and measuring floor-normalized HellaSwag retention; if the linear map consistently shows high calibration R2 yet near-zero retention, the claim that matched KV supports a transferable linear fit is falsified.

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Extended reading notes

Core claim

For matched-KV pairs, the target model's keys and values are largely linear functions of a small set of source layers: on Qwen3 14B to 32B, one source layer explains 56% of key variance and multiple source layers reach 79%. The authors build a per-head ridge mapper that strips rotary position embeddings from keys, selects the top-k most predictive source layers for each target layer, fits a closed-form linear regression in position-free content space, and re-applies the target's rotation. This mapper retains 73-98% of standalone accuracy on four of six matched-KV pairs, remains stable over multi-turn handoff, and is faster than re-prefill at every measured sequence length, while two harder p

Load-bearing premise

The mapper is fitted on 500 FineWeb-Edu sequences of 1,024 tokens, and the entire method assumes that this small calibration sample is representative of the prompts the receiver will actually serve; the paper's own two Ministral failures show the premise can break.

Editorial extensions

If this is right

A serving stack can skip the receiver's prefill during model-family swaps by applying one batched matrix multiply per target layer, cutting prefill latency by 2.7-25x at long context.
The fit is gradient-free and small-scale: 500 calibration sequences and one node fit a pair in under an hour, with no backpropagation through either model.
Transfer quality depends on where residual error lands relative to attention-sensitive directions, not on average reconstruction error, so attention-output cosine predicts cross-pair retention better than R2 does.
A nonlinear MLP drop-in recovers much of the accuracy that linear ridge loses on harder pairs, with HellaSwag retention gains up to 36.8 percentage points.
Multi-turn handoff between two Qwen3 sizes accumulates only small drift over ten turns, indicating that mid-conversation model switching does not cascade immediately.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The RoPE-stripped, position-free design suggests the same fitted weights should apply at context lengths far beyond the 1,024-token calibration window; the paper measures latency at 32K but does not report whether accuracy holds there, so a long-context accuracy test is the natural next step.
Nothing in the ridge solver requires matching KV head counts or per-head dimensions, so the same closed-form machinery could be tried on mismatched-KV pairs; the paper explicitly leaves this untested.
Attention-output cosine is measured only after fitting; a pre-fit proxy built from static source-target attention similarity on a few shared prompts could turn the diagnostic into a screening tool, though the paper does not construct one.
The two Ministral failures suggest that training-recipe or data-recipe differences, not just architecture, decide how linear the cross-model KV relationship is; comparing matched-architecture pairs with deliberately different fine-tuning data would separate those factors.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this paper is a solid, honestly-written empirical contribution to the LLM-serving literature. The headline claim — closed-form ridge mapping of cross-model KV caches works on four of six matched-KV pairs and preserves 73–98% of standalone accuracy — holds up as far as I can tell from the reported numbers. It doesn't open a new paradigm; it makes a specific optimization plausible, and the paper is candid that two of six pairs fail.

What is actually new: the observation of substantial linear structure in cross-model KV after RoPE stripping, the per-head ridge mapper with top-k source-layer selection, and the empirical result that attention-output cosine predicts per-pair retention better than R2. The ablations are real: component removal, calibration sensitivity to λ, N and domain, leave-one-benchmark-out k re-selection, held-out benchmarks, multi-turn drift, and latency across seven pairs. That is more reproducible scaffolding than most papers at this level, and the limitations section names the main gaps rather than hiding them.

The soft spots are proportionate. The stress-test concern about calibration-to-eval shift is real: Table 4 shows deeply negative eval-domain R2 on both Ministral failures, and even one Tier 1 pair has negative K R2 on HellaSwag tokens. So the “practical” claim is conditional on the deployment distribution resembling FineWeb-Edu-like prompts, and the paper offers no pre-fit screening to tell an operator which matched-KV pair will land in Tier 1. That is a genuine gap. It is not fatal to the paper’s core claim, because the paper already scopes success to the four pairs and labels the rest as failures. But a deployment-minded reader should not assume the method will transfer to arbitrary prompt distributions without checking the mapped cache’s attention-output cosine on representative data.

Other weaknesses: k is selected on eval benchmarks, though the leave-one-out bound of 2.49 pp is a reasonable mitigation; there are no error bars over calibration draws or eval seeds; large-to-small transfer accuracy is only shown on HellaSwag. These are minor in context. The citation pattern looks appropriate for a systems/ML paper.

Who is it for: anyone working on multi-model serving, model routing, or KV-cache reuse. It is not a theory paper and not a general claim about all LLM families. It deserves a serious referee: the right reviewer will ask for more pairs, a real screening signal, and variance estimates, but this is not a desk reject. I’d bring it to a reading group and would likely cite it when writing about prefill reuse.

Referee Report

3 major / 6 minor

Summary. The paper proposes cross-model KV cache transfer: for matched-KV pairs within an LLM family, the source model's KV cache is mapped to the target via per-head ridge regression. The mapper selects the top-k most predictive source layers per target layer, strips RoPE from keys before fitting and reapplies target RoPE at inference, and is calibrated on 500 FineWeb-Edu sequences of 1,024 tokens. The method is evaluated on six matched-KV pairs across Qwen3, Llama 3.1, and Ministral 3. Four pairs retain 73–98% of the target's standalone accuracy across five benchmarks, while two Ministral pairs degrade sharply (42–44% retention). An MLP recovers +24.3 to +36.8 pp HellaSwag retention on the failures. The mapper runs 2.7–25x faster than re-prefill and shows small multi-turn CoQA drift. The paper also reports ablations, calibration sensitivity, leave-one-out k re-selection, and held-out benchmarks.

Significance. If the result holds, cross-model KV cache transfer would be a meaningful prefill-skipping technique for multi-model serving, and the finding that substantial linear structure exists across matched-KV pairs is valuable. The paper is honest about the two failing pairs and provides useful ablations, calibration sensitivity analysis, held-out benchmarks, and a bounded analysis of k selection. These are strengths. However, the practical claim is only partially supported: success is demonstrated on a subset of pairs, the calibration distribution is a single domain, and no pre-fit screening identifies which pairs will succeed. The paper is not internally inconsistent, but the abstract and conclusion claim practicality more strongly than the evidence supports.

major comments (3)

[§4.5, Table 4; §3.1; Appendix C] The abstract and conclusion claim the mapper is practical, but this rests on the 500-sequence FineWeb-Edu calibration set being representative of deployment prompts. Table 4 shows eval-domain ridge R2_K = -7.81 (3B→14B) and -3.22 (8B→14B), and even the Tier 1 Ministral 3B→8B pair has R2_K = -0.10 on HellaSwag tokens; the paper's own text says the calibration-fit linear mapper 'does not extrapolate to HellaSwag tokens.' Appendix C measures calibration-domain sensitivity only on Qwen3 14B→32B (CodeAlpaca costs 5.24 pp on HellaSwag), so it does not bound the domain shift for the failure pairs. Because attention-output cosine is computed post hoc using the fitted mapper and target on the eval distribution, it cannot serve as a deployment-time screening signal. The practical claim needs either a pre-fit transferability criterion, multi-domain calibration with coverage of failing pairs, or a s
[§4.1; Table 1; Appendix H] The headline retention numbers are partially in-sample: k is selected per pair by maximizing accuracy on ARC-C, HellaSwag, WinoGrande, and MMLU, the same benchmarks averaged in Table 1. Appendix H estimates the maximum inflation at 2.49 pp via leave-one-out re-selection, which is useful and transparent, but the reported Avg retention should be presented as 'selected-k' rather than as an out-of-sample estimate, or supplemented with a fixed-k analysis. This matters most for Ministral 8B→14B, where leave-one-out changes k from 12 to 20 and moves the held-out benchmark by 2.49 pp. The central 73–98% claim is not invalidated, but its precision is weaker than the text suggests.
[§4.2; §4.5] The paper's central success story is that four of six pairs work, but no architectural or calibration-time property is shown to separate the two tiers before fitting; matched KV correlates with success but does not guarantee it. The proposed predictor, attention-output cosine, is measured post hoc on the fitted mapper and target using eval-distribution tokens. Its reported r=+0.57 is computed over 12 evaluations drawn from only six pairs in both directions, so the effective sample size is small and the observations are not independent. The claim that this diagnostic 'predicts cross-pair retention' is therefore not established at the level the practical story requires. I would ask for confidence intervals, an independence-aware analysis, and a clear statement that cosine is a post-hoc diagnostic rather than a pre-fit predictor.

minor comments (6)

[Title; §3.1] The term 'closed-form' may mislead. Equation (4) is the ridge normal equations solution fit from calibration data, not a parameter-free derivation from model weights. Suggest 'closed-form linear-solve mapper' or 'gradient-free mapper' and state explicitly that calibration requires supervised access to target KV.
[Table 1; §4.1] No uncertainty or confidence intervals are reported. Many retention differences are within a few points (e.g., 97.6% vs 98.5% Avg on Qwen3 14B→32B). Report error bars or state that evaluation is deterministic under fixed prompts.
[Table 4] The meaning of 'eval-domain R2_K' and how deeply negative values arise should be defined precisely. R2 is not bounded below once evaluated on a shifted distribution, and the reader must infer the token subset, the baseline mean, and the exact computation.
[Appendix C] Domain sensitivity is measured only on Qwen3 14B→32B. A sentence explaining whether this pair is representative of the other families, or why it is not, would help the reader calibrate the limitation.
[§4.5] The correlation r=+0.57 should be accompanied by the number of points, a p-value or confidence interval, and a caveat about non-independence across directions and families.
[Appendix D; §4.1] The manual override of Ministral 3B→8B to k=all is noted in appendix, but a brief justification in the main text would avoid confusion, especially because Table 1 reports k=all while the selection criterion would have chosen k=20.

Circularity Check

1 steps flagged · score 2.0 of 10

No constructional circularity; the only mild in-sample issue is the disclosed per-pair k selection on the same benchmarks whose retention is reported, bounded by the paper at 2.49 pp and confirmed by held-out benchmarks.

fitted input called prediction [§4.1 Mapper configuration (and Appendix H)]
"The number of source layers k is a hyperparameter selected per pair by a sweep (§4.1). ... We select a single k per pair as the value that maximizes the arithmetic mean of the log-likelihood benchmark accuracies (ARC-C, HellaSwag, WinoGrande, MMLU), breaking near-ties toward larger k for evaluation coverage. GSM8K, CoQA multi-turn, and prefill latency are held out from this selection. Including a benchmark in the criterion raises its own reported accuracy by at most 2.49 pp (Appendix H)."

The headline retention numbers in Table 1 are reported at the per-pair k that was selected by maximizing accuracy on ARC-C, HellaSwag, WinoGrande, and MMLU—the same benchmarks whose retention is then advertised as 73–98% on the four Tier-1 pairs. For those four benchmarks, the reported 'prediction' is therefore not a blind out-of-sample evaluation; the reported accuracy is the objective of a hyperparameter search over eval data, so the result is partially fitted to the quantity it is said to predict. The paper's own leave-one-benchmark-out analysis bounds this inflation at 2.49 pp, and the held-out PIQA/BoolQ/ARC-Easy benchmarks and GSM8K are genuinely out of sample and reproduce the tier structure, so this is a mild selection effect rather than a constructional equivalence.

full rationale

The paper's central derivation chain is otherwise self-contained. The per-head ridge mapper is fitted on a calibration set of 500 FineWeb-Edu sequences; the reported downstream accuracy is measured on external benchmarks with the target model, so the weights themselves are not tuned to the evaluation labels. The linear-structure analysis (R2 probes, source-layer selection) is an empirical characterization, not a definitional tautology: the mapper's success is not encoded in the probe's construction. Attention-output cosine is a post-hoc diagnostic and is not used to fit the mapper, so its correlation with retention is an empirical finding rather than a circular prediction. There are no load-bearing self-citations, no imported uniqueness theorems, and no ansatz smuggled in via prior work. The only mild circularity is the per-pair selection of k on four of the five reported benchmarks. The paper explicitly discloses this, bounds the effect at 2.49 pp, and verifies the tier structure on fully held-out benchmarks (PIQA, BoolQ, ARC-Easy) and on GSM8K, which never enters selection. Thus the central claim—that a closed-form linear mapper can retain substantial accuracy on matched-KV pairs—has independent content and is not forced by construction. The more serious weakness, calibration-to-eval distribution shift on Ministral pairs (Table 4), is a correctness and generalization risk, not a circularity. Overall score 2 reflects the minor, bounded, and disclosed k-selection effect rather than any deeper circular structure.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central method is a fitted regression, so the free parameters are the ridge penalty and the per-pair source-layer count. The key domain assumptions are the matched-KV constraint and calibration representativeness. No new physical or learned entities are introduced.

free parameters (2)

ridge regularization lambda = 0.01
Chosen by hand to stabilize the inverse; ablation shows flat region over four orders of magnitude with collapse at lambda=1.
source layer count k = per pair: 8 (Qwen3 14B->32B), 12 (Qwen3 8B->32B, Ministral 8B->14B), 20 (Llama 3.1 8B->70B, Ministral 3B->14B), all (Min
Selected per pair by sweeping on the same log-likelihood benchmarks reported, Appendix H bounds the effect to at most 2.49 pp.

assumptions (3)

domain assumption Source and target share KV head count and per-head dimension (matched-KV).
All six pairs are matched-KV; the paper does not test mismatched-KV.
domain assumption Calibration set of 500 FineWeb-Edu sequences is representative of evaluation distribution.
The linear fit must extrapolate; on two Ministral pairs it does not (R2 negative on HellaSwag), so this is load-bearing.
standard math RoPE rotation is orthogonal and exactly invertible.
Used for RoPE stripping in Section 3.3.

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Cite this review

Pith. "Pith review of Cross-Model KV Cache Transfer in LLM Families: A Closed-Form Linear Mapping for Prefill Reuse." pith.science (2026). https://pith.science/paper/ZLHEVXOV

@misc{pith2026260803893,
  author       = {Pith},
  title        = {Pith review of: Cross-Model KV Cache Transfer in LLM Families: A Closed-Form Linear Mapping for Prefill Reuse},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZLHEVXOV}},
  note         = {Machine review of arXiv:2608.03893}
}

read the original abstract

Production deployments often swap between different-sized models in a family for cost-quality cascading, mid-conversation switching, and routing, and each swap forces the receiver to repay the prefill from scratch. We propose cross-model KV cache transfer, where the receiver reuses the source's KV cache, skipping prefill. We find that cross-model KV has substantial linear structure across matched-KV pairs, where source and target share KV head count and per-head dimension. On Qwen3 14B->32B, one source layer explains 56% of variance in the target's keys and 32% in values, rising to 79% and 65% with multiple source layers. Building on this, we design a closed-form ridge mapper that operates per head and proceeds in three steps. First, for each target layer we select the top-k most predictive source layers and concatenate their KV as input. Second, we strip RoPE from the keys before mapping, so the fit is position-free and reusable across context lengths. Third, we fit ridge regression on a small calibration set of 500 FineWeb-Edu sequences of 1,024 tokens each. Surprisingly, across six pairs in three families, this linear mapper retains 73-98% of the receiver's standalone-prefill accuracy on four pairs, while two degrade sharply. A nonlinear MLP recovers up to +37 pp HellaSwag retention on the failures. The mapper runs 2.7-25x faster than re-prefill and remains stable across multi-turn handoff, making cross-model KV cache transfer practical.

Figures

Figures reproduced from arXiv: 2608.03893 by the authors.

**Figure 1.** Cross-model KV cache transfer pipeline. A per-head linear map converts the source’s prefilled KV cache into the target’s expected format, so the target decodes without re-prefilling. Cross-model KV cache transfer is challenging because source and target can differ in layer count, hidden dimension, and KV head configuration. Prior work bridges these gaps with neural fusers [Fu et al., 2026], learned latent-space adap… view at source ↗

**Figure 2.** Cross-model KV exhibits substantial linear structure. Each heatmap cell shows headaveraged R2 from a single-source linear regression mapping source layer l ′ (row) to target layer l (column), for raw keys (Krope), RoPE-stripped keys (Kstripped), and values (V ). We seek a mapping f : CS → Cˆ T such that the target model, decoding from Cˆ T in place of its own CT , produces equivalent outputs: m [PITH_FULL_IMAGE:fi… view at source ↗

**Figure 3.** Per-head linear mapper. For each target (l, h), the top-k source layers (selected per target layer by head-averaged R2 ) are concatenated. Independent ridge regressions Wl,h K and Wl,h V project to the target’s K and V spaces. No parameters are shared across heads or between K and V. across the n t kv target heads to give a head-averaged R2 for each (l ′ , l) pair. Visualizing this as a heatmap with rows indexing so… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: CoQA F1 across ten turns for Qwen3 14B↔32B multi-turn handoff. Solid lines are the target’s standalone accuracy, dashed lines the mapper at the single-turn k of §4.1, k=8 (S→L) and k=20 (L→S), and dotted lines the k a multi-turn sweep would select [PITH_FULL_IMAGE:fig…

**Figure 5.** Figure 5: R2 vs. number of source layers selected via greedy forward selection, for Kstripped and V (rows) and Qwen3 8B→32B, 14B→32B (columns). Each curve is one of nine representative target layers. Curves climb steeply from k=1 to k=4 and are close to their k=all value by k=6.…

**Figure 6.** Figure 6: Transfer accuracy vs. source layer count [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

**Figure 7.** Figure 7: Sequential removal of mapper components on Qwen3 14B [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

**Figure 8.** Figure 8: Accuracy retention (% of target standalone) across transfer pairs, on ARC-C, HellaSwag [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]

**Figure 9.** Figure 9: Mapper application (solid) vs. target re-prefill (dashed) across sequence length, [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]

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Works this paper leans on

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Reviewed August 5, 2026 · model on record in the stance chip above.

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− all RoPE

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arXiv