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arxiv: 2605.05219 · v1 · submitted 2026-04-17 · 💻 cs.LG · cs.AI

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Sparse Prefix Caching for Hybrid and Recurrent LLM Serving

Mikhail Shirokikh , Sergey Nikolenko
Authors on Pith no claims yet

Pith reviewed 2026-05-10 08:46 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords recurrentcachingprefixcheckpointexactsparsecachechange
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The pith

Sparse prefix caching via dynamic programming for optimal checkpoint placement under overlap distributions improves the Pareto frontier for recurrent and hybrid LLM serving on shared-prefix data.

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

Standard prefix caching reuses key-value pairs for every repeated token in language model serving. Recurrent models like state-space models work differently: they can restart from a single stored hidden state instead of the full history. The authors suggest placing these states only at selected sparse checkpoints rather than densely. On a cache hit, the system jumps to the deepest matching checkpoint and recomputes the remaining tokens exactly. They model checkpoint selection as an optimization problem given a distribution of how much prefix overlap occurs across requests. A dynamic programming algorithm solves this exactly in O(NM) time. Experiments on datasets like QuALITY and system prompts show the distribution-aware placement beats fixed heuristics like block caching, especially at low checkpoint budgets where overlaps are uneven. The technique preserves exact model outputs, applies to extractable recurrent states, and can combine with existing KV-cache methods for hybrid models.

Core claim

distribution-aware placement dominates every fixed-budget baseline on the measured layer-group Pareto frontier and matches or outperforms the strongest heuristic (block caching) while typically using substantially fewer checkpoints, with the largest gains at low checkpoint budgets where the overlap distribution is most non-uniform.

Load-bearing premise

Requests share a non-trivial prefix (e.g., asking different questions about a single long document) and that the distribution over overlap depths is known or estimable in advance; also that recurrent states can be extracted and restored exactly without changing the computation.

Figures

Figures reproduced from arXiv: 2605.05219 by Mikhail Shirokikh, Sergey Nikolenko.

Figure 1
Figure 1. Figure 1: Empirical overlap depth distributions across datasets. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Recurrent-work reduction factor vs. checkpoint budget on NarrativeQA. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Prototype layer-group Pareto fronts: measured layer-group time vs. checkpoint budget [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Real wall-time vs amount of recurrent work on System Prompts dataset. Marker size [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Checkpoint placements for sampled conversations (a) QuALITY, (b) System Prompts [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
read the original abstract

Prefix caching is a key latency optimization for autoregressive LLM serving, yet existing systems assume dense per-token key/value reuse. State-space models change the structure of the problem: a recurrent layer can resume from a single stored state rather than requiring the entire token history. This asymmetry opens a new design point between no reuse and dense caching: store exact recurrent states at a sparse set of checkpoint positions and, on a cache hit, resume from the deepest stored checkpoint and recompute the remaining suffix exactly. We formalize sparse prefix caching as checkpoint placement under a distribution over overlap depths, yielding an exact O(NM) dynamic program. For use cases where requests share a non-trivial prefix (e.g. asking different questions about a single long document), we show that our method consistently improves the Pareto frontier traced by standard heuristics on real-world data. Across QuALITY and System Prompts, distribution-aware placement dominates every fixed-budget baseline on the measured layer-group Pareto frontier and matches or outperforms the strongest heuristic (block caching) while typically using substantially fewer checkpoints, with the largest gains at low checkpoint budgets where the overlap distribution is most non-uniform. The method is most relevant when many requests share a substantial but not identical prefix within a retained cache entry. It preserves exact outputs, does not change the recurrent computation itself or require new recurrent update kernels, applies to recurrent/SSM layers whose hidden state can be extracted and restored exactly, and for hybrid models can be combined with existing KV-cache compression techniques.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper proposes sparse prefix caching for hybrid and recurrent LLM serving. It formalizes checkpoint placement under a distribution over prefix overlap depths as an exact O(NM) dynamic program. On QuALITY and System Prompts, distribution-aware placement is shown to dominate fixed-budget baselines on the layer-group Pareto frontier, match or exceed block caching while using fewer checkpoints, and yield largest gains at low budgets where the overlap distribution is most non-uniform. The method preserves exact outputs, requires no new kernels, and applies to recurrent/SSM layers with extractable states; it can be combined with KV-cache compression.

Significance. If the DP is correct and the empirical results hold under the stated assumptions, the work provides a principled, distribution-aware alternative to heuristic caching for recurrent and hybrid models. It exploits the asymmetry that a single recurrent state suffices for resumption rather than full token history, achieving better memory-latency trade-offs in shared-prefix workloads while remaining exact. The explicit Pareto dominance over strong baselines on real data, combined with the O(NM) exact solver, strengthens the case for adoption in serving systems.

major comments (2)
  1. [§3] §3, DP recurrence: the manuscript claims an exact O(NM) solution, but the cost function definition (how the overlap-depth distribution enters the expected recomputation cost) is not shown to be independent of any fitted parameters; if the distribution must be estimated from data, the optimality guarantee becomes conditional on estimation quality.
  2. [§4.2] §4.2, Pareto frontier results: the claim that distribution-aware placement 'dominates every fixed-budget baseline' is load-bearing, yet the reported curves do not include error bars or sensitivity to distribution mismatch; without this, it is unclear whether the observed gains remain statistically significant when the overlap distribution is estimated rather than known exactly.
minor comments (3)
  1. [Figure 2] Figure 2: axis labels and legend for the layer-group Pareto plots are too small; enlarge and clarify which recurrent layers belong to each group.
  2. [§5] §5: the limitations paragraph should explicitly list the assumption that recurrent states can be extracted and restored without numerical drift or kernel changes.
  3. [Related Work] Related work: the citation to prior KV-cache compression techniques is present but the discussion of how sparse prefix caching composes with them is only one sentence; expand to a short paragraph.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation for minor revision. We address each major comment below with clarifications and proposed manuscript updates.

read point-by-point responses

  1. Referee: [§3] §3, DP recurrence: the manuscript claims an exact O(NM) solution, but the cost function definition (how the overlap-depth distribution enters the expected recomputation cost) is not shown to be independent of any fitted parameters; if the distribution must be estimated from data, the optimality guarantee becomes conditional on estimation quality.

    Authors: The dynamic program yields an exact optimum for any fixed input distribution p over overlap depths. The expected recomputation cost is formed by weighting the per-depth recomputation cost by p(d) and the recurrence follows directly from this expectation; no auxiliary fitted parameters appear in the DP. In the experiments we compute p(d) as the empirical frequency over the QuALITY and System Prompts evaluation sets, so the reported solutions are optimal for those exact distributions. In deployment p(d) would be estimated from historical logs, rendering the guarantee conditional on estimation accuracy. We will revise §3 to state explicitly how p enters the cost and to note the conditional optimality when p is estimated. revision: partial

  2. Referee: [§4.2] §4.2, Pareto frontier results: the claim that distribution-aware placement 'dominates every fixed-budget baseline' is load-bearing, yet the reported curves do not include error bars or sensitivity to distribution mismatch; without this, it is unclear whether the observed gains remain statistically significant when the overlap distribution is estimated rather than known exactly.

    Authors: The Pareto curves are deterministic given the empirical p(d) extracted from each dataset, so no stochastic error bars apply to the placement itself. Dominance holds exactly under these measured distributions and is consistent across both QuALITY and System Prompts. We agree that sensitivity to mismatch between the estimated and true p is not shown. We will revise §4.2 to state the assumption of an accurate distribution estimate and add a brief discussion of robustness under small perturbations of p(d), thereby clarifying the scope of the dominance claim. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives an exact O(NM) dynamic program for checkpoint placement directly from a given overlap-depth distribution, treating the distribution as an external input that is either known or estimated separately from data. This formulation is self-contained and does not reduce any claimed optimality or prediction back to fitted parameters, self-definitions, or prior self-citations by construction. Empirical Pareto comparisons on QuALITY and System Prompts are performed against independent baselines (fixed-budget and block caching) using the DP outputs, with the method explicitly preserving exact recurrent computation and outputs. No load-bearing step collapses to renaming, ansatz smuggling, or uniqueness imported from the authors' prior work; the central result follows from standard DP optimality applied to the stated inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on the ability to extract and restore recurrent hidden states exactly and on the availability of an overlap depth distribution for the target workload.

axioms (2)
  • domain assumption Recurrent/SSM layers allow exact extraction and restoration of hidden states without approximation or kernel changes
    Invoked in the abstract as a prerequisite for the caching scheme to preserve exact outputs
  • domain assumption A distribution over prefix overlap depths is known or can be estimated from data
    Central to the DP formulation and placement optimization

pith-pipeline@v0.9.0 · 5564 in / 1313 out tokens · 40997 ms · 2026-05-10T08:46:55.843948+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

38 extracted references · 20 canonical work pages · 8 internal anchors

  1. [1]

    Klawe, Shlomo Moran, Peter Shor, and Robert Wilber

    Alok Aggarwal, Maria M. Klawe, Shlomo Moran, Peter Shor, and Robert Wilber. Geometric applications of a matrix-searching algorithm.Algorithmica, 2:195–208, 1987

    1987

  2. [2]

    Onthecomplexityoflearningfromdriftingdistributions

    RakeshD.BarveandPhilipM.Long. Onthecomplexityoflearningfromdriftingdistributions. Information and Computation, 138(2):170–193, 1997

    1997

  3. [3]

    On the convergence of the empirical distribution

    Daniel Berend and Aryeh Kontorovich. On the convergence of the empirical distribution. arXiv preprint arXiv:1205.6711, 2012

    work page arXiv 2012

  4. [4]

    PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling

    Zefan Cai, Yichi Zhang, Bofei Gao, Yuliang Liu, Tianyu Liu, Keming Lu, Wayne Xiong, Yue Dong, Baobao Chang, Junjie Hu, and Wen Xiao. PyramidKV: Dynamic KV cache compression based on pyramidal information funneling.arXiv preprint arXiv:2406.02069, 2024

    work page internal anchor Pith review arXiv 2024

  5. [5]

    Training Deep Nets with Sublinear Memory Cost

    Tianqi Chen, Bing Xu, Chiyuan Zhang, and Carlos Guestrin. Training deep nets with sublinear memory cost, 2016. URLhttps://arxiv.org/abs/1604.06174

    work page internal anchor Pith review arXiv 2016

  6. [6]

    Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality

    Tri Dao and Albert Gu. Transformers are SSMs: Generalized models and efficient algorithms through structured state space duality.arXiv preprint arXiv:2405.21060, 2024

    work page internal anchor Pith review arXiv 2024

  7. [7]

    Fu, Stefano Ermon, Atri Rudra, and Christopher Ré

    Tri Dao, Daniel Y. Fu, Stefano Ermon, Atri Rudra, and Christopher Ré. FlashAttention: Fast and memory-efficient exact attention with IO-awareness.Advances in Neural Information Processing Systems (NeurIPS), 35, 2022. 11

    2022

  8. [8]

    Springer, 2001

    Luc Devroye and Gábor Lugosi.Combinatorial Methods in Density Estimation. Springer, 2001

    2001

  9. [9]

    Challenges in deploying long-context transformers: A theoretical peak performance analysis.arXiv preprint arXiv:2405.08944, 2024

    Yao Fu, Peter Bailis, Ion Stoica, and Hao Zhang. Challenges in deploying long-context transformers: A theoretical peak performance analysis.arXiv preprint arXiv:2405.08944, 2024

    work page arXiv 2024

  10. [10]

    L. K. Grover. A new algorithm for thek-median problem.Information Processing Letters, 57(3):151–155, 1996

    1996

  11. [11]

    Mamba: Linear-Time Sequence Modeling with Selective State Spaces

    Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces. arXiv preprint arXiv:2312.00752, 2023

    work page Pith review arXiv 2023

  12. [12]

    Improved complexity bounds for location problems on the real line.Operations Research Letters, 10(7):395–402, 1991

    Refael Hassin and Arie Tamir. Improved complexity bounds for location problems on the real line.Operations Research Letters, 10(7):395–402, 1991

    1991

  13. [13]

    The NarrativeQA reading comprehension challenge

    Tomáš Kočiský, Jonathan Schwarz, Phil Blunsom, Chris Dyer, Karl Moritz Hermann, Gábor Melis, and Edward Grefenstette. The NarrativeQA reading comprehension challenge. Transactions of the Association for Computational Linguistics, 6:317–328, 2018

    2018

  14. [14]

    Efficient Memory Management for Large Language Model Serving with PagedAttention

    Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph E. Gonzalez, Hao Zhang, and Ion Stoica. Efficient memory management for large language model serving with pagedattention.arXiv preprint arXiv:2309.06180, 2023

    work page internal anchor Pith review arXiv 2023

  15. [15]

    xFormers: A modular and hackable transformer modelling library.https://github

    Benjamin Lefaudeux, Francisco Massa, Diana Liskovich, Wenhan Xiong, Vittorio Caggiano, Sean Nber, Tian Xu, Jieru Hu, Marta Tintore, Susan Ho, Patrick Labatut, and Daniel Haziza. xFormers: A modular and hackable transformer modelling library.https://github. com/facebookresearch/xformers, 2022

    2022

  16. [16]

    SnapKV: LLM Knows What You are Looking for Before Generation

    Yuhong Li, Yingbing Huang, Bowen Yang, Bharat Venkitesh, Acyr Locatelli, Hanchen Ye, Tianle Cai, Patrick Lewis, and Deming Chen. SnapKV: LLM knows what you are looking for before generation.arXiv preprint arXiv:2404.14469, 2024

    work page internal anchor Pith review arXiv 2024

  17. [17]

    arXiv preprint arXiv:2305.17118 , year =

    Zichang Liu, Aashiq Desai, Fangshuo Liao, Weitao Wang, Victor Xie, Zhaozhuo Xu, Anas- tasios Kyrillidis, and Anshumali Shrivastava. Scissorhands: Exploiting the persistence of importance hypothesis for LLM KV cache compression at test time.arXiv preprint arXiv:2305.17118, 2024

    work page arXiv 2024

  18. [18]

    Nonparametric density estimation under distribution drift

    Alessio Mazzetto and Eli Upfal. Nonparametric density estimation under distribution drift. InInternational Conference on Machine Learning (ICML), pages 24251–24270, 2023

    2023

  19. [19]

    On the method of bounded differences

    Colin McDiarmid. On the method of bounded differences. In J. Siemons, editor,Surveys in Combinatorics, volume 141 ofLondon Mathematical Society Lecture Note Series, pages 148–188. Cambridge University Press, 1989

    1989

  20. [20]

    Nimrod Megiddo and Kenneth J. Supowit. The complexity of some common geometric location problems.Journal of Algorithms, 5(4):544–554, 1984

    1984

  21. [21]

    New analysis and algorithm for learning with drifting distributions

    Mehryar Mohri and Andrés Muñoz Medina. New analysis and algorithm for learning with drifting distributions. InAlgorithmic Learning Theory (ALT), pages 124–138, 2012

    2012

  22. [22]

    Piotr Nawrot, Adrian Łancucki, Marcin Chochowski, David Tarjan, and Edoardo M. Ponti. Dynamic memory compression: Retrofitting LLMs for accelerated inference.arXiv preprint arXiv:2403.09636, 2024. 12

    work page arXiv 2024

  23. [23]

    Marconi: Prefix caching for the era of hybrid llms, 2025

    Rui Pan, Zhuang Wang, Zhen Jia, Can Karakus, Luca Zancato, Tri Dao, Yida Wang, and Ravi Netravali. Marconi: Prefix caching for the era of hybrid LLMs.arXiv preprint arXiv:2411.19379, 2024

    work page arXiv 2024

  24. [24]

    Richard Yuanzhe Pang, Alicia Parrish, Nitish Joshi, Nikita Nangia, Jason Phang, Angelica Chen, Vishakh Padmakumar, Johnny Ma, Jana Thompson, He He, and Samuel R. Bowman. QuALITY: Question answering with long input texts, yes!Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL), pages 533...

    2022

  25. [25]

    Splitwise: Efficient generative llm inference using phase splitting,

    Pratyush Patel, Esha Choukse, Chaojie Zhang, Aashaka Shah, Íñigo Goiri, Saeed Maleki, and Ricardo Bianchini. Splitwise: Efficient generative LLM inference using phase splitting. arXiv preprint arXiv:2311.18677, 2024

    work page arXiv 2024

  26. [26]

    RWKV: Reinventing RNNs for the Transformer Era

    Bo Peng, Eric Alcaide, Quentin Anthony, Alon Albalak, Samuel Arcadinho, Huanqi Cao, Xin Cheng, Michael Chung, Matteo Grber, et al. RWKV: Reinventing RNNs for the transformer era.arXiv preprint arXiv:2305.13048, 2023

    work page internal anchor Pith review arXiv 2023

  27. [27]

    Qwen3.5 technical report.https://qwen.ai/blog?id=qwen3.5, 2025

    Qwen Team. Qwen3.5 technical report.https://qwen.ai/blog?id=qwen3.5, 2025

    2025

  28. [28]

    ShareGPT.https://sharegpt.com, 2023

    ShareGPT Community. ShareGPT.https://sharegpt.com, 2023

    2023

  29. [29]

    Preble: Efficient distributed prompt scheduling for llm serving.arXiv preprint arXiv:2407.00023, 2024

    Vikranth Srivatsa, Zijian He, Reyna Abhyankar, Dongming Li, and Yiying Zhang. Preble: Efficient distributed prompt scheduling for LLM serving.arXiv preprint arXiv:2407.00023, 2024

    work page arXiv 2024

  30. [30]

    System prompts leaks

    Ásgeir Thorsteinsson. System prompts leaks. https://github.com/asgeirtj/system_ prompts_leaks, 2024

    2024

  31. [31]

    Pyramid- infer: Pyramid kv cache compression for high-throughput llm inference

    Dongjie Yang, XiaoDong Han, Yan Gao, Yao Hu, Shilin Zhang, and Hai Zhao. Pyramid- Infer: Pyramid KV cache compression for high-throughput LLM inference.arXiv preprint arXiv:2405.12532, 2024

    work page arXiv 2024

  32. [32]

    Gated Linear Attention Transformers with Hardware-Efficient Training

    Songlin Yang, Bailin Wang, Yikang Shen, Rameswar Panda, and Yoon Kim. Gated linear attention transformers with hardware-efficient training.arXiv preprint arXiv:2312.06635, 2024

    work page internal anchor Pith review arXiv 2024

  33. [33]

    flash-linear-attention

    Songlin Yang et al. flash-linear-attention. https://github.com/fla-org/ flash-linear-attention, 2024

    2024

  34. [34]

    CacheBlend: Fast Large Language Model Serving for RAG with Cached Knowledge Fusion

    Jiayi Yao, Hanchen Li, Yuhan Liu, Siddhant Ray, Yihua Cheng, Qizheng Zhang, Kuntai Du, Shan Lu, and Junchen Jiang. Cacheblend: Fast large language model serving for RAG with cached knowledge fusion.arXiv preprint arXiv:2405.16444, 2024

    work page arXiv 2024

  35. [35]

    Chunkattention: Efficient self-attention with prefix-aware kv cache and two-phase partition

    Lu Ye, Ze Liang, Yong Guan, Zhen Jia, and Lingfei Li. ChunkAttention: Efficient self-attention with prefix-aware KV cache and two-phase partition.arXiv preprint arXiv:2402.15220, 2024

    work page arXiv 2024

  36. [36]

    Gyeong-In Yu, Joo Seong Jeong, Geon-Woo Kim, Soojeong Kim, and Byung-Gon Chun. Orca: A distributed serving system for transformer-based generative models.Proceedings of the 16th USENIX Symposium on Operating Systems Design and Implementation (OSDI), pages 521–538, 2022. 13

    2022

  37. [37]

    arXiv preprint arXiv:2306.14048 , year=

    Zhenyu Zhang, Ying Sheng, Tianyi Zhou, Tianlong Chen, Lianmin Zheng, Ruisi Cai, Zhao Song, Yuandong Tian, Christopher Ré, Clark Barrett, Zhangyang Wang, and Beidi Chen. H2O: Heavy-hitter oracle for efficient generative inference of large language models.arXiv preprint arXiv:2306.14048, 2024

    work page arXiv 2024

  38. [38]

    SGLang: Efficient Execution of Structured Language Model Programs

    Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Sun, Jeff Huang, Cody Hao Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E. Gonzalez, Clark Barrett, and Ying Sheng. SGLang: Efficient execution of structured language model programs.arXiv preprint arXiv:2312.07104, 2023. 14 A Proofs All theorem and lemma statements in this appendix appear in the ...

    work page internal anchor Pith review arXiv 2023