Fewer Tokens, Smaller Cache: Reward-Coordinated Efficient Reasoning

# Fewer Tokens, Smaller Cache: Reward-Coordinated Efficient Reasoning
Source: [https://arxiv.org/html/2608.04771](https://arxiv.org/html/2608.04771)
Qiyuan Zhu1\\equalcontrib, Dezhi Li1\\equalcontrib, Pengyu Cheng2\\equalcontrib, Tianle Chen2, Jiacheng Wang2, Ruijie Shen3, Hao Gu1, Sida Lin1, Zirui Liu4, Jiacheng Liu1\\corresponding, Sirui Han1\\corresponding

###### Abstract

Large Reasoning Models \(LRMs\) excel on complex tasks through long chain\-of\-thought \(CoT\) reasoning, but their lengthy intermediate steps cause severe overthinking that inflates inference cost\. KV\-cache compression is a common solution, yet existing reasoning\-oriented methods apply a uniform policy across the trajectory and judge compression only by what it removes from the cache\. Two observations point the other way\. First, a reasoning state’s tolerance to context loss varies along the trajectory, and process reward tracks it: deleting tokens at high\-reward steps preserves accuracy far better than deleting the same budget at random\. Second, compression is not free on the generation side, since a smaller cache leads the model to generate more tokens, partly canceling the saving\. Together these motivate coordinating both sides under a single process reward\. We propose ReCo \(Reward\-Coordinated Compression\), a step\-wise framework in which a lightweight process\-reward estimator scores each completed step and drives three components: \(1\) reward\-adaptive KV\-cache compression that shrinks the retained cache harder at high\-reward steps and less at low\-reward ones, \(2\) a reward\-banded penalty on reflection tokens that curbs redundant generation, and \(3\) confidence\-based early stopping that triggers when the reasoning is reliable\. Across three reasoning models and six benchmarks, ReCo reduces generated tokens by37%37\\%–65%65\\%and end\-to\-end latency by2\.08×2\.08\\times–2\.35×2\.35\\timesover Full CoT, all while largely preserving accuracy\.

## 1Introduction

![Refer to caption](https://arxiv.org/html/2608.04771v1/x1.png)Figure 1:Introduction overview on DeepSeek\-R1\-Distill\-Qwen\-7B\. Top: accuracy vs\. average response length; ReCo is the most accurate compressed method while generating far fewer tokens\. Bottom: per\-problem latency; ReCo is the fastest overall, cutting latency by2\.35×2\.35\\timesover Full CoT\.Large Reasoning Models \(LRMs\), such as OpenAI\-o1\(Jaechet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib47)\), DeepSeek\-R1\(Guoet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib41)\), and Gemini\(Comaniciet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib2)\), have recently achieved remarkable progress across a wide range of domains, demonstrating strong capabilities on complex tasks such as mathematical reasoning, code generation, and scientific problem solving\(Zhuet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib53); Xuet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib54); Caoet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib56),[2026](https://arxiv.org/html/2608.04771#bib.bib58); Guet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib59)\)\. However, such capabilities are largely driven by long chain\-of\-thought \(CoT\) reasoning, where the model produces lengthy intermediate steps before arriving at a final answer\. While effective on hard problems, this paradigm frequently causes models to*overthink*\(Chenet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib48)\): they generate excessively long reasoning chains even for simple inputs, incurring token overhead, increased latency, and high computational cost\.

![Refer to caption](https://arxiv.org/html/2608.04771v1/x2.png)Figure 2:Overview ofReCo\. After each stepcic\_\{i\}, a process rewardviv\_\{i\}drives three components:❶ KV Compressionsets a reward\-modulated retention ratio, shrinking the cache harder at high\-reward steps;❷ Reflection Controlmapsviv\_\{i\}to a reward\-banded logit penaltyβi\\beta\_\{i\}on reflection tokens; and❸ Early Stoppinghalts once answer perplexity satisfiesPPL​\(a\)≤τp\\mathrm\{PPL\}\(a\)\\leq\\tau\_\{p\}\.A common strategy for mitigating these inference costs is KV\-cache compression, since the key\-value \(KV\) cache accumulated during autoregressive decoding dominates both memory footprint and per\-token attention cost\(Liet al\.[2024a](https://arxiv.org/html/2608.04771#bib.bib23); Shiet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib24); Huet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib57)\)\. Classical methods evict cache entries deemed unimportant by attention scores \(e\.g\., SnapKV\(Liet al\.[2024b](https://arxiv.org/html/2608.04771#bib.bib25)\)and PyramidKV\(Caiet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib26)\)\), merge redundant entries into representative ones\(Zhanget al\.[2024](https://arxiv.org/html/2608.04771#bib.bib29)\), or quantize them into low\-bit formats\(Hooperet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib32)\)\. These methods, however, were designed primarily for long\-context settings, where the cache is dominated by a long*static*prompt that can be pruned once after prefilling; in reasoning, by contrast, the cache is dominated by the model’s own*growing*chain of thought, whose content must keep supporting the very generation that produces it\. Recent work has begun to adapt KV compression to this reasoning setting\(Caiet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib39); Songet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib45)\), yet it still applies a*uniform*compression policy across the entire trajectory, ignoring that reasoning steps differ in how much they can afford to be compressed\. More fundamentally, they weigh compression only by what it removes from the cache, and leave unexamined whether discarding context affects the reasoning the model has yet to generate\.

A closer look at these gaps reveals two observations\.*First, compression tolerance varies along the reasoning trajectory\.*A process reward, which scores how promising and on\-track the current path is, reliably tracks it: at high\-scoring steps the reasoning state is on\-track and withstands aggressive pruning of its context, whereas a low\-scoring state is still exploring and fragile, so deleting tokens from high\-reward steps consistently outperforms deleting the same budget at random \(Sec\.[2\.1](https://arxiv.org/html/2608.04771#S2.SS1)\)\.*Second, the saving from KV compression is partly offset by longer generation*: at a fixed compression rate the average output length exceeds the full\-cache baseline, and on MATH\-500 up to79\.8%79\.8\\%of problems generate more tokens once the cache is compressed \(Sec\.[2\.2](https://arxiv.org/html/2608.04771#S2.SS2)\)\. Together these show that, on reasoning models,compression must respect how the reasoning trajectory varies from step to step, and it cannot be decoupled from generation length: shrinking the cache while the output grows can erode the savings\.

Concretely, we proposeReCo\(Reward\-Coordinated Compression\), a framework that improves KV\-cache compression and resolves its length inflation on reasoning models by coordinating it with generation control \(Figure[2](https://arxiv.org/html/2608.04771#S1.F2)\)\. As each step completes, a lightweight3030M process\-reward estimator assigns it a scalar reward reflecting how promising and on\-track the current reasoning path is, and this single reward drives three coordinated components\.*\(1\) KV\-cache compression*maps the reward to a step\-dependent retention ratio for the accumulated cache, shrinking the whole cache harder when the latest step scores high and less when it scores low, replacing the uniform policy of prior reasoning\-oriented KV methods\.*\(2\) Reflection control*maps the same reward to a reward\-banded logit penalty on self\-reflection tokens that steers the model toward more concise reasoning when the step scores highly, curbing the length inflation that would otherwise erode the compression saving\.*\(3\) Early stopping*, triggered by persistently high reward, terminates the chain of thought once an answer\-confidence probe judges the model ready to commit\. Because all three share the same per\-step reward, they stay consistent, spending compute where reasoning is still productive and withholding it where the model has already settled\.

Across three reasoning models and six benchmarks, ReCo cuts the average generated tokens by37%37\\%–65%65\\%and lowers end\-to\-end latency by2\.08×2\.08\\times–2\.35×2\.35\\timesover full\-cache CoT, with minimal accuracy loss\. Under matched settings, it attains the smallest accuracy drop among all compressed methods: cache\-only baselines lose far more accuracy and, consistent with the length\-inflation effect above, often generate*more*tokens than the full\-cache model, whereas length\-only baselines reach a comparable speedup only by sacrificing accuracy\.

![Refer to caption](https://arxiv.org/html/2608.04771v1/x3.png)Figure 3:Motivating observations for reward\-guided KV\-cache compression and generation control\. \(a\) Deleting tokens from high\-reward steps preserves accuracy better than deleting the same budget from randomly chosen steps, indicating that process reward tracks compression tolerance\. \(b\) Cache compression can backfire and lengthen generation on MATH\-500\. \(c\) Over half of MATH\-500 problems generate longer outputs once compressed, and this holds across compression rates\.Our contributions are summarized as follows:

- •We argue that, on reasoning models, KV\-cache compression is insufficient on its own and should be coupled with generation control: compressing the cache alone can backfire by lengthening the very reasoning it is meant to make cheaper, so the two are better governed jointly\.
- •We show that*process reward*provides a reliable step\-wise signal of compression tolerance, telling when the state can run on a smaller cache and when it needs more context, in contrast to the uniform policies of existing KV compression methods\.
- •We design a reward\-coordinated, step\-wise framework that unifies KV\-cache compression, reflection control, and early stopping under one signal, reducing both token count and latency while preserving accuracy across three models and six benchmarks\.

## 2Motivation and Observation

### 2\.1Higher Process Reward, Higher Compression Tolerance

Reasoning steps leave the model in distinct states\(Chenet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib52)\): at some the path is already settled, at others it is still being worked out, so compression should adapt to the state the trajectory is in rather than treat every step alike \(steps split at newline tokens, see Sec\.[3\.1](https://arxiv.org/html/2608.04771#S3.SS1)\)\. To test whether process reward captures this, we score trajectories from DeepSeek\-R1\-Distill\-Qwen\-7B and DeepSeek\-R1\-Distill\-Llama\-8B on GSM8K and MATH\-500 with Skywork\-o1\-Open\-PRM\-7B\(Heet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib49)\), and compare two deletions that remove the*same*number of tokens: reward\-guided, dropping70%70\\%of tokens within the top\-50%50\\%high\-reward steps, versus random, removing the same amount from50%50\\%of randomly chosen steps\.

As Figure[3](https://arxiv.org/html/2608.04771#S1.F3)\(a\) shows, concentrating deletion on high\-reward steps consistently outperforms random step selection across both models and datasets, by4\.04\.0/3\.53\.5points on GSM8K/MATH\-500 for Llama\-8B and a larger6\.56\.5/5\.95\.9for Qwen\-7B\. Since both settings remove the same number of tokens, the only difference is the state of the steps that bear the loss\.

We attribute this to what the reward measures: how likely the current reasoning state lies on a reliable path, not how indispensable its tokens are\. High\-reward steps are on\-track and consistent with their context, so removing tokens loses less information, whereas low\-reward steps are where the model is still exploring, so each token carries more information and removing it more easily breaks the chain\.Higher process reward thus marks a reasoning state that tolerates more disruption to its context: the same removal loses less information and hence costs less accuracy\.We call this its*compression tolerance*: the reward decides*how much*context the current state can afford to lose\. Here that loss is deleting tokens within steps; in ReCo it is a smaller retained cache \(Sec\.[3\.2](https://arxiv.org/html/2608.04771#S3.SS2)\)\.

### 2\.2KV Cache Compression Can Induce Longer Reasoning

KV cache compression reduces inference cost by shrinking the retained context\. For reasoning models, however, this saving is not free: compressing the cache can lengthen the subsequent reasoning, so the model may spend more tokens generating than it saves on the cache\.

Figure[3](https://arxiv.org/html/2608.04771#S1.F3)\(b\) illustrates this effect on MATH\-500 under R\-KV\(Caiet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib39)\)at a25%25\\%compression rate\. Relative to the full cache, R\-KV raises the average generation length from3268\.73268\.7to4538\.14538\.1tokens \(\+38\.8%\+38\.8\\%\) on DeepSeek\-R1\-Distill\-Qwen\-7B, and from4409\.84409\.8to7891\.77891\.7tokens \(\+79\.0%\+79\.0\\%\) on DeepSeek\-R1\-Distill\-Llama\-8B, matching the R\-KV rows of Table[1](https://arxiv.org/html/2608.04771#S3.T1)\. Thus, while KV compression lowers the per\-token attention cost, the extra tokens it induces partly cancel this saving\.

*Moreover, this is a pervasive per\-problem phenomenon, not a few outliers\.*Figure[3](https://arxiv.org/html/2608.04771#S1.F3)\(c\) reports the fraction of MATH\-500 problems whose compressed output exceeds the full\-cache output across compression rates\. The ratio peaks at79\.8%79\.8\\%\(399/500399/500problems\) at a25%25\\%compression rate and stays above50%50\\%over the whole1515–40%40\\%range, confirming that length inflation is systematic\.On reasoning models, therefore, KV compression should not be treated as a pure cache problem, but coupled with generation control to account for its effect on output length, exactly what our method does\.

## 3Methodology

We proposeReCo\(Figure[2](https://arxiv.org/html/2608.04771#S1.F2)\), which operates at the granularity of reasoning steps: after each step, it scores the current reasoning state with a single lightweight reward and uses that score to drive KV\-cache compression \(Sec\.[3\.2](https://arxiv.org/html/2608.04771#S3.SS2)\), reflection control, and early stopping \(Sec\.[3\.3](https://arxiv.org/html/2608.04771#S3.SS3)\)\.

### 3\.1Preliminary

We begin by describing how the reasoning trajectory is partitioned into steps and how the per\-step reward signal is obtained, which together form the basis for all three components of ReCo\.

#### Reasoning steps as the unit of control\.

For a queryqq, the LRMℳ\\mathcal\{M\}produces a reasoning trajectory𝒞\\mathcal\{C\}before emitting the final answer\. Following\(Huanget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib37)\), we define reasoning steps by splitting𝒞\\mathcal\{C\}at newline tokens \(\\n\), and write𝒞=\{c1,…,cT\}\\mathcal\{C\}=\\\{c\_\{1\},\\dots,c\_\{T\}\\\}, whereci∼ℳ\(⋅∣q,c<i\)c\_\{i\}\\sim\\mathcal\{M\}\(\\cdot\\mid q,c\_\{<i\}\)denotes the autoregressive generation of theii\-th step\. Since a completed step typically corresponds to a semantically coherent reasoning unit, it provides a natural online decision point: given the partial trajectoryc≤ic\_\{\\leq i\}, our framework determines how to compress the accumulated KV cache and how to control the subsequent generation\.

#### Reward signal\.

After each completed stepcic\_\{i\}, we assign a scalar rewardvi∈\[0,1\]v\_\{i\}\\in\[0,1\]to the current reasoning trajectoryc≤ic\_\{\\leq i\}, estimating the likelihood of eventually reaching a correct answer\. For lightweight online, per\-step use, we adoptPilot\(Huanget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib37)\), a compact3030M\-parameter estimator distilled from Skywork\-o1\-Open\-PRM\-7B, the same PRM behind our observation in Sec\.[2\.1](https://arxiv.org/html/2608.04771#S2.SS1), givingvi=Pilot​\(c≤i\)v\_\{i\}=\\mathrm\{Pilot\}\(c\_\{\\leq i\}\)\. Trained to match this teacher, Pilot retains its step\-level discriminability while staying light enough to score every step online, so motivation and method share one reward family rather than two unrelated scorers\. This score is the*unified signal*in ReCo that guides how the next stepci\+1c\_\{i\+1\}is produced, coordinating both KV\-cache compression and generation\-side control\.

### 3\.2Reward\-Adaptive KV Compression

This component compresses the accumulated KV cache periodically as reasoning proceeds, under one guiding principle:*the step reward decides how much context to keep*\. As established in Sec\.[2\.1](https://arxiv.org/html/2608.04771#S2.SS1), a high\-reward state tolerates more disruption to its context\. Inspired by this, ReCo compresses while decoding, pruning more aggressively when the reward is high and retaining more when it is low\. We therefore let the rewardviv\_\{i\}of the just\-completed step set the retention ratioλi\\lambda\_\{i\}for the whole accumulated cache, refreshing this ratio at every step rather than following a fixed, uniform schedule\.

#### Reward\-driven retention\.

Whenever the cache has grown bySStokens since the last compression, i\.e\.,L−Li−1≥SL\-L\_\{i\-1\}\\geq SwithLLthe current cache length andLi−1L\_\{i\-1\}that after the previous compression \(L0L\_\{0\}being the prompt length\), we compress theLLcached tokens down tomi=λi​Lm\_\{i\}=\\lambda\_\{i\}L\. The ratioλi\\lambda\_\{i\}is where the reward takes control: a high reward marks a reliable reasoning state, so the accumulated context can tolerate more aggressive pruning, while a low reward marks a step that is still exploring, where the reasoning is fragile and more of the cache should be retained\. We thus compare the latest reward against the trajectory’s own reward statistics, compressing harder when it is above average and retaining more when below:

λi=λ⏟base ratio−δ​vi−v¯vmax−vmin⏟reward adjustment,\\lambda\_\{i\}\\;=\\;\\underbrace\{\\lambda\}\_\{\\text\{base ratio\}\}\\;\-\\;\\underbrace\{\\delta\\,\\frac\{v\_\{i\}\-\\bar\{v\}\}\{\\,v\_\{\\max\}\-v\_\{\\min\}\\,\}\}\_\{\\text\{reward adjustment\}\},\(1\)wherev¯\\bar\{v\},vminv\_\{\\min\},vmaxv\_\{\\max\}are the mean, minimum, and maximum step rewards in the current trajectory,λ\\lambdais the base ratio, andδ\\deltabounds the adjustment so thatλi∈\[λ−δ,λ\+δ\]\\lambda\_\{i\}\\in\[\\lambda\-\\delta,\\lambda\+\\delta\]\. This normalization turns the raw reward into a within\-trajectory relative position, soλi\\lambda\_\{i\}depends on whether a step is high or low*for that trajectory*rather than on its absolute reward value\. In effect, the latest step’s reward sets a single retention level for the whole cache: when the current reasoning state scores high, we shrink the accumulated cache more aggressively; when it scores low, we retain more of it\. This level is refreshed with the latest reward everySSgenerated tokens at negligible overhead\.

#### Attention\-guided selection\.

Within the reward\-allocated budgetmim\_\{i\}, we retain the tokens most relevant to the ongoing reasoning, scored by the attention they attract from thewwmost recent tokens:

sj=∑t=L−w\+1Lsoftmaxj​\(qt⊤​kj\),s\_\{j\}\\;=\\;\\sum\_\{t=L\-w\+1\}^\{L\}\\mathrm\{softmax\}\_\{j\}\\\!\\big\(q\_\{t\}^\{\\top\}k\_\{j\}\\big\),\(2\)whereqtq\_\{t\}andkjk\_\{j\}are the query and key of tokensttandjj\. Themim\_\{i\}highest\-scoring tokens are kept, with the latestwwtokens always retained as the query window; sincesjs\_\{j\}is recomputed at each compression, tokens no longer attended to are evicted automatically\. This yields a clean division of labor: the reward decides*how much*survives each compression, and attention only decides*what*survives within that allowance\.

### 3\.3Reward\-Adaptive Generation Control

Compressing the cache alone is insufficient on its own: as shown in Sec\.[2\.2](https://arxiv.org/html/2608.04771#S2.SS2), compressing the cache tends to lengthen the subsequent reasoning, and the added generation partly cancels the savings\. ReCo therefore also governs the tokens still to be generated, reusing the same per\-step rewardviv\_\{i\}that drives compression\.

#### Reward\-banded reflection penalty\.

Long reasoning traces spend many tokens on explicit self\-reflection, opening new branches with reflection tokens such as “Wait”, “Hmm”, and “Alternatively”, which drives much of the overthinking on easy or already\-settled steps\(Wanget al\.[2025](https://arxiv.org/html/2608.04771#bib.bib19); Lotfiet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib50)\)\. Rather than injecting instructions or fixing a global budget, we suppress this*directly at the decoding level*\. We curate a setℛ\\mathcal\{R\}of such reflection tokens \(with their tokenizer variants\) and penalize these reflection tokens during decoding, with the penalty strength set by the just\-completed step’s reward, using two thresholdsτℓ<τh\\tau\_\{\\ell\}<\\tau\_\{h\}that split the reward into three bands: no penalty in the lowest, a half penalty in the middle, and the full penaltyβ\\betain the highest:

βi=\{0,vi≤τℓ,β/2,τℓ<vi<τh,β,vi≥τh,β\>0\.\\beta\_\{i\}\\;=\\;\\begin\{cases\}0,&v\_\{i\}\\leq\\tau\_\{\\ell\},\\\\\[2\.0pt\] \\beta/2,&\\tau\_\{\\ell\}<v\_\{i\}<\\tau\_\{h\},\\\\\[2\.0pt\] \\beta,&v\_\{i\}\\geq\\tau\_\{h\},\\end\{cases\}\\qquad\\beta\>0\.\(3\)While generating the\(i\+1\)\(i\{\+\}1\)\-th step, we subtract the band penalty from the logit of every reflection tokenu∈ℛu\\in\\mathcal\{R\}at each positiontt,

z~t​\(u\)=\{zt​\(u\)−βi,u∈ℛ,zt​\(u\),u∉ℛ,\\tilde\{z\}\_\{t\}\(u\)\\;=\\;\\begin\{cases\}z\_\{t\}\(u\)\-\\beta\_\{i\},&u\\in\\mathcal\{R\},\\\\\[2\.0pt\] z\_\{t\}\(u\),&u\\notin\\mathcal\{R\},\\end\{cases\}\(4\)then sample fromsoftmax​\(z~t\)\\mathrm\{softmax\}\(\\tilde\{z\}\_\{t\}\)\. The penalty is monotone in the reward: a low\-reward step reflects and explores freely \(βi=0\\beta\_\{i\}=0\), a mid\-reward step is mildly discouraged, and a high\-reward step, likely on a reliable track, is strongly suppressed so the model drives toward its conclusion instead of re\-opening branches\. Acting purely on logits, this adds no tokens and no extra forward pass\.

#### Early stopping via answer confidence\.

Additional reasoning helps only while the model is uncertain; once it is confident, further steps burn tokens without changing an answer it has settled on\. A persistent high\-reward state signals such a trajectory, but reward alone cannot decide whether to*commit*: it scores each reasoning*step*, not confidence in the*final answer*\. We therefore add a confidence probe: once the reward stays in the top band \(vi≥τhv\_\{i\}\\geq\\tau\_\{h\}\) for two consecutive steps, we insert a closing prompt \(*“Okay, I think I have finished thinking\.”*\) that exits the thinking phase and elicits a tentative answera=\(x1,…,xn\)a=\(x\_\{1\},\\dots,x\_\{n\}\), whose perplexity

PPL​\(a\)=exp⁡\(−1n​∑t=1nlog⁡p​\(xt∣x<t\)\)\\mathrm\{PPL\}\(a\)=\\exp\\\!\\left\(\-\\frac\{1\}\{n\}\\sum\_\{t=1\}^\{n\}\\log p\(x\_\{t\}\\mid x\_\{<t\}\)\\right\)\(5\)measures how confident the model is in that answer\. We stop and commit when

PPL​\(a\)≤τp,\\mathrm\{PPL\}\(a\)\\leq\\tau\_\{p\},\(6\)and otherwise discard the probe and resume reasoning\. Reward and perplexity are complementary, reward certifies that the*trajectory*is sound, while perplexity gauges confidence in the*answer*, and coupling them helps in two ways a perplexity threshold alone cannot\. It suppresses*confident\-but\-wrong*stops, since a fluent answer can have low perplexity even when the reasoning never converged; and it confines the probe, which costs an extra generation, to already\-promising trajectories rather than running it at every step\.

Table 1:Main results on DeepSeek\-R1\-Distill\-Llama\-8B and DeepSeek\-R1\-Distill\-Qwen\-7B across six benchmarks\. All reported numbers are averaged over three independent runs\. “Avg\.” averages over the six datasets\. Latency is per\-problem end\-to\-end wall\-clock time \(s\) measured on a single NVIDIA H20 GPU, including Pilot scoring and the confidence probe for ReCo; speedup is relative to Full CoT\.Table 2:Results on Qwen3\-8B\. Metrics follow Table[1](https://arxiv.org/html/2608.04771#S3.T1)\.

## 4Experiments

### 4\.1Experimental Setup

#### Models and datasets\.

We evaluate on three reasoning models across two families and scales: DeepSeek\-R1\-Distill\-Qwen\-7B, DeepSeek\-R1\-Distill\-Llama\-8B\(Guoet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib41)\), and Qwen3\-8B\(Yanget al\.[2025a](https://arxiv.org/html/2608.04771#bib.bib42)\)\. We benchmark on six datasets from grade\-school arithmetic to competition level: five math datasets, GSM8K\(Cobbeet al\.[2021](https://arxiv.org/html/2608.04771#bib.bib43)\), MATH\-500\(Hendryckset al\.[2021](https://arxiv.org/html/2608.04771#bib.bib51)\), AMC2023, AIME24, AIME25, and the scientific GPQA\(Reinet al\.[2023](https://arxiv.org/html/2608.04771#bib.bib44)\)\.

#### Baselines\.

We compare against representative methods from both sides of reasoning efficiency\.*\(i\)*Full CoT, the uncompressed model that keeps the full KV cache without length control, serving as the accuracy reference\.*\(ii\)*KV\-cache compression: SnapKV\(Liet al\.[2024b](https://arxiv.org/html/2608.04771#bib.bib25)\), R\-KV\(Caiet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib39)\), and RPC\(Songet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib45)\), which evict cache entries but do not control generation length\.*\(iii\)*Generation\-length and early\-exit methods: SAT\(Huanget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib37)\), which shortens reasoning via prompt\-based control, and Dynasor\(Fuet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib46)\), which early\-stops decoding; both keep the full cache\. Each addressing only the cache or only the generation, these baselines let us isolate the benefit of our*joint, reward\-coordinated*design\.

#### Implementation details\.

All experiments are conducted on a single NVIDIA H20 GPU\. For KV\-cache compression, we set the base retention ratio toλ=0\.25\\lambda=0\.25, the reward\-adjustment range toδ=0\.1\\delta=0\.1, and the attention window tow=32w=32; all KV\-cache baselines use a comparable ratio of0\.250\.25\. For generation control, we set the state thresholds toτℓ=0\.4\\tau\_\{\\ell\}=0\.4andτh=0\.8\\tau\_\{h\}=0\.8, and the early\-stopping perplexity threshold toτp=1\.1\\tau\_\{p\}=1\.1\. For a fair comparison, SAT and Dynasor are tuned to a comparable level of acceleration\.

### 4\.2Main Results

Tables[1](https://arxiv.org/html/2608.04771#S3.T1)and[2](https://arxiv.org/html/2608.04771#S3.T2)report accuracy, average generated tokens, and end\-to\-end latency across three models\. We highlight three observations, one per metric\.

#### ReCo best preserves accuracy under compression\.

ReCo stays closest to Full CoT: its average accuracy is60\.2%60\.2\\%vs\.62\.8%62\.8\\%on Llama\-8B,60\.0%60\.0\\%vs\.61\.9%61\.9\\%on Qwen\-7B, and69\.6%69\.6\\%vs\.72\.3%72\.3\\%on Qwen3\-8B, the smallest gap among all compressed methods\. KV compression baselines fall much further behind \(e\.g\. SnapKV to37\.5%37\.5\\%and R\-KV to48\.1%48\.1\\%on Llama\-8B\), and the gap widens on the hardest benchmarks: on AIME25, ReCo retains33\.3%33\.3\\%on Llama\-8B while every KV baseline collapses to≤20%\\leq 20\\%\. Compressing the cache without accounting for the role of each step disrupts the context most at the fragile, information\-dense states that complex reasoning depends on, whereas ReCo’s reward\-guided retention holds back compression exactly when the state is fragile\.

#### ReCo reduces tokens without inflation, unlike cache\-only compression\.

ReCo uses37%37\\%,65%65\\%, and46%46\\%fewer tokens than Full CoT on Llama\-8B, Qwen\-7B, and Qwen3\-8B, attaining the shortest average length on the latter two\. In sharp contrast, the cache\-only methods SnapKV, R\-KV, and RPC all*increase*token count \(e\.g\.7,078→11,2667\{,\}078\\\!\\to\\\!11\{,\}266under SnapKV on Llama\-8B\), directly corroborating the length\-inflation effect of Sec\.[2\.2](https://arxiv.org/html/2608.04771#S2.SS2)\. Length\-only methods \(SAT, Dynasor\) can emit even fewer tokens on some sets, but only by sacrificing accuracy \(e\.g\. Dynasor drops to82\.3%82\.3\\%on Llama\-8B GSM8K, below Full CoT’s89\.8%89\.8\\%\)\. Coupling compression with generation control lets ReCo cut tokens aggressively while staying close to Full CoT accuracy\.

#### ReCo delivers strong speedups without trading away accuracy\.

Reducing both the per\-token attention cost and the generation length, ReCo reaches2\.08×2\.08\\times,2\.35×2\.35\\times, and2\.18×2\.18\\timesspeedup over Full CoT on Llama\-8B, Qwen\-7B, and Qwen3\-8B\. Cache\-only baselines gain only modest speedups \(1\.091\.09–1\.33×1\.33\\timeson Llama\-8B\), since their inflated generation cancels much of the per\-token attention saving\. Length\-only methods \(SAT, Dynasor\), tuned to a comparable level of acceleration, reach similar latency but only by trading away accuracy \(e\.g\. SAT at58\.1%58\.1\\%vs\. ReCo at60\.2%60\.2\\%on Llama\-8B\)\. These results validate our central claim: coordinating cache compression and generation control under a single reward reduces both token count and latency while preserving reasoning quality, a balance that handling either alone cannot achieve\.111ReCo’s own components add only a small fraction of end\-to\-end inference time: Pilot scoring0\.60%0\.60\\%, KV compression0\.11%0\.11\\%, the reflection penalty1\.24%1\.24\\%, and early stopping1\.98%1\.98\\%on average\.

### 4\.3Ablation Studies and Analysis

![Refer to caption](https://arxiv.org/html/2608.04771v1/x4.png)Figure 4:Component ablation on DeepSeek\-R1\-Distill\-Llama\-8B: \(a\) accuracy \(%\) and \(b\) average tokens\.#### The three components are complementary\.

Figure[4](https://arxiv.org/html/2608.04771#S4.F4)keeps only one component at a time\. No single variant matches ReCo’s accuracy–cost balance\. “KV Comp\.” alone leaves generation unconstrained and is the most expensive on hard problems \(12\.812\.8k tokens on AIME25 vs\. ReCo’s8\.68\.6k\), echoing the length inflation of Sec\.[2\.2](https://arxiv.org/html/2608.04771#S2.SS2)\. “Refl\. Ctrl\.” and “Early Stop” curb tokens but, lacking reward\-guided retention, lose accuracy on the harder sets\. ReCo is best on all three, AIME25 \(33\.3%33\.3\\%\), AMC \(80\.0%80\.0\\%\), MATH500 \(80\.6%80\.6\\%\), showing the components are complementary, not redundant\. Intuitively, reward\-guided compression decides*what*to keep, while reflection control and early stopping decide*how far*to reason; removing either half breaks the accuracy–cost trade\-off that the full framework maintains\.

![Refer to caption](https://arxiv.org/html/2608.04771v1/x5.png)Figure 5:Hyper\-parameter sensitivity of ReCo \(Llama\-8B\)\.
#### Sensitivity to the base retention ratio\.

Row \(a\) of Figure[5](https://arxiv.org/html/2608.04771#S4.F5)sweeps the base retention ratio from15%15\\%to35%35\\%\(δ=0\.10\\delta=0\.10\)\. Aggressive pruning both destabilizes accuracy \(at15%15\\%, AIME25 falls to20\.0%20\.0\\%, AMC to65\.0%65\.0\\%\) and, as our analysis reveals,*inflates*tokens \(AIME25 rises from7\.87\.8k at35%35\\%to9\.29\.2k at15%15\\%\), exactly the length\-inflation failure mode of Sec\.[2\.2](https://arxiv.org/html/2608.04771#S2.SS2)\. Accuracy stabilizes over2525–35%35\\%; we adopt the more aggressive25%25\\%, which already delivers high accuracy \(80\.6%80\.6\\%MATH500,80\.0%80\.0\\%AMC\) at the lowest per\-token attention cost in this stable range\.

#### Sensitivity to the reward\-adjustment range\.

Row \(b\) fixesλ=0\.25\\lambda=0\.25and variesδ\\deltafrom0\.000\.00to0\.120\.12\. Atδ=0\.00\\delta=0\.00the policy is uniform and reward\-agnostic, and is consistently among the weakest \(65\.0%65\.0\\%on AMC\), direct support for our motivation that reward\-guided allocation beats treating all steps alike\. Accuracy peaks atδ=0\.10\\delta=0\.10\(80\.0%80\.0\\%AMC,80\.6%80\.6\\%MATH500,33\.3%33\.3\\%AIME25\), which we adopt as a robust default\.

#### Sensitivity to the early\-stopping threshold\.

Row \(c\) variesτp\\tau\_\{p\}from1\.051\.05to1\.201\.20, trading length for accuracy: a stricter threshold preserves accuracy but emits more tokens, a looser one halts earlier at some accuracy risk \(MATH500 drops80\.6%→68\.4%80\.6\\%\\\!\\to\\\!68\.4\\%from1\.101\.10to1\.201\.20\)\.τp=1\.10\\tau\_\{p\}\\\!=\\\!1\.10is best on all three sets \(33\.3%33\.3\\%AIME25,80\.0%80\.0\\%AMC,80\.6%80\.6\\%MATH500\) while already saving many tokens\. We use one configuration \(λ=0\.25\\lambda=0\.25,δ=0\.10\\delta=0\.10,τp=1\.10\\tau\_\{p\}=1\.10\) for all models and datasets, without per\-task tuning\.

Table 3:Peak GPU memory on AIME25 \(Llama\-8B\)\.
#### Peak memory usage\.

Table[3](https://arxiv.org/html/2608.04771#S4.T3)reports the maximum GPU memory on AIME25 with DeepSeek\-R1\-Distill\-Llama\-8B\. ReCo uses17\.9217\.92GB, a37\.7%37\.7\\%reduction over full cache \(28\.7828\.78GB\) and below both R\-KV \(20\.720\.7GB\) and SAT \(26\.926\.9GB\)\. A KV\-only compressor like R\-KV still trails ReCo because its inflated outputs enlarge the very cache it tries to shrink; by coupling compression with generation control, ReCo attains the lowest footprint\.

## 5Related Work

Efficient Reasoning\.Long CoT boosts LRMs but inflates token and compute cost\(Fenget al\.[2025](https://arxiv.org/html/2608.04771#bib.bib3); Quet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib5); Yueet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib6)\)\. Prior work spans length\-aware RL, fine\-tuning, or distillation for compact reasoning\(Yeoet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib10); Chenget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib11); Luoet al\.[2026b](https://arxiv.org/html/2608.04771#bib.bib12); Zenget al\.[2025](https://arxiv.org/html/2608.04771#bib.bib13); Ninget al\.[2025](https://arxiv.org/html/2608.04771#bib.bib7); Tanget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib4); Luoet al\.[2026a](https://arxiv.org/html/2608.04771#bib.bib8); Aggarwal and Welleck[2025](https://arxiv.org/html/2608.04771#bib.bib9)\), inference\-time prompting or explicit token budgets\(Hanet al\.[2025b](https://arxiv.org/html/2608.04771#bib.bib14); Huanget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib37); Renze and Guven[2024](https://arxiv.org/html/2608.04771#bib.bib15); Nayabet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib16)\), early stopping\(Yanget al\.[2025b](https://arxiv.org/html/2608.04771#bib.bib17); Qiaoet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib18); Wanget al\.[2025](https://arxiv.org/html/2608.04771#bib.bib19)\), and model routing\(Onget al\.[2024](https://arxiv.org/html/2608.04771#bib.bib20); Chenet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib21); Songet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib22)\)\. Yet these methods typically retrain the reasoning model or touch only the generated text, leaving the KV cache untouched\. ReCo needs no training of the reasoning model and no per\-task prompt engineering, only a3030M step\-level reward estimator, allocates per step under a single process reward, and controls cache and length jointly\.

KV Cache Compression\.The KV cache is a major latency and memory bottleneck in LLM inference\(Liet al\.[2024a](https://arxiv.org/html/2608.04771#bib.bib23); Shiet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib24)\), addressed by token eviction\(Liet al\.[2024b](https://arxiv.org/html/2608.04771#bib.bib25); Caiet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib26); Fenget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib27); Yanget al\.[2026](https://arxiv.org/html/2608.04771#bib.bib55)\), merging\(Zhanget al\.[2024](https://arxiv.org/html/2608.04771#bib.bib29); Wanget al\.[2024](https://arxiv.org/html/2608.04771#bib.bib30); Wanet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib31)\), quantization\(Hooperet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib32); Zandiehet al\.[2025](https://arxiv.org/html/2608.04771#bib.bib33); Hanet al\.[2025a](https://arxiv.org/html/2608.04771#bib.bib34)\), and low\-rank decomposition\(Changet al\.[2024](https://arxiv.org/html/2608.04771#bib.bib35),[2025](https://arxiv.org/html/2608.04771#bib.bib36)\), but they assume a static prompt pruned once after prefilling\. Recently adapted to reasoning, where the cache instead grows with the chain of thought, R\-KV\(Caiet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib39)\)and RPC\(Songet al\.[2026](https://arxiv.org/html/2608.04771#bib.bib45)\)use heuristic eviction that ignores step importance and acts on the cache alone, so length inflation erodes the saving\. ReCo instead ranks retention by per\-step process reward and couples compression with generation control\.

## 6Conclusion

We presented ReCo, a step\-wise framework that coordinates KV\-cache compression with generation control under a single per\-step process reward\. Our analysis shows that reasoning states differ in how much compression they tolerate and that compressing the cache alone often lengthens the subsequent reasoning, so the extra generation cancels much of the intended saving\. By governing the cache and the reasoning length jointly, ReCo cuts token count and latency across three reasoning models and six benchmarks, and lowers peak memory, while staying close to full\-cache accuracy, indicating that KV compression is better coupled with generation control\.

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