VeriThinker: Learning to Verify Makes Reasoning Model Efficient
Authors: Zigeng Chen
Xinyin Ma
Gongfan Fang
Ruonan Yu
Xinchao Wang
Venue: NeurIPS 2025 poster ()
Keywords: cot compression
efficient reasoning model
Primary area: deep_learning
TL;DR: We introduce VeriThinker, a simple yet effective approach for CoT compression.

Abstract: Large Reasoning Models (LRMs) have garnered considerable attention for their ability to tackle complex tasks through the Chain-of-Thought (CoT) approach. However, their tendency toward overthinking results in unnecessarily lengthy reasoning chains, dramatically increasing the inference costs. To mitigate this issue, we introduce VeriThinker, a novel approach for CoT compression. Unlike conventional methods that fine-tune LRMs directly on the original reasoning task using synthetic concise CoT data, we innovatively fine-tune the model solely through an auxiliary verification task. By training LRMs to accurately verify the correctness of CoT solutions, the LRMs inherently become more discerning about the necessity of subsequent self-reflection steps, thereby effectively suppressing overthinking. Extensive experiments validate that VeriThinker substantially reduces reasoning chain lengths while maintaining or even slightly improving accuracy. When applied to DeepSeek-R1-Distill-Qwen-7B, our approach reduces reasoning tokens on MATH500 from 3790 to 2125 while improving accuracy by 0.8% (94.0% to 94.8%), and on AIME25, tokens decrease from 14321 to 10287 with a 2.1% accuracy gain (38.7% to 40.8%). Additionally, our experiments demonstrate that VeriThinker can also be zero-shot generalized to speculative reasoning.

VeriThinker: Learning to Verify Makes Reasoning Model Efficient
Zigeng Chen, Xinyin Ma, Gongfan Fang, Ruonan Yu, Xinchao Wang" National University of Singapore zigeng99Cu. nus edu, xinchao@nus.. edu.
SFT Methods
Model Merging or CoT Truncating
Reasoning Problem
Reasoning Model
Solution: Okay, I need to figure out many fe....ennnier brought home total of 100 cans of milk. Tokens:
Target Chain
Extensive Sampling
Low Reward
Solution: Okay, so I need to figure out many ......Wait,
Methods
double
Negative Chain
check .....Jennnifer brought home total cans milk.
Reasoning Problem
Reasoning Model
Tokens: 1204
High Reward
Solution: To determine how many
Target Chain
cans answer is 100. Tokens: 788
VeriThinker (ours) Reasoning Problem
Yes, I'm that every step is absolutely correct.
Verification:
Small Short-CoT LLM Generated
Reasoning Model
Solution: To determine how many cons ....... brought home total
Varification: No, think there might be mistakes in the solution.
100 cans of milk.
# Tokens: 218
Figure 1: The key distinction between VeriThinker and traditional SFT or RL-based long-to-shore methods. We uniquely train LRMs auxiliary CoT verification task, achieving effective CoT compression without relying on synthetic target reasoning chains.
Abstract
Large Reasoning Models (LRMs) excel at complex tasks using Chain-of- Though (CoT) reasoning. However, their tendency to overthinking leads to unnecessarily lengthy reasoning chains, dramatically increasing inference costs. To mitigate this issue, introduce VeriThhinker, a novel approach for CoT compression. Unlike conventional methods that fine-tune LRMs directly on the original reasoning task using synthetic concise CoT data, we innovatively fine-tune the model solely through an auxiliary verification task. By training LRMs to accurately verify the correctness of CoT solutions, the LRMs inherently become more discerning about the necessity of subsequent self-reflection steps, thereby effectively suppressing overthinking. Extensive experiments validate that VeriThinker substantially reduces reasoning chain lengths while maintaining even slightly improving accuracy. our approach reduces reasoning
When applied to DeepSeek-RR R Distill-Qwen- tokens MATH500 from 3790 to 2125 while improving accuracy by 0.8% (94.0% to 94.8% and on AIME25, tokens decrease from 14321 to 10287 with 2.1
"Correspoding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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accuracy gain (38.7% 7% to 40.8%). Additionally, our experiments demonstrate that VeriThinker can also be zero-shot generalized speculative reasoning. Code is available at http:::////// thub.
Thinker
Introduction
Large Reasoning Models (LRMs), such as GPT-ol [20], DeepSeek-RI 113 Kimi-k1.5 [54], and QwQ [55]. have shown exceptional performance in tackling complex reasoning tasks. Their success stems from the ability to generate effective Chuin-of- ThoTThhgh (CoT) reasoning [59 32 By decomposing
intricate problems into manageable steps and meticulously verifying each intermediate result, these models achieve superior reasoning performance. Furthermore, this test-time scaling method has demonstrated notable potential beyond reasoning tasks, extending its impact diverse fields such as vision- lasoun-anguuae models [9 63 72 28), image generation 40 21 62]. and video synthesis 7 33).
However, the long reasoning chains generated by LRMs often contain numerous redundant self- checking steps-a a phenomenon commonly known as "overthinkkig" [5) Specifically, these models incorporate frequent self- elf-verification steps to ensure the accuracy of their reasoning, but most of these self-verifications prove ineffective or even add confusion to the reasoning process. This extensive overthinking dramatically inflates inference costs and hinders the efficient deployment of LRMs.
have focused on compressing lengthy reasoning chains into shorter, more concise forms. These methods typically generate concise reasoning chain data through extensive sampling, model merging, or selective truncation of original long reasoning chains. Subsequently, these synthetic reasoning chains serve as targets, with Supervised Fine-TTming Tuning (SFT) 588 or Reinforcement Learning (RL) used to align the LRM's ' output distribution closely to these target chains. Thus, the performance of these compression strategies heavily depends on the quality and quantity of the synthesized reasoning chain data. However, generating high-quality concise reasoning chains is computationally intensive and time-consuming. Moreover, simultaneously achieving brevity while preserving essential self-reflection steps remains challenging. Consequently, models compressed through these methods struggle to balance conciseness and high accuracy, especially when tackling highly complex reasoning tasks. A key question arises: Can we effectively compress lengthy reasoning chains without relying on synthetic target reasoning chains?
Several recent studies
60 35
43 38
Our Approach. To address this challenge, we introduce VeriThinker, a straightforward yet effective method for CoT compression without the dependence on synthetic target data. VeriThinker's 's core innovation lies in novel fine-tuning strategy named Supervised Verification Fine- Timiii (SVFT). Unlike previous methods that directly fine-tune LRMs on reasoning tasks through SFT or RL, SVFT uniquely fine-tunes the model on an auxiliary verification task to achieve CoT compression. Specif- ically, we create CoT verification dataset, providing the LRM with question-solution pairs and training it to verify the correctness of the CoT solution through binary classification. By learning to distinguish between correct and incorrect solutions, the LRM can more accurately determine when self-reflection is necessary. Empirical studies demonstrate that after SVFT, the model significantly reduces unnecessary double-checking of correct reasoning steps while slightly increasing verification of incorrect steps. This effectively mitigates overthinking and maintains or slightly improves rea- soning accuracy. Furthermore, by utilizing its ability to recognize correctness, VeriThinker can also generalize to solution wise speculative reasoning for higher inference throughput
We evaluate VeriThinker on three state-of-the-art reasoning models: ---a-eee----isiil---ee---- DeepSeek-RR -i-ee-----sttll---- Qwen-14B, and DeepSeek-B R -DiiisilllLLlama-- [13. Extensive experiments show that fine-tuning solely on the CoT verification task enables LRMs to substantially reduce token usage while preserving high accuracy, even on extremely challenging problems like the AIME dataset. Additional experiments show that VeriThinker can also be applied to speculative reasoning, achieving a significant throughput increase when using a short-CoT LLM as the draft model.
In conclusion, we present VeriThinker, a simple yet effective CoT compression method that elim- inates the need for synthetic target chain data. Key to our approach is the proposed SVFT, which innovatively mitigates the overthinking problem by fine-tuning the LRM exclusively on an auxiliary CoT verification task. Comprehensive experiments demonstrate that VeriThinker efficiently shortens reasoning chains while preserving or slightly improving model accuracy, even on highly challenging reasoning tasks. Additionally, our method can also generalize to speculative decoding, achieving significant improvements in inference throughput.

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2 Related Works
enables large reasoning models (LRMs) to solve complex reasoning tasks, such as mathematical and coding problems, by leveraging inference-time scaling laws. Advanced LRMs, including GPT-o1 [20]. DeepSeek-RI [13. Kimi-k1.5 (54), and QwQ [55], have set new benchmarks in reasoning capabilities. These models utilize reinforcement learning to encourage multiple self-reflection steps during inference, substantially increasing response accuracy. Furthermore, other methods, such self-consistency [57], beam search, and Monte Carlo [2].
Chain-of-thought.
Chain-of-thought [59 32
Tree Search (MCTS) [2]. have been employed to facilitate parallel inference scaling laws, further enhancing LRM reasoning effectiveness. Beyond language models, the principles underlying CoT have also demonstrated significant performance improvements in domains like visual reasoning image generation
19
440
62
and video synthesis
Efficient Reasoning Models. Despite these substantial gains, the tendency of LRMs towards overthinking often results in excessively extended reasoning chains, significantly raising inference costs. Recent research has investigated methods for compressing CoT to enable more efficient reasoning processes. Specifically, [5] comprehensively analyzes the overthinking phenomenon and employs SimPO to fine-tune L.Mss. Kimi-K1.5 [54) proposes weight merging strategies between long-Col and short-CoT models and introduces Langth-penalized loss functions effectively compress COT. Additional studies [41 [4 achieve tengghy-oontrollbbe CoT compression, while
others 660 33
69
synthesize concise reasoning chain data to guide long-to-short compression via
SFT. Methods 38
71
26 17 adopt reinforcement learning and extensive sampling to reduce
the number of tokens required CoT processes. Furthermore, adaptive methods [68] 37 [0 [0]
have been proposed to conditionally activate long-CoT modes based on input query. Simpler yet effective prompt-guidane
methods for direct CoT compression have also been explored [36 [55]
24
53
Additionally, there is increasing interest in converting explicit CoT processes into latent [5]. However, these latent approaches currently face significant challenges about
CoT accuracy degradation.
49
Beyond CoT compression, other techniques involving model compression and optimized decoding have also gained prominence. Knowledge distillation approaches have allowed smaller reasoning
models approximate the performance larger counterparts effectively 66
27 74). Additionally,
[51 34 [3 explore model pruning and quantization techniques on LRMss. Decoding optimization
techniques have also been widely adopted to accelerate inference [56]
52
39
64
67]. Methods such
as speculative decoding [31] 46) and parallel inference strategies
45 demonstrate a notable
decoding acceleration ratio, further enhancing the practical applicability LRMs.
3 Methods
3.1 Problem Setup
Recent efforts in improving the efficiency of LRMs have focused on compressing lengthy reasoning chains into shorter, more concise reasoning sequences without redundant over-thinkings. Formally, let Mg represent an LRM parameterized by 9. Given a query q. the model generates a long reasoning chain Ct. obtained by sampling from the model's conditional output distribution: C₁ MM(- 9)- We hypothesize the existence of an ideal concise reasoning chain C, characterized by minimality in length and maximal retention of essential self- seff-verification steps, ensuring the correctness of the final solution. The objective of CoT compression is thus to finetune M, such that the generated reasoning chain closely approximates the ideal concise chain C,:
min [D(a (.),, 8
where D denotes a suitable distance metric in the distribution space.
commonly employed approach involves constructing synthetic short reasoning chain C.. In SFT-based variants [60 35 43
69 41), this is typically done via model merging or by selectively
truncating the original long chain data, whereas RL-based approaches [38 71 2 I 26 [7] rely on extensive sampling. Under the assumption that the synthetic chain C, is distributionally close to the ideal chain C,, they train the LRMs either by supervised fine-tuning on C, or by reinforcement leaming-rewardinng the shorter sequences C2 more highly than the longer ones Cj.
3

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In essence, these approaches regard the synthesized short CoT sequences as the target reasoning chain and train the model to approximate them. Therefore, their efficacy depends critically on both the quality and volume of the generated C.. However, generating high-quality short chains is extremely costly in computing and time, which limits efficient scalability. Furthermore, synthetic short reasoning chains typically struggle to simultaneously achieve brevity and retain the essential self-reflection steps, resulting in a mismatch from the ideal distribution C.. This discrepancy often inevitably leads to substantial degradation in the model's reasoning capabilities during the long-to-short process, particularly when confronted with complex, high-difficulty problems.
A critical problem arises: Can we devise a method that effectively compresses an LRM's overex- tended reasoning chains while preserving its original reasoning ability, without relying on explicitly synthesized target chains?
3.2 Supervised Verification Finetuning
To address the aforementioned issue, we begin by revisiting the fundamental principles underlying LRM's overthinking. During reasoning, when determining whether to engage in additional self- reflection, the LRM essentially operates as a binary classifier that evaluates the correctness of previously generated reasoning steps. Formally, the LRM encodes prior solution into hidden state, denoted as h, and the language modeling head (LM head) subsequently classifies this state as either correct incorrect. If the classification is correct, the model proceeds to subsequent reasoning steps; if incorrect, it triggers further self- elff-veifiiation.
The prevalence of overthinking stems from insufficient accuracy in this binary classification task. Specifically, the hidden state fails to adequately encode the critical information required for precise correctness judgments. Consequently, LRMs frequently misclassify correct solutions as incorrect, leading to unnecessary self-reflection steps. Let p(acc h) denote the probability that the LRM accurately classifies the correctness of a prior solution. By increasing p(ace h), redundant reflections are progressively reduced, preserving only essential verification steps for genuinely incorrect solutions. In the ideal case where p(acc h) 100%, the LRM outputs the optimal reasoning chain C, invoking self-reflection solely when prior solutions are indeed erroneous.
Existing methods that employ synthetic target chains for CoT compression implicitly aim to maximize p(ace h). These methods synthesize concise target chain approximating the optimal scenario where p(ace h) x 100%. As the LRM's output distribution aligns with this target, p(ace | h) naturally increases, thereby mitigating overthinking. However, such approaches are inefficient and indirect, as most tokens in the synthetic chains contribute negligibly to improving p(ace h). Consequently, these methods yield only marginal gains in p( p(ccc h). Moreover, the probability of triggering self-reflection decreases even when errors occur in earlier steps, inadvertently leading to performance degradation on highly complex problems.
Since the primary cause of overthinking in LRMs arises from their inability to accurately determine the correctness of solution, a natural and intuitive strategy is to explicitly train LRMs to discern solution correctness, thus fundamentally addressing the overthinking issue. Motivated by this insight, we introduce VeriThinker, a straightforward yet effective method for CoT compression. The key idea of VeriThinker is novel fine-tuning strategy, termed Supervised Verification Fine-Tuming (SVFT). Distinct from prior approaches, SVFT does not rely on optimizing the model to match a target reasoning chain distribution. Instead, it aims to directly enhance the model's is capability to classify solutions as correct or incorrect, optimizing the binary classification accuracy p( acc h). Specifically, we fine-tur tune the reasoning model on auxiliary CoT verification task, providing the LRM with question paired with a CoT solution, and the model is explicitly trained to accurately classify whether this provided solution is entirely correct or not.
Firstly, we need to construct a CoT verification dataset, denoted as: Dvenr = (gi, 8i, v5) where each data instance consists of problem description y:, a CoT solution 8; without self-reflection steps, and a verification result o, indicating the correctness of the solution. The prompt for each instance is formed by the pair (gi, st), and the corresponding verification response es is explicitly defined as:
Yes,, I'm sure that every step is absolutely correct.". 1:
if s; is correct, "No, I think there might be some mistakes in the proposed solution.", ", otherwise.
(2)

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200
SiFTMode
4230
36.6
140
Accuracy
Reffectionn
2230
Borerr Training Datasets
01gas Lowrr Serur
Cameic
Foamd
Training Datasets
Step
(a)
Reasoning Token
(b) Reasoning Accuracy
(c) SelffRefflectin Probability
Figure 2: (a)-(b): Token counts and accuracy in reasoning tasks across different training datasets. (c)
Probability of self-reflection during reasoning for correct and incorrect solutions.
Then we used this CoT-verification dataset to fine-tune the LRMs. During finetuning, only tokens within the verification response contribute to the training loss. This design effectively mitigates potential undesirable biases introduced by the input solution from affecting the model's output distribution. Formally, given tokenized prompt-response pair (æ, y), the SVFT training loss is defined as:
SSVIT
Σ log po (yels, Vcc))
where pe denotes the probability distribution output by the LRM parameterized by 6.
Since the judgments of correct and incorrect in the data are represented as two completely fixed responses, and we only compute the loss on the response tokens, the entire SVFT essentially performs a binary classification on the question-solution pairs which is fundamentally similar how the LRM decides whether to perform self-reflection after each step during reasoning.
Experiments demonstrate that by learning verify the correctness of CoT solutions. SVFT effectively mitigates LRM's overthinking phenomenon. While significantly reducing the number of tokens required for reasoning, SVFT does not lead noticeable degradation reasoning capability.
3.3 Empirical Analysis
To better understand why SVFT facilitates effective compression of CoT without compromising the original reasoning capability of LRMs,, conducted additional experiments thoroughly investigate the underlying mechanisms of SVFT.
What Capabilities Does SVFT Impart to the Model? A primary question we sought to explore was the specific competencies instilled the LRM through SVFT. To this end, we constructed five distinct CoT-verification datasets and conducted SVFT the RI RI-Distill-Qwen-11 model, observing differences in outcomes across these datasets. These five datasets shared identical prompts, each consisting of question, CoT solution, and concise instructions. However, varied the response tokens in five distinct ways: Dataset (1): Maintained the original setting. Dataset (2): Reversed responses, assigning affirmative responses to incorrect solutions and negative responses to correct
solutions. Dataset (3): Simplified responses to single tokens, "Yes" and "No,". Dataset (4): Further simplified responses semantically neutral tokens "North" and "South." Dataset (5): Randomly assigned responses irrespective of solution correctness.
Figure 4 (a) and (b) illustrate the changes in average tokens per response and accuracy the MATH500 16] dataset after SVFT training with the aforementioned datasets. We observed that, apart from Dataset (5), all other datasets showed similar trends: a significant reduction in reasoning chain length, accompanied by maintained or slightly improved accuracy. These findings suggest that SVFT is fundamentally akin contrastive lcarning. The model learns the capability to distinguish differences between correct and incorrect solutions through binary classification rather than learning explicit correctness semantics. In contrast, Dataset (5), which utilized responses entirely unrelated to solution correctness, did not facilitate CoT compression. This indicates that SVFT does not merely cause the LRM to adopt more concise expression style to directly output conclusions, reinforcing our earlier conclusions.
Conclusion: In summary. SVFT empowers the LRM to differentiate between correct and incorrect solutions rather than intrinsically learning which solution is right. The core mechanism of SVFT closely resembles that of contrastive learning.
5

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Why Does SVFT Enhance CoT Compression? Next, we investigate the reasons behind SVFT's effectiveness in achieving CoT compression. As SVFT trains the model to perform binary classifica- tion based on the correctness of CoT solutions, the model inherently learns to focus on the crucial elements in the CoT affecting solution correctness. We hypothesize that this enhanced attention allows the model, during reasoning tasks, to more accurately determine whether self-reflection step is necessary, thereby eliminating redundant double-checking and enabling effective CoT compression.
To empirically validate this hypothesis, we randomly selected 50 problems from the MATH500 dataset and generated correct long CoT solutions for each problem using the R1- RI-distill- Qwen- model. We extracted sub-solutions from each solution, spanning from the start until the appearance of the first pivot word "Wait." " We then performed forward computations using the original RI-Distill- Qwen-7B, the SFT model and the SVFT model on these question- subtiionnuu-oolutioon pairs, examining the generation probabilities of the pivot word "Wait." " As shown in Figure (c), we found that both the SFT and SVFT models exhibit a significantly lower probability of generating the pivot word for correct sub-solutions compared to the original model.
Next, we manually introduced mistakes into each correct sub-solution- instance, changing "3 x 7 = 21" "3 x 7 27"-2 evaluated the models' probabilities for generating the pivot word "Wait" again. In this case, the SVFT model showed no probability reduction but instead marginal (1%) increase compared to the original model, while the SFT model continued exhibit significantly reduced probabilities.
These results strongly support our hypothesis: SVFT enhances the LRM's precision in evaluating reflection necessity. Specifically, for the SVFT model, we observe: (1) substantial reduction in redundant verification when preceding steps are correct, and (2) slight increase in reflection probability when mistakes are introduced. This adaptive behavior enables effective CoT compression while preserving and occasionally improving reasoning accuracy. In contrast, the SFT model uniformly reduces reflection probability regardless of solution correctness, explaining its chain-shortening capability at the cost of accuracy degradation.
To further validate this hypothesis, we compared the changes in response token counts of the SVFT- finetuned model on the MATH500 dataset. For questions correctly answered by the SVFT model, the token count in the reasoning chain decreased by 41 % compared to the original model. In contrast, for incorrectly answered questions, the token count decreased by only 8%. This experimental result further robustly supports our hypothesis.
In summary, SVFT achieves effective CoT compression primarily by enhancing the ac- curacy of LRMs' self-reflection decisions during reasoning. It minimizes unnecessary self-reflections for correct steps while retaining critical verification steps for mistaken steps, significantly reducing token usage without compromising reasoning accuracy.
Conclusion:
3.4 Solution-wise Speculative Reasoning
As LRMs acquire the capability to verify solution correctness through SVFT, we leverage this ad- vancement to propose a collaborative inference pipeline termed Solution-wise Speculative Reasoning (SSR). This approach significantly boosts inference throughput by orchestrating interactions between a short-CoT LLM and an SVFT-enhanced LRM.
Distinct from conventional token-wise speculative decoding methods 25 draft model proposes multiple candidate tokens subsequently verified in parallel by larger LLM through token probability evaluation (accepting or rejecting each individual draft token), our approach introduces a novel solution-level paradigm specifically tailored for reasoning tasks. Given a problem, the T LLM first rapidly generates concise solution candidate. This candidate is then assessed by the SVFT-enhanced LRM for correctness verification. If the proposed solution is deemed correct, it is immediately output as final answer; otherwise, the system activates the LRM's full long-CoT reasoning process to ensure accurate results.
30 61. where smaller
This pipeline adaptively engages the LRM: For simple problems, the LRM only validates the draft solution without invoking costly long-CoT; For challenging problems, the LRM intervenes to ensure accuracy when the draft fails. By selectively triggering long-CoTT reasoning based on problem difficulty and draft quality, our speculative reasoning pipeline achieves substantial throughput gains while preserving high reasoning accuracy.

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Table 1: CoT compression performance, We evaluate the proposed VeriThinker on three advanced reasoning models, comparing token efficiency and accuracy against the original model and baseline methods over three mathematical reasoning benchmarks.
Method
MATH500
AIME 2024
AIME 2025
Average
Tokens
Accuracy?
Accuracy1
4 Accuracyt
4
Accuracy!
Deepseek- RI Hi--istill-Qwen-12
Original Model
94.0%
13108
54.1%
14321
38.7%
10407
62.3%
Truncating
2306
80.4%
9550
45.3%
10232
36.3%
7363(-29%)
14.0%(-8.3%))
Fast- Pest-Promtiing
2425
83.8%
11867
53.3%
13378
38.3%
9223(-30%%
58.5%(-3.8%%)
Cal-Valvee
2440
92.4%
11238
39.2%
10884
30.4%
8187(-22%)
(.33%)
SFT
2064
91.2%
8843
49.1%
9686
32.1%
6864(-349)
(7.5%)-4.8%)
VeriThinker
2125
94.8%
56.5%
10287
40.8%
(264(-30%)
(+1.%)++))%))
Deepseek- Beaeeekk-----iiiie Ri--istill-Qwee---ee
Original Model
3529
95.2%
11724
69.0%
L3409
49.6%
9554
71.2%
Truncating
2479
85.8%
8658
57. 1%
9247
42.9%
6795(-309%
61.9%)(-9.6%)
Past-Prompiig
2405
82.0%
64.0%
10645
49.3%
7113(-2696
65.1%(-6.18%
CoT-Valve
2102
91.0%
8691
41.7%
9558
25.0%
67831-29%)
52.6%)(-18%
SFT
2226
92.8%
9021
58.3%
10644
43.3%
7297(-249)
64.8% (4.8%(-7744))
VeriThinker
2255
95.0%
7423
73.0%
9304
54.8%
6327(-349)
74.3%(+3.19)))
Deepseek-RI-De -I----RR----iiiLLaaaee Llama-5
Original Model
4361
90.6%
14005
44.6%
14420
30.15
10928
55.1%
Truncating
3193
81.6%
11577
39.1%
11635
28.6%
8802( (802((209%)
49.8% 5.3%)
Fast- Prompting
9762(-115)
52.09-(-311))
CoT-Valve
4614
81.4%
12650
23.3%
12520
17.5%
9928(-99)
40.7%((14%%
SFT
2439
81.2%
9500
31.3%
10136
26.0%
7358(-33%)
46.29%(8.7%%
VeriThinker
2953
89.9%
11285
46.9%
10557
29.7%
8265(-249)
55.5%(++044%)
4 Experiments
4.1
Experimental Setup
Models. To comprehensively evaluate our approach. we apply the proposed VeriThinker to three
state-of-the-arr long-CoT reasoning models with varying architectures and sizes, including DeepSeck- -i--RRiiiiill-UU
Distill--wen-7B
14B, and DeepScck-Rl-Distinee RI-Distill-LLMMA-B [[3].
Additionally, also evaluate our approach three short-CoT models:
Qwen-2.5-Math-1155 -.5tttruttt
(66), and Qwen-2.5-78 2-5------B-
Instruct (66]
Training and Evaluation Details. For the proposed SVFT, we adopt Low-Rank Adaptation (LoRA)
18 for efficient fine-tuning, which significantly improves training efficiency and effectively mitigates catastrophic forgetting, as training and inference occur on different tasks. All training procedures are conducted using Hugging Face's 's SFTTrainer integrated with DeepSpeed ZeRO-2 optimization
47, distributed across four RTX 6000 Ada GPUs. For evaluation, inference results and throughput metrics are also obtained using RTX 6000 Ada GPUs with the vLLM inference framework [23]. We adhere the models' default sampling configurations, specifically setting temperature to 0.6 and top-p to 0.95. During inference, the prompt appended to each question is: "Please reason step by step, and put your final answer with boozed. To evaluate LRM's performance, report the reasoning accuracy and the average token count of the reasoning chain (between <think> and </think>).
During the fine-tuning phase, we utilize our self-constructed CoT-verification dataset comprising approximately 340k question-CoT pairs, each labeled with correctness indicators. We provide more details about training set construction in the Appendix. For evaluation, we employ multiple mathematical benchmark datasets, including MATH500 [16), GSM8K (6), and two highly challenging competition datasets, AIME2024 and AIME2025. The results reported for each dataset represent averages computed over 2 to independent runs, depending on the dataset's size.
Datasets.
Baselines. To demonstrate the superiority of our innovative method, we compare it against several conventional CoT compression approaches, including: (1) Truncation, which reduces the maximum allowable token length; (2) Fast-Prompting. method leveraging prompt engineering to enforce reasoning completion within a specified token limit; (3) CoT-VVlle
[41] enabling model to dynamically adjust the length of reasoning chains; and (4) SFT (58) supervised fine-tuning method that uses synthesized concise CoT chains as targets for long-to- thort compression. To synthesize concise reasoning chains for the SFT baseline, follow CoT- Valve [1] by merging the base and
7

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Table 2: CoT correctness verification results. We apply VeriThinker to three advanced LRMs and assess their verification accuracy on CoT solutions generated by two short-CoT models. For comprehensive analysis, we report classification accuracy, precision, recall, and Fl score.
MATH500
GSM8K
Method
Acc.
Precision 1
Recall
Fl Score
Ace.
Precision 1
Recall
Fl Score
11-Distil-Qwee--TT Beern-B---eeiiiooe Vhinkeinker
88,4%
0.926
0.924
0.926
93.6%
0.964
0.962
0.963
RI-Distill Qwen- 14B+ VeriThinker
90.6%
0.953
0.927
0.940
95.7%
0.971
0.978
0.975
RI-Disuill Llama SD+Veri VeriThinker
88.0%
0.954
0.892
0.922
91.5%
0.954
0,947
0.950
RI-Distill Owen-7B++ VeriThinker
0.931
0.939
94.8%
0.981
0.965
0.973
RI-Distill-Quer Seel--wwn---hh VeriThiker
91.0%
0.973
0.922
0.947
95.5%
0.986
0.966
0.976
RI-Distill Llama SD+VeriThinker
87.4%
0.880
93.9%
0.968
Table 3: Speculative Reasoning Results. We applied VeriThinker to three LRMs and employed two short-CoT LLMS as draft models to evaluate the performance of solution-wise speculative reasoning. We report accuracy, token counts, throughput, and AcR (Iong-Co'T reasoning Activation Rate). Underlined numbers indicate the token counts during the draft phase for short-CoT LLMs.
MATH500
GSMBK
Method
Tokens |
Throughput
AcR L
Tokens
Throughput
AcR
RI-Distill-Qwen-1
94.0%
3791
1.0x
100.0%
92.8%
1555
1.0x
100.0%
+Qwen-2.5-Math--1 1.5-Inttett
91.8%
589+889
4.4x
20.8%
93.3%
321+229
5.1x
14.0%
+Qwen-2.5 Instrutttt
93.4%
614+656
96.1%
294-1113
RI-Distill-Qwen 14B
95.2%
3529
1.0x
100.0%
95.6%
1309
1.0x
100.0%
+Quenn-25-Math-I1 1.5B-Inntrree
93.0%
589-1130
3.6x
22.8%
95. 1%
321+175
5.3x
13.2%
+Qwen-2.5 2.5thhh--7t TB-Inmtect
95.7%
614+954
3.5x
17.6%
96.6%
294+93
5,4x
5.5%
RI-Distil-Llama---
90.6%
4361
1.0x
100.0%
89.2%
1643
1.0k
100.0%
+Qwen-2.5- 2.55MMthh-11 1.5B-Instruut
90.4%
589+1589
3.3x
25.8%
91.7%
32143077
4.7%
14.5%
+Qwen 2.5 Math 7B Instruct
91.6%
614-1265
3.2x
21.2%
96.4%
294+161
4.8x
6.0%
reasoning models at a 0.2:0.8 ratio to generate concise reasoning chains on PRM12K and GSM8K. Only correct CoT solutions are retained, and the average length of these concise chains is about 60% of the original. Both SET and our VeriThinker method are finetuned with same LoRA configuration.
4.2 Experimental Results and Analysis
CoT Compression Results. We present comprehensive experimental results on CoT compression in T Our VeriThinker significantly reduces the number of tokens while maintaining or even slightly improving reasoning accuracy. In contrast, other baseline methods fail to achieve a good trade-off between efficiency and accuracy. When the accuracy successfully maintained, the length of the reasoning chain shows little variation; when the token count is significantly reduced, the reasoning accuracy inevitably decreases substantially this phenomenon particularly evident in challenging problems. Among the baselines, the SFT method using target chain optimization objective, while significantly reducing token count, leads to notable degradation in the model's self-refiection capability. Consequently, some incorrect steps fail to be double-checker resulting in erroneous outcomes. Our Vhr'Thinker, by contrast, enables the model to distinguish between correct and incorrect solutions, enhaneing its ability to judge when self-checking is needed, thereby maximally preserving reasoning accuracy with even slight improvements.
As shown in the T our method demonstrates consistent superior performance across all three LLMs, with particularly outstanding results on the challenging AIME dataset. Our approach reduces the COT length by approximately 29% (from 13, 108 to 9,381 tokens) for the R1 2e1-Ditilll-wen--7 model on AIME 2024 while increasing reasoning accuracy by 2.4%. On AIME 2025, the token count decreases by about 28% (from 14.321 to 10.287) with 2.1% accuracy improvement. We also observe that our method shows higher sensitivity to CoT compression on LLaMA architecture models. Although VeriThinker maintains good accuracy preservation on RI-Distill-LLaie -LLMMA-SB, the compression ratio of reasoning chains is relatively smaller. These comprehensive experimental results strongly support and highlight the contributions of our method.
CoT Correctness Verification Results. As VeriThinker trains LLMs to verify the correctness of CoT solutions, we conducted additional experiments to analyze its verification accuracy. Specifically, we generated CoT solutions using Qwen-2.5-Math- 1.Bahhh.5B-nnttrucc and Qwen-2.5-Math. -nntructt on GSM8K and Math500 datasets. We then employed SVFT LRMs to evaluate the correctness of these
8

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GSNEK
GSKDK
H500
05-400
14.0%
NATHE00
02.47%
NATH500
22 40
100
20
100
60
(4) RL-VerrTBinkkk---oaa--78
(b) R.L-VerrThiikkk--eee....k 148
(e) VigeeeTThin loma-88
Figure 3: Speculative reasoning results on three reasoning models. When using Qwen-2.5-Maite Instruct-7B as the draft model, most problems in MATH500 and GSM8K can be solved with short CoT model, while only a few require activation of the long CoT model for more complex solutions.
solutions. As shown in Table 2 all three SVFT LRMs demonstrate high verification accuracy. The verification accuracy on GSM8K is higher than on MATH500, indicating that more concise and clear solutions are easier to classify correctly. We also observe a positive correlation between the model's verification accuracy and its reasoning capability. For reasoning tasks, the performance ranking is RI-Distill-144 14B > RI RI-Distill-7B R1- Distill--BB. and the verification accuracy follows exactly the same trend. Furthermore, we find that LLMS generally exhibit notably higher precision than recall. This suggests that LLMs adopt a conservative approach when judging solution correctness they rarely misclassify incorrect solutions as correct ones.
Speculative Reasoning Results. The above experiments demonstrate that SVFT LRMs achieve high verification accuracy, particularly in precision. Building on this strength, we conduct extensive experiments to assess their performance in speculative reasoning tasks. We employ Qwen-2.5-Mathh In5t-Instruct and Qwen-2.5 2.5-Mathh Beich--7BInssstuee Instrrctt as draft models to observe the performance of SVFT- enhanced RI-Distill- 7B, R1 R1-Distill-88 -BB, and R1-Distill-144 14B solution-wiss speculative reasoning. In addition to accuracy and average token count, we report throughput (the time cost for completing all problems in the dataset) and AcR (the activation ratio of LRM), which indicates the proportion of problems that activate the LRM's long-Cor reasoning. As shown in Table 3] speculative reasoning significantly improves the LRM's throughput while maintaining or even enhancing reasoning accuracy. This is attributed to its remarkably low AcR. For instance, as presented in Figure 33 when using as the draft model, RI-Distill-BB only needs to conduct its own reasoning for 14.6% of problems in MATH500 and 5% in GSM8K. This implies that the draft model solves the majority of problems, while the LRM is only engaged for the few truly challenging problems requiring long-CoT reasoning, resulting in substantial efficiency gains. Speculative reasoning also boosts accuracy, particularly on GSM8K, because the LRM sometimes underperforms the short-CoT model on simple problems, and in these cases, it accepts the correct draft solution. The overall accuracy of speculative reasoning approximates the union of the draft model's and LRM's accuracies.
Unlike traditional speculative decoding, we observe that for speculative reasoning, a smaller draft model does not necessarily yield higher throughput. This is because the computational cost of short-CoT LLMs is negligible compared to the substantial inference cost of LRMs. For example, on the MATH500 dataset, -rren-2.5-Matt--BB--nes
achieves approximately 20x the throughput of R1-Dittill-7BB Thus, the primary factor affecting speedup is AcR: the fewer problems requiring LRM activation, the greater the throughput improvement. Larger draft models typically exhibit lower AcR due to their higher accuracy, thus not suffering throughput disadvantages compared to smaller draft models. However, this raises a potential issue: problem difficulty increases, the throughput benefits of speculative reasoning may diminish.
Applied to Short-CoT LLM. We also applied and
VeriThinker to Qwen- 2.5--255-MM Qwen-2.5-Instruet models to explore the effect of SVFT on short-CoT LLMs. As shown in Ta- ble|4] since short-CoTT does not suffer from over- thinking, our method does not significantly alter the average token count. However, SVFT im- proves reasoning accuracy on both MATH500 and GSMSK datasets, indicating that learning to verify helps the LLM better focus on key elements that influence reasoning correctness, thereby enhancing reasoning performance.
Table 4: Results on Short-CoT LLMs. We apply VeriThinker to three short-CoT models and evalu- ate their reasoning performance.
Method
MATH500I
GSMSK
Tokens
Acc.
Tokens ]
Acc. 1
Qwen 2.5 2.5-Math--PP BB-nnstuctt VeriThinker
700
85.0%
319
95.6%
611
87.6%
30:
96.7%
M.Mee--.--Muh--..----. VeriThinker
568
77.0%
696
589
80.2%
321
86.1%
Owen 2.5-78-
635
78.6%
91.8%
VeriThinker
80.2%
92.4%
9

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Limitations
The primary limitation of our approach that does not effectively enable CoT compression in smaller models (e.g., a 1.5B- -araametee reasoning model). This is largely due to our fine-tuning strategy: instead of optimizing directly on the original reasoning task, we fine-tune the model on CoT verification as an auxiliary task. Since smaller models have limited capacity, they are more prone to catastrophic forgetting during SVFT. As a result, they struggle to maintain high reasoning accuracy while performing effective CoT compression.
6
Social Impacts
In this paper, we propose VeriThinker, a simple yet effective method for compressing reasoning chains while preserving high accuracy. As large reasoning models become increasingly prevalent, their lengthy reasoning chains lead to dramatically higher inference costs, hindering efficient deployment and limiting practical utility. Our method addresses this critical challenge by significantly reduc- ing token usage without compromising reasoning performance, thereby enhancing the real-world applicability of reasoning models.
7 Conclusion
In this paper, we introduce VeriThinkerr, a novel approach for CoT compression. Our key innovation a new fine-tuning method called supervised verification fine-tuning. For the first time, we fine-tune the LRM on an auxiliary verification task instead of the reasoning task itself to achieve effective CoT compression. This approach eliminates the dependency on target chain data, which can be difficult and expensive to obtain. We have performed an in-depth analysis to explain the underlying principles of the proposed methods. Extensive experiments demonstrate that our method significantly shortens the reasoning chain while preserving accuracy, even on highly challenging problems. Additionally, VeriThinker can generalized to speculative decoding, achieving substantially higher throughput.
Ackonwledgement
This project is supported by the National Research Foundation, Singapore, and Cyber Security Agency of Singapore under its National Cybersecurity R&D Programme and CyberSG R&D Cyber Research Programme Office (Award: CRPO-GCI-NTU-002)
10

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In this document, we provide supplementary materials that extend beyond the scope of the main manuscript, constrained by space limitations. These additional materials include in-depth information about training details, dataset construction, and case studies.
A Training Details
We provide additional training details in this section. We employ Low-Rank Adaptation (LoRA) for efficient fine-tuning, which significantly enhances training efficiency and effectively mitigates catastrophic forgetting. as training and inference are performed on different tasks.
T8
Our LoRA configurations are presented in Table We utilized different LoRA ranks and alpha values for the three distinct models achieve the optimal balance between underfitting and catastrophic forgetting. All other training hyperparameters remain consistent across models: learning rate = 3e-5, LoRA dropout 0.05, weight decay 0.01, and batch size 64. All models were trained for epochs on our self-constructed CoT- Verificitia dataset.
Table 5: The LoRA configuration in our training process.
Models
LoRA Module
LoraLoRARank
LoRA Alpha
DeepSeck-RIe 1-isssll-----ll
QKVO QKVO QKVO
256
512
DeepSeek-R Maaeck-R----Ae (1Distill-Qwen-44h
128
128
DeepSeek-R 1-Distill-Llama--ll
128
128
B Construct the CoT-Verification Dataset
As SVFT trains the LLM to directly distinguish whether CoT solution is correct, crucial challenge lies in constructing the CoT verification dataset for SVFT.
Problem Collection. The first step involves collecting problems for our dataset. To ensure diverse range of topics and difficulty levels, we aggregate problems from four mathematical datasets known for their breadth of content and varying difficulties: PRM12K B22. GSM8K (6), LIMO (70) and Numina-Man Mathh 29) Specifically, we extract all problems from the training set of PRM12K GSM8K, and LIMO. For Nutina-Math, we only select problems whose solutions are integer-valued prthh-eord-sosllens simplifying correctness labeling. Following this procedure, we collected approximately 300K mathematical problems spanning diverse topics and difficulty levels.
CoT Solution Collection. The second step entails generating numerous CoT solu- tions for the collected problems, which will serve as targets for our verification task. To achieve efficiency and variety, we employ several small, non-reasoning language models: Qwen-2. 22on-2.55 5.0. 5B 1...-B-Inss Instruct, Q 50-5-B-IIn Instruct, and ------Math------t--
2ven-2.5-1.55 1e.1..B-Innst Instruct, Qwen 5...5---Instrcct [66]. We utilize a CoT prompting strategy to generate step-by-step solutions for the previously collected 300K problems. Notably, none of our CoT solutions are generated by reasoning models, and none include explicit relf-reflection steps. Experiments indicate that reasoning models producing long-chain solutions complicate opti- mization in SVFT, as a single response might contain multiple correct or incorrect sub-steps. This collection method offers two main advantages:
Computational efficiency: All selected models are lightweight and only generating short- CoT solutions, significantly accelerating the data generation process. For instance, using Qwen-Math-1.. 1. 5B- IB-Irrttut, we generate solutions for all 300K problems within 3 to hours using only four NVIDIA A6000 GPUs.
Solution diversity: The selected models exhibit varying reasoning capabilities, producing diverse set of correct and incorrect solutions for each problem. This diversity greatly enhances the robustness of subsequent fine-tuning.
Consequently, we obtain five different short CoT solutions per problem, yielding total of million problem-solution pairs.
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Original Long-Co'T Data
Tokens: 3100
Prompt: What the least positive integer multiple of 30 that can he written with only the digits O1 and 2? Please resson step step.
Response:
Okay, so need to find the lenst positive integer multiple of 30 that can be written using only the digits 0 and 2. Hom,, let's break this must multiple of both
down, ininFistt know that 30 equal multiplied 10, So, any multiple I'm looking for has to satisfy the divisibility niles for both 3 and 10 ....... ......Wai Wait, hold on. Les me check if there's a smaller number with five digits might smaller..... Wait. 2220 four four-digit number, so smaller any five-digit... ........ **Final Answer *aeTh least positive integer multiple of 30 that can be writenn with only the digits O and 2 is Whoxed (2220).
10, means the number
Synthetic Concise-Cov T Data
Tokens: 1084
Prompt: What the least positive integer multiple of 30 that can be written with only the digits 0 and 2? Please reason step by step.
Okay, so need to find the least positive integer muhtiple of 30 that can be writeen using only the digits 0 and 2. Hmm, let's break this down, IninFinst, know that 30 equal multiptied by 10. So, any multiple of must multiple of both
Response:
means the number I'm loaking for has to satisffy the divisibility rules for both 3 and 10 **iinal Answer**iaT'a least positive integer mulriple of 30 that can he wristen with only the digits and is lboood (2220).
Co CoT-Verification Data (Ours)
# Tokens: 421
Prompt:
de Instruction: Please carefully verify each step of the solution, tell me if every step is absolutely correct. that de Sulation: To find the least positive integer multiple of 30 that can be written with only the digits 0 and 2, we need to...... Therrffrre,,,, the least positive integer multiple 30 that can written with only the digits and (1sboodd(2200)))
Question: What the least positive integer multiple
writeen only the digits and Please resson step by step.
Respoase Yes, sure that every step is absolurely correct.
Response B: No, I thinks there might be some mistakes in the proposed solution.
Figure 4: Training data format comparison.
Correctness Labeling. In the third step, label the correctness of each generated CoT solution. Rather than evaluating each reasoning step, we simplify labeling by verifying only the final answers against known ground-truth solutions. As all collected problems have deterministic solutions, correctness labeling is straightforward: we employ the Hugging Face math_ math_verify function to automatically extract final answers from CoT solutions and compare them against ground truths. Following this procedure, each of the 1.5 million problem-solution pairs is labeled as either correct or incorrect.
Verification Data Selection. Finally, we select a subset from the 1.5 million labeled pairs for fine-tuning. Initially, we discard problems where all five CoT solutions uniformly correct or incorrect. Such problems lack informative training signals due to being either too trivial or excessively challenging, and this process also helps filter out inherently problematic data. Next, we apply straightforward deduplication strategy using Qwen-Math-i. IB-Intrtuct as a reference model. Specifically, for problems correctly solved by the reference model, retain its correct solutions along with incorrect solutions generated by the other models. Conversely, for problems incorrectly solved by the reference model, we retain its incorrect solutions and also incorrect solutions from the other models. This selection strategy ensures each problem contributes at least one correct and one incorrect CoT solution. Ultimately, this process yields fine-tuning dataset consisting of 350K instances, comprising approximately 160K correct and 190K incorrect CoT solutions. Each instance reformatted according to the structure illustrated in Figure
C Cross-Domale Generalization
Our proposed VeriThinker method demonstrates strong generalization ability. Even when there exists a domain gap between the verification data used for training and the reasoning tasks during inference, our method continues to perform effectively. To substantiate this claim, we conduct two additional experiments.
We first construct a small CoT verification dataset using only questions from PRM12K and GSM8K, and fine-tune our reasoning model on this restricted data. We then evaluate the model on the much more challenging AIME datasets. As shown in Table even with training data limited to PRM12K and GSM8K, our method significantly reduces token usage while maintaining comparable accuracy on the AIME benchmarks.
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Table 6: Fine-tuned on PRM12K and GSM8K, evaluated the more difficult AIME datasets.
Model
MATH500
AIME24
AIME25
RI-Distill-7B
94.0% (3791 tokens)
54.1% (13108 tokens)
38.7% (14321 tokens)
+ +VeriThinker
95.0% (2534 tokens)
56.4% (10302 tokens)
39.8% (11270 tokens)
RI-Distill-14B
95.2% (3529 tokens)
69.0% (11724 tokens)
49.6% (13409 tokens)
+VeriThinker
95.2% (2505 tokens)
68.7% % (8425 tokens)
49.2% (10580 tokens)
To further illustrate this generalization ability, we evaluate our model, trained exclusively on mathe- matical reasoning tasks, on the GPQA-Diamond dataset [48]. This benchmark consists of multiple- choice questions spanning diverse scientific domains (e.g., chemistry, physics, biology), and differs substantially in both format and content from our training data. As shown in Table 7 approach consistently compresses the length of CoTs while maintaining accuracy.
Table 7: Cross-domain performance on
Model
GPQA-Diamond
R1-Distill-7B
51.0% (7407 tokens)
+ VeriThinker
50.0% (4984 tokens)
R1-Distill-
60.1% (6996 tokens)
+VeriThinker
60.6 % (4309 tokens)
Overall, these results demonstrate that VeriThinker achieves robust performance even in the pres- ence of substantial domain shifts between training and testing, confirming strong cross-domain generalization capability.
D Comparison of Verification Capability
To further validate our approach, we use Qwen-2.5 2.55-..5-..BInttru to generate CoT solutions on MATH500 and evaluated the verification accuracy of several models. We compared VeriThinker- 7B with two strong open-source models 2.wee-2.5-7B-Instreee
and LLaMA-3. 1.B...---B-m- (8-sructtct) and two advanced closed-source models (OpenAI GPT-4o and GPT-4.1). As shown in Table 8 method achieves substantially higher verification accuracy than the open-source models and even surpasses the two large closed-source models from OpenAl.
Table Comparison of CoT correctness verification capability.
Model
Accuracy (%)
Precision
Recall
F1
2enn-225-7-----ee LLaMA-3.1-8P
74.8
0.714
0.934
0.810
70.0
0.668
0.948
0.783
OpenAl GPT-4o
85.0
0.889
0.843
0.866
OpenAl GPT-4.1
86.4
0.910
0.847
0.877
VeriThinker-78 (Ours)
90.4
0.972
0.857
0.911
E Case Study
We also present additional case studies on cot compression in Figure and Figure
24

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CoT Compression Case Study
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Tokens: 2330
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given by lince compatz enple
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is ((Vmatiistt) O3.2, 55% wiaNeo, moving in the socmaa
lidro [s] (6) wilty doyyrit lifra [s] (4) hereeffie the direction vector is given by the coetiicents of (55l)) which is W1 111 (6), -1.-
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# Tokens: 1267
Figure 5: Case study on COT Compression.
25

---

CoT Compression Case Study
Prompt: 25j6-315.
Okay, so need to evaluate the expression (1 2066 Ji. 1mm,, let me think about how to approuch this, remember that when dealing with complex numbers, multiplied by and then subtracting complex number by a real number is strightfooward You just distribute the real number to both the real and imaginary pasts of the complex number, So, 6 times I 6, and & times 2i 121. Therefore, (1 + 20) multiplied by should give me 6+ 1iit write that down/ning + 2)) * 6- 61 ++ 2i m6 expression this result
Original Response:
perform operations like addition, subimction, multiplication, and division, this break down stop step/alaa
seems like have complex number multopyynng
muitiply the complex number
by
1aikwinkkay, the first part 6- 121,
So,
subtmatt from 125.
WinSubtracting
from 122 the same as adling to 120. So, can write that acle/n6 12i- 31 WinNo I can combine the like terms, which are the imaginery parts, So, 12 minus 3i is.. let mo calcalate that. 12 mimus 3 so that should be 90 iinnintt all ingether, the real part is 6, and the imaginary port is 9i.
Therefore, the result 6 Whitt let make Iinnn that gives
didntt make misake. So, startigg with (1 20 6. Multiplying each temmnn'n "6 6inn 6 cornect guess
way think about factor out the 3: or somethinn. but in this case, since it's just subtracting S0 combining like temms straightforwand ninLet me also consider there was difforest interpretation of the original expression. could he intereeted as (1 + 22) multiplled (6- 30) but the original expeesiion (1 + 2116 31, which is times 21), subtrect SilninBut
subtractnng Di: 12i
indeed 91,
That
with the right the parcnthesss would be fffrren? Let caleulate that for fan wal leing distibutive property. (1)65 + (1(-31) (2106) + (21y-19 ianaalallain each
think
thorough, what
(1 21y6-
6 6/winl " (-51) -ii/win2i 6 121/iin2i (-3i) -6i2 NalaNoo combine the wemns/wanl- - 31 121 6P2 tansinipll like to mi -3 + 121 Wonno
the original exprossion was 2166 /nlniil wait, P22 equal to -I 2 is -6*(-)) which 16 minSo, 6 9 12 9imnin resulting our problem.
300, the result would
onginal expression is
which dfd
So.
interpretation was currect wineee//iTTeerefeee I think my answer is 96 minttt to recap. the steps areintal. Maltiply () 25) by 6*1 6 =6 m2immin2.
Subtract 3i from the result: 6 12i- 31- 6- WiniaY that seems correct. I don't think made mistales here intaltemativelyy if were represent this is the real and the imaginary coefficient
the form
expeession simplified ovoluate it, probably Castesian form sufficient winBot
9ilalae also consider
represent this
polar forms, but since the question just
practice let convert -% to polar
form winFirs, find the medulus: spm8622 902) - sqoi 36 81) (17) Hmm, aqrit 7) can simplified as spst B3 -)- 3Papp(13) 13) So, modulus
3x15 iiiintin,,,,, the oegument è aretangent of (915) which is arctangere (/2) So, 6 arctann That's oppronimancly 56.31 dagrees, but we laave as (in(ancam(3277))) But Chrtesian form SelaSo, after evalatinn 2066 31, the resulf 91 think that's the final answer inin Final Anower The reult evalusting V[( 2006 381) is liboree (6 9i).
arctann3 rddian ininSo, in polar
313 (posaarcttn(3322)
think the question requines this,
the
Tokens:
evaluate expeession 2066 21 Hmm. me think complex numbers, you have to distrbutcc and thas combine like tenae So, fisst I should penbably handle the mustiplication past, which is + 20) mulippiedd by and then subtract 3i from the result wal et write fhat down distrihuting the
Response: Okay, so
approach remember
dealing with
The original expression is (1+ 2066 31 I can rowrile this 6*(1 20- 3i Now, 5
submnet 121 3i, Now, I can combine the like terms which are the imaginury parts. 121 31 Si Therofore, the expression simplifies
inside the parentheses.
gives
winSo
nutting it all together, 96 Wiit,, let me make sure I did that correclly So, 6*(1 + 20) indoed + 121. Then subtracting 30 gives me 6 12 3i Yos, comniniing 12 and -3 gives So, the final result 6 Sinnis there anything the need do here? don't think It seems stnightfoowand. just multiplied the cumplex number by and subtracted St
double-check my multipiication to be sure. times 6, that's carrer. times 12), that's right. Then subtreting 34 gives
So. yes. the answer should be 6 93/alal guess that's I don't see any mistakes in my calculations. So, can confidently say that the evaluased expression 6 - Final Answar The value of the expression is (6 - 9i).
Tokens:
Figure 6: Case study on COT Compression.
26


Reviews:
[{"review_id": "VNa7JQcyzJ", "reviewer": "Reviewer_ZRxU", "summary": "In this paper, the authors propose VeriThinker to address the issue of overthinking in LLMs. The core idea of VeriThinker is to train LLMs to predict the correctness of CoTs. The authors argue that equipping LLMs with this capability enables them to avoid unnecessarily lengthy responses when the solution is correct, while still retaining the ability to revise incorrect ones. They also develop a solution-wise speculative reasoning mechanism based on this insight. Experiments on three benchmarks demonstrate that VeriThinker maintains—or even slightly improves—reasoning accuracy while reducing the number of output tokens.", "questions": "1. In line 138, the authors state that \"The prevalence of overthinking stems from insufficient accuracy in this binary classification task.\" However, there is no evidence or existing work provided to support this statement. I am very skeptical of this claim, as many reasoning models are well capable of judging the correctness of CoTs.\n\n2. In line 147, it is unclear why \"these methods synthesize a concise target chain approximating the optimal scenario where p(acc | h) ≈ 100%.\" First, I do not understand why the authors emphasize that \"current models that employ synthetic target chains for CoT implicitly aim to maximize p(acc | h).\" Don’t other models also aim to maximize accuracy? Second, there is no justification for why a concise target chain leads to the optimal scenario.\n\n3. In Section 3.3, the authors find that, apart from Dataset (5), all other datasets result in maintained or slightly improved accuracy. However, this result is strange because, in Dataset (2), the labels for solution correctness are completely reversed, i.e., correct solutions are labeled as \"wrong\". This phenomenon suggests that the model’s ability to predict correctness does not matter at all, which contradicts the main hypothesis of the paper.\n\n4. The authors need to conduct an ablation study on the training data, as the current experimental setup raises concerns about whether the accuracy improvement comes from the model having seen the correct answers during training (even if not trained on them directly). For example, the Numina-Math dataset includes AIME data. It is also important to test whether the model can classify the correctness of solutions to problems it has never encountered before (e.g., more difficult problems), which is crucial for evaluating the generalization ability of the proposed method.\n\n5. In section 4.2 \"CoT Correctness Verification Results\", the authors need to add more baselines to compare how well a basic LLM performs on the correctness verification task.", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The paper is clearly written and easy to understand.\n2. The proposed method shows potential in balancing reasoning accuracy with computational cost.\n\nHowever, several important issues remain:\n1. Many key claims lack sufficient evidence or support, which weakens the overall motivation and persuasiveness of the paper (please refer to Q1 and Q2 below).\n2. Many experimental results are questionable and require further clarification or validation (please refer to Q3-Q5 below).\n3. The experiments do not include comparisons with recent RL-based methods, which limits the completeness of the evaluation.\n4. There are a number of typos. For example:\n– Line 61: \"represent\" should be \"represents\".\n5. The paper is overly verbose in several sections, leading to redundancy and reduced clarity. For instance, in Section 4.2 \"CoT Compression Results\", the conclusions in two consecutive paragraphs are essentially identical, which gives the impression of filler content.", "was_revised": true, "final_justification": "As the authors provide sufficient experiments in the rebuttal phase, which address my concerns (especially the concern about self-verification), I think this paper poses great value to the community. Therefore, I have increased the score to Borderline accept.", "rebuttal": "Thanks for the insightful and valuable feedback. We have provided detailed responses below and hope they address your concerns. If you have any further questions or require additional clarification, we would be glad to continue the discussion. We really appreciate your time and consideration.\n\n> **Q1: The statement of \"The prevalence of overthinking stems from insufficient accuracy in this binary classification task.\" is not supported. I am very skeptical of this claim, as many reasoning models are well capable of judging the correctness of CoTs.**\n\n**A:** Thanks for the insightful comments. Prior work [1,2,3] has also found that reasoning models often struggle to judge the correctness of their own CoT outputs, frequently triggering unnecessary self-reflection even when previous steps are correct. We further investigated this issue by analyzing R1-Distill-7B’s behavior. Specifically, we measured the probability of generating a \"reflection\" token (such as \"Wait\") after correct and incorrect reasoning steps on the MATH500 dataset.\n\nAs shown in Table 1, even after fully correct steps, large reasoning models initiate self-reflection more than 11% of the time. For incorrect steps, this probability jumps to 36.8%. After fine-tuning with our method, the reflection rate on correct steps drops by nearly threefold, while the rate for incorrect steps increases slightly. These results highlight the core problem and demonstrate how our approach effectively reduces unnecessary self-reflections without sacrificing reasoning accuracy.\n#### *Table 1 Reflection probability when facing correct and incorrect steps*\n| Model| Correct Steps | Incorrect Steps |\n|--|--|--|\n| R1-Distill-7B | 11.1%| 36.6%  |\n| +VeriThinker  | 4.1% | 37.6%  |\n\n\n\n> **Q2: It is unclear why \"these methods synthesize a concise target chain approximating the optimal scenario where p(acc | h) ≈ 100%.\"** \n\n**A:** Thanks for the comments. We apologize for the confusion and would like to clarify this point.\n\nIn our paper, $p(\\text{acc}|h)$ does not refer to the probability that the generated CoT is correct. Instead, it represents the probability that the model correctly identifies whether reflection is necessary at each reasoning step. Ideally, models should avoid reflecting on correct steps while always reflecting when encountering incorrect ones, corresponding to $ p(\\text{acc}|h) = 100\\%$.\n\nPrevious CoT compression methods indirectly improved reflection accuracy by training models to imitate concise chains, which contain minimal, necessary reflections. In contrast, our method directly fine-tunes the model to explicitly distinguish correct from incorrect reasoning steps. This direct training significantly enhances the model’s judgment of when to reflect, as clearly supported by our experimental results in Table 1.\n\n\n> **Q3: In Section 3.3, the authors find that, apart from Dataset (5), all other datasets result in maintained or slightly improved accuracy. This result is strange.**\n\n**A:** Thanks for the comments. We appreciate the chance to clarify this further.\n\nIn our SVFT method, the model is trained to discriminate between correct and incorrect CoT solutions. Importantly, the model does not know which group represents true correctness; it essentially learns to separate the two categories based on their features. The labels during training serve only as group identifiers and their inherent meaning does not matter. This is why, in Dataset (2), even if the labels are reversed, our method still works. In fact, as shown in paper section 3.3, our method performs just as well if we label the groups as \"north\" and \"south\" instead.\n\nAfter fine-tuning, the model's parameters are adjusted to become more sensitive to tokens that differentiate correct and incorrect CoTs. As a result, when deciding whether to self-reflect during reasoning, the finetuned model can more accurately identify when reflection is truly needed. Consequently, the model can avoid unnecessary self-reflections while keeping the essential ones. Our experimental results in Table 1 also confirm this point.\n\n\n\n> **Q4: The authors need to conduct an ablation study on the training data, as the current experimental setup raises concerns about whether the accuracy improvement comes from the model having seen the correct answers during training (even if not trained on them directly).** \n\n**A:** Thanks for the valuable comments. We conducted two additional experiments to clarify this issue.\n\nFirst, we constructed a small CoT verification dataset using only questions from PRM12K and GSM8K, and fine-tuned our reasoning model on this restricted data. We then evaluated the fine-tuned model on the more challenging AIME datasets. As shown in Table 2, even with training data limited to PRM12K and GSM8K, our method significantly reduced token usage and maintained accuracy on the AIME benchmarks.\n#### *Table 2 Finetuned on PRM12K and GSM8K, evaluated on the much more difficult AIME Datasets*\n| Model| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B | 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| **+VeriThinker**  | **95.0% (2534 tokens)**| **56.4% (10302 tokens)** | **39.8% (11270 tokens)**|\n| R1-Distill-14B| 95.2% (3529 tokens)| 69.0% (11724 tokens) | 49.6% (13409 tokens)|\n| **+VeriThinker**| **95.2% (2505 tokens)**| **68.7% (8425 tokens)** | **49.2% (10580 tokens)**|\n\nSecondly, to further illustrate this point, we evaluated our model (trained exclusively on mathematical problems) on the GPQA Diamond dataset. GPQA Diamond is a multiple-choice benchmark covering diverse disciplines (chemistry,physics, biology......) and significantly differs in both format and domain from our training data. As shown in Table 3, our method still significantly compressed the length of CoTs while maintaining accuracy.\n#### *Table 3 Cross-Domain Performance on GPQA-Diamond*\n| Model| GPQA-Diamond |\n|--|--|\n| R1-Distill-7B | 51.01% (7407 tokens)| \n| **+VeriThinker**  | **50.00% (4984 tokens)**|\n| R1-Distill-14B | 60.1% (6996 tokens)| \n| **+VeriThinker**  | **60.6%  (4309 tokens)**|\n\nThe above results demonstrate that our method still achieves strong performance even when there is a domain gap between the training and test sets.\n\n> **Q5: the authors need to add more baselines to compare how well a basic LLM performs on the correctness verification task.**\n\n**A:** Thanks for the comments. To further validate our approach, we used Qwen-2.5-1.5B-Instruct to generate CoT solutions on MATH500 and evaluated the verification accuracy of several models.\n\nWe compared our VeriThinker-7B with two strong open-source models (Qwen-2.5-7B-Instruct and Llama-3.1-8B-Instruct) and two advanced closed-source models (OpenAI GPT-4o and GPT-4.1). As shown in Table 4, our method achieves substantially higher verification accuracy than the open-source models, and even outperforms the two large closed-source models from OpenAI.\n#### *Table 4 Comparison of CoT correctness verification capability*\n|Model|accuracy|pre|rec|F1|\n|-|-|-|-|-|\n| Qwen-2.5-7B-Instruct  | 74.8%| 0.714| 0.934| 0.810|\n| Llama-3.1-8B-Instruct | 70.0%| 0.668| 0.948 | 0.783|\n| OpenAI-GPT-4o  | 85.0% | 0.889| 0.843| 0.866|\n| OpenAI-GPT-4.1 | 86.4% | 0.910| 0.847 | 0.877|\n| **VeriThinker-7B (Ours)**| **90.4%**| **0.972**| **0.857**| **0.911**|\n\n> **Q6: The experiments do not include comparisons with recent RL-based methods**\n\n**A:** Thanks for the valuable comments. As shown in Table 5, we compare VeriThinker with two recent RL-based methods (AdaptThink [4] and LC-R1 [5]), both of which use improved GRPO algorithms for CoT compression. VeriThinker outperforms AdaptThink in both token reduction and accuracy. While LC-R1 achieves a higher compression rate, VeriThinker delivers much better accuracy.\n\nImportantly, RL-based methods require much higher computational resources due to the use of rollout strategies and full-model finetuning. For example, AdaptThink needs 32 H100 GPUs (80GB) for 28 hours of training, while VeriThinker achieves strong results with only 8 A5000 GPUs (24GB) and 14 hours of training.\n#### *Table 5 Comparison to recent RL-based methods*\n| Model| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B | 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| +LC-R1 [5] | 89.6% (1425 tokens)| 47.5% (6495 tokens) | 35.4% (7523 tokens)|\n| +AdaptThink [4] | 91.6% (2080 tokens)| 53.3% (9998 tokens) | 38.75% (11330 tokens)|\n| **+VeriThinker (ours)** |**94.8% (2125 tokens)**| **56.5% (9381 tokens)** | **40.8% (10287 tokens)**|\n\n> **Q7: Typos and redundancy in paper:**\n\n**A:** Thanks for the thorough and thoughtful review. We are committed to addressing all of these issues comprehensively in the next version. We truly appreciate your valuable suggestions, which will certainly help us improve the quality of our paper. \n\n### Reference\n[1] Can Large Language Models Detect Errors in Long Chain-of-Thought Reasoning?. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 18468–18489\n\n[2]\"No free labels: Limitations of llm-as-a-judge without human grounding.\" arXiv preprint arXiv:2503.05061 (2025).\n\n[3] \"Do not think that much for 2+ 3=? on the overthinking of o1-like llms.\" arXiv preprint arXiv:2412.21187 (2024).\n\n[4] \"Adaptthink: Reasoning models can learn when to think.\" arXiv preprint arXiv:2505.13417 (2025).\n\n[5] \"Optimizing Length Compression in Large Reasoning Models.\" arXiv preprint arXiv:2506.14755 (2025)."}, {"review_id": "mGE7MPE5d7", "reviewer": "Reviewer_FWSD", "summary": "The paper proposes a novel approach to enable concise reasoning, called VeriThinker. Instead of directly training on short CoTs, it trains the model to verify solutions effectively, which results in fewer solution changes and improved accuracy.", "questions": "Please refer to the weaknesses for details. Here are some key points:\n\n- Any ablation on the number of verifier datasets?\n- Any training details for the baselines?\n- Any comparisons that match accuracy and compare compression rates instead?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\n- The motivation is strong, although somewhat obvious, and the focus on verification is quite interesting.\n- Sections 3.2 and 3.3 offer insightful analyses that justify the method well.\n- The paper is easy to read, and I personally appreciated the narrative of how the authors arrived at their method.\n\n**Weaknesses:**\n\nThe primary weakness, in my opinion, lies in the experimental setup, which lacks sufficient detail and raises concerns about reliability.\n\n- **Data Construction for Training with Verifier Objectives:**\n    - This is a crucial aspect, yet the main paper omits important details. Even in the appendix, the rationale for using five models and the number of generations is not clearly justified. I would also like to see how the size of the verification dataset affects performance.\n    - While the authors note that synthetic data generation is costly, constructing a large verification dataset is also non-trivial. Although each CoT is short, unlike longer reflective reasoning, it’s still a significant effort as you generated a lot of data pairs.\n    - Moreover, there’s no guarantee that each CoT step is correct, even if the final answer is.\n- **Lack of Baseline Training Details:**\n    - For baselines such as SFT, what data was used? Am I missing something? If different datasets were used for SFT and other baselines, can we consider the comparison fair? VeriThinker uses quite a variety of datasets, and such differences matter, especially considering prior work that maintains accuracy while significantly improving compression rates [1].\n    - What does “comparable CoT compression for baselines” mean? Is there any way to control the level of compression in baselines? If so, corresponding graphs or analyses should be included.\n- **Statistical Significance:**\n    - Statistical significance is not reported, which is especially important for datasets like AIME 2024 and 2025.\n\n**References**\n\n[1] Munkhbat et al. *Self-Training Elicits Concise Reasoning in Large Language Models*", "was_revised": true, "final_justification": "As outlined in the review, the idea itself seems interesting. However, the evaluation setting is not clear. The authors provided a detailed response, but it did not fully justify their design choices. Therefore, I believe borderline acceptance is the right score.", "rebuttal": "Thanks for the thoughtful and valuable feedback. Please find our responses below, we hope they adequately address your concerns. If you have any further questions or need additional clarification, we’d be happy to discuss them with you. Thanks again for your time and efforts.\n\n> **Q1: the rationale for using five models and the number of generations is not clearly justified. I would also like to see how the size of the verification dataset affects performance.**\n\n**A:** Thanks for the insightful comments. We would like to clarify this issue.\n\nIn our data construction procedure, we first generated CoT solutions for each problem using five different short-CoT models with greedy decoding (one solution per model per problem). Using multiple models of varying reasoning abilities allowed us to produce diverse reasoning paths for the same question, also ensuring almost every problem had both correct and incorrect solutions. Such diverse and contrastive data help the model robustly distinguish between correct and incorrect CoTs, thus benefiting efficient reasoning.\n\nTo validate this, we conducted two additional experiments:\n* We trained the R1-Distill-7B model on a raw dataset (290k samples) generated using only one short-CoT model (Qwen-math-1.5b-instruct), instead of five.\n* We also trained the same model on a smaller dataset (32k samples) constructed solely from PRM12K and GSM8K using our original pipeline.\n\nAs shown in Table 1:\n* The model trained on the single-model raw dataset performed worse in both token reduction and accuracy retention compared to our carefully constructed five-model dataset (340k samples), confirming the effectiveness of our approach.\n* The model trained on the smaller dataset achieved good accuracy but lower token reduction, highlighting the impact of dataset size on our method's performance.\n\n#### *Table 1 Performance comparison using different training data*\n| Method| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B | 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| +VeriThinker w/ raw dataset (290k) | 94.8% (2349 tokens)| 52.7% (12023 tokens) | 36.7% (13286 tokens)|\n| +VeriThinker w/ small dataset (32k) | 95.0% (2534 tokens)| 56.4% (10402 tokens) | 39.8% (11270 tokens)|\n| +VeriThinker w/ our dataset (340k) | 94.8% (2125 tokens)| 56.5% (9381 tokens) | 40.8% (10287 tokens)|\n\n\n> **Q2: the cost of short-cot data pairs generation.**\n\n**A:** Thanks for the valuable comments. Generating large-scale datasets typically relies on inference engines like vLLM [3], which support batch inference. However, inference speed in batch scenarios heavily depends on the longest sequence within each batch. For instance, the Qwen-Math-7B-instruct model produces CoT solutions for the PRM12K dataset with a maximum token length of only 1K tokens, making it 20x faster than the R1-Distill-7B model, which has a maximum token length of 16K tokens. Additionally, short-CoT sequences consume significantly less memory, enabling much larger batch sizes and further accelerating data generation. \n\nTo illustrate, using vLLM, our entire CoT verification dataset (initially 1.45M samples, 340K after filtering) was generated in just 48 hours on eight A5000 GPUs. These results clearly demonstrate the convenience and efficiency of our short-CoT data collection process.\n\n\n> **Q3: there’s no guarantee that each CoT step is correct, even if the final answer is.**\n\n**A:** Thanks for the insightful comments. All our generated solutions are short-CoT, meaning only have one single reasoning path without any self-reflection or branching. As a result, if a mistake occurs at any step, the model cannot recover and will almost always produce an incorrect final answer.\n\nTo demonstrate this, we conducted an additional experiment: We randomly selected 50 correct short-CoT solutions from Qwen-Math-7B-instruct on PRM12K and introduced a calculation error at a random step in each chain. After using the Qwen-Math-7B-instruct model to continue reasoning from that step, every final answer was incorrect. This result clearly supports our point.\n\n\n> **Q4: For baselines such as SFT, what data was used?**\n\n**A:** Thanks for the valuable comments. For the SFT baseline, we followed the CoT-Valve [1] to synthesize concise CoT chains: we merged the base and reasoning models at a 0.2:0.8 ratio, then sampled concise CoT responses on the PRM12K and GSM8K datasets. We selected the correct CoT responses as SFT data. These concise CoTs are about 60% the length of the original chains. Both SFT and our VeriThinker method are finetuned using LoRA with same configuration.\n\nTo ensure a fair comparison, we also constructed a small verification dataset using only PRM12K and GSM8K, and trained our SVFT method on this data. As shown in Table 2, our method consistently outperforms the SFT baseline, especially on the more challenging AIME datasets, where SFT methods always suffer from a significant drop in accuracy.\n\nImportantly, generating concise CoT data for SFT is much more expensive than collecting verification data for our method\n#### *Table 2 Performance comparison with SFT on the same training dataset.*\n| Method| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B| 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| +SFT (PRM12K+GSM8K)| 91.2% (2064 tokens)| 49.1% (8843 tokens) | 32.1% (9686 tokens)|\n| **+VeriThinker(PRM12K+GSM8K)**| **95.0% (2534 tokens)**| **56.4% (10402 tokens)** | **39.8% (11270 tokens)**|\n| R1-Distill-14B| 95.2% (3529 tokens)| 69.0% (11724 tokens) | 49.6% (13409 tokens)|\n| +SFT (PRM12K+GSM8K) | 92.8% (2226 tokens)| 58.3% (9021 tokens) | 43.3% (10644 tokens)|\n| **+VeriThinker(PRM12K+GSM8K)**| **95.2% (2505 tokens)**| **68.7% (8425 tokens)** | **49.2% (10580 tokens)**|\n\n\n> **Q5: What does “comparable CoT compression for baselines” mean? Is there any way to control the level of compression in baselines?**\n\n**A:** Thanks for the comments. The compression rate of our VeriThinker cannot be controlled. However, the compression rate of the baseline SFT-based method can be controlled. For SFT, we control the compression rate by adjusting the length of the synthetic concise chains used as training data. The synthetic concise chains we used for SFT are approximately 60% of the original length, which closely matches our VeriThinker's compression rate. This allows us to compare both methods at comparable compression levels, ensuring a fair and meaningful accuracy evaluation.\n\n> **Q6: Statistical significance is not reported, which is especially important for datasets like AIME 2024 and 2025.**\n\n**A:** Thanks for the valuable suggestions. For the AIME dataset, the accuracy we report is calculated by running inference on each question 16 times and then taking the average. In Table 3 below, we present both the mean accuracy and the standard deviation to demonstrate the statistical significance of our results.\n#### *Table 3 Statistical significance on AIME datasets*\n|Method|AIME24|AIME25|\n|-|-|-|\n| R1-Distill-7B |  54.1%+-6.2% (13108 tokens) | 38.7%+-3.3% (14321 tokens)|\n| +VeriThinker  |  56.5%+-7.0% (9381 tokens) | 40.8%+-5.9% (9686 tokens)|\n| R1-Distill-8B |  44.6%+-5.2% (14005 tokens) | 30.1%+-4.6% (14420 tokens)|\n| +VeriThinker  |  46.9%+-5.7% (11285 tokens) | 29.7%+-6.3% (10557 tokens)|\n| R1-Distill-14B |  69.0%+-6.8% (11724 tokens) | 49.6%+-5.2% (13409 tokens)|\n| +VeriThinker  |  73.0%+-6.0% (7423 tokens) | 54.8%+-5.5% (9304 tokens)|\n\n\n> **Q7: Any comparisons that match accuracy and compare compression rates instead?**\n\n**A:** Thanks for the comments. Since SFT-based CoT compression methods inevitably cause a significant drop in accuracy on challenging tasks (AIME) and our method can maintain the accuracy, we conduct an additional comparison with the advanced RL-based method AdaptThink[2] to better match accuracy and compare compression rates. As shown in Table 4, when both methods maintain high accuracy on AIME, our approach achieves lower token usage compared to AdaptThink.\n\n#### *Table 4 Comparing compression rates under similar accuracy*\n| Model| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B | 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| +AdaptThink [2] | 91.6% (2080 tokens)| 53.3% (9998 tokens) | 38.75% (11330 tokens)|\n| **+VeriThinker (ours)** | **94.8% (2125 tokens)**| **56.5% (9381 tokens)** | **40.8% (10287 tokens)**|\n\n### Reference\n[1] CoT-Valve: Length-Compressible Chain-of-Thought Tuning. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics.\n\n[2] \"Adaptthink: Reasoning models can learn when to think.\" arXiv preprint arXiv:2505.13417 (2025).\n\n[3] \"Efficient memory management for large language model serving with pagedattention.\" Proceedings of the 29th symposium on operating systems principles. 2023."}, {"review_id": "Ymu9N5zzN9", "reviewer": "Reviewer_c9kd", "summary": "This paper considers the problem of overthinking by the reasoning LLMs. It proposes a method for compressing the chain of thoughts in reasoning LLMs. The idea is to “fine-tune the model solely through an auxiliary verification task” instead of the previous approaches where models are fine-tuned on the original reasoning task using synthetic concise CoT data. When the model is trained to verify the correctness of CoT solutions, it becomes more diligent about its own chain of thoughts, and ultimately becomes less prone to overthinking. The paper experiments on several reasoning tasks reporting that the proposed method reduces the computational cost and increases the accuracy. Three models are considered: DeepSeek-R1-Distill-Qwen-7B, 57 DeepSeek-R1-Distill-Qwen-14B, and DeepSeek-R1-Distill-Llama-8B.", "questions": "Please see weaknesses. I'd be happy to adjust my score after reading sufficient information about the dataset used for fine-tuning.", "limitations": "The checklist indicates that limitations are discussed in the appendix, but I couldn't locate the appendix. Even in the supplementary materials, I did not see a pdf file.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\nThe method itself is intuitive and well implemented. It can be useful for the community as it both reduces the computational cost and increases the accuracy. Table 1 is impressive.\n\nPaper is well written. Motivation is clear and interesting. \n\nPosing the problem of overthinking as a binary classification task and formulating it as such is a sound and interesting approach in my view.\n\n&nbsp;&nbsp;\n\n\n### Weaknesses:\n\nThe models used in the experiments are very similar. All of them are DeepDeek-R1-Distill models. And their size slightly varies. To convince a reader about the advantage of the proposed method, one would need to see experiments on other LLMs.\n\n-------\n\nVery little is explained about the self-constructed dataset used for training the model. Page one mentions that dataset is explained in the Appendix, but I can only see the checklist and no appendix at the end of the paper.\n\nAre authors planning to release their fine-tuning dataset?\n\n-------\n\nSensitivity to the verification task is not investigated. It is not clear if the dataset was a different dataset with a different verification task, the results would have been similar. Is there any overlap between the datasets used for testing and the fine-tuning dataset? How did the authors create their dataset? Without adequate information, it will be difficult to evaluate the usefulness of the method.\n\n-------\n\nIn my view, the paper has considerable redundancy and repetitions. Starting from page 3, I felt that problem is already explained and I’m reading text that is mostly repetitive. At some points throughout the paper, the text asks questions from the reader. If you just isolate those questions, the repetitions become more clear.", "was_revised": true, "final_justification": "Authors addressed all my questions and concerns in the rebuttal.\n\nOriginally when I downloaded their supplementary material, the pdf file would not open, perhaps because the download on my end was corrupted. In the rebuttal, authors suggested I download the file again. This time I was able to see the supplementary materials and detailed information about the dataset used for fine-tuning. I am impressed to hear that authors have made sure there is no overlap between the training and test sets.\n\nOverall, the method proposed in the paper is novel and useful, both for research and practice. The idea behind data generation is smart and fast for practical purposes. The empirical results reported by the paper is also impressive.\n\nI suggested to authors to experiment with more LLMs. They promised to include results on Qwen3-30B-A3B-Thinking model. If such result is positive, I would give a score of 5.5 or 6 to the paper. Since that result is still unknown, for now, I give a score of 5.", "rebuttal": "Thanks for the insightful and valuable feedback. We have provided detailed responses below and hope they address your concerns. If you have any further questions or require additional clarification, we would be glad to continue the discussion. We really appreciate your time and consideration.\n\n> **Q1: The models used in the experiments are very similar. All of them are DeepDeek-R1-Distill models.**\n\n**A:** Thanks for the valuable suggestions. To better demonstrate the effectiveness of our method on different LLMs, we also applied our proposed VeriThinker approach to Phi-4-mini-reasoning-3.8B [1] (produced by Microsoft), which has a different architecture and parameter size. As shown in Table 1, our method significantly reduces the token usage of Phi-4-mini-reasoning-3.8B while maintaining its original reasoning accuracy. \n#### *Table 1 Performance comparison on other LLM.*\n| Method| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| Phi-4-mini-reasoning-3.8B [1]| 92.8% (3554 tokens)| 46.3% (13108 tokens) | 34.6% (14261 tokens)|\n| **+VeriThinker (ours)** | **93.0% (2495 tokens)**| **45.9% (9204 tokens)** | **36.7% (9991 tokens)**|\n\n\n> **Q2: Very little is explained about the self-constructed dataset used for training the model.**\n\n**A:** Thanks for the thoughtful comments. We would like to clarify that all details of our dataset construction process are provided in **Section B of appendix.pdf** in the **supplementary.zip** submitted with our paper. We have confirmed that appendix.pdf is included in the supplementary.zip as downloaded from OpenReview. If you are unable to access it, this may be due to a technical issue on the platform, and we kindly suggest downloading the file again.\n\nOur data construction pipeline includes 4 steps: \n- **Step 1: Problem Collection.** We gather problems from the training sets of four mathematical datasets (PRM12K, GSM8K, LIMO, and Numina-Math) to ensure diversity in topics and difficulty. Specifically, we extract all problems from the training set of PRM12K, GSM8K, and LIMO. For Numina-Math, we only select problems whose solutions are integer-valued math-word-problems, simplifying correctness labeling.\n- **Step 2: CoT Solution Collection.** We generate multiple short-CoT solutions for each problem using five small language models (*Qwen-2.5-0.5B/1.5B/7B-Instruct*, *Qwen-Math-1.5B/7B-Instruct*). These solutions are step-by-step and do not include any self-reflection.\n- **Step 3: Correctness Labeling.** We label each solution as correct or incorrect by comparing its final answer to the ground truth, using the Hugging Face *math\\_verify* tool for automated labeling.\n- **Step 4: Verification Data Filtering and Selection.** Initially, we discard problems where all five CoT solutions are uniformly correct or incorrect. Such problems lack informative training signals due to being either too trivial or excessively challenging, and this process also helps filter out inherently problematic data. Next, we apply a deduplication strategy using *Qwen-Math-1.5B-Instruct* as a reference model. Specifically, for problems correctly solved by the reference model, we retain its correct solutions along with incorrect solutions generated by the other models. Conversely, for problems incorrectly solved by the reference model, we retain its incorrect solutions and also incorrect solutions from the other models. This selection strategy ensures each problem contributes at least one correct and one incorrect CoT solution. This deduplication and selection process results in a fine-tuning dataset of 340K instances (150K correct and 190K incorrect solutions), formatted as shown in Appendix Figure 1\n\nThis pipeline is highly efficient, the full dataset can be generated in 48 hours using just eight A5000 GPUs.\n\nWe hope this clarifies our data construction process. Please refer to the appendix.pdf for full details.\n\n\n> **Q3: It is not clear if the dataset was a different dataset with a different verification task, the results would have been similar. Is there any overlap between the datasets used for testing and the fine-tuning dataset?**\n\n**A:** Thanks for the thoughtful comments. We confirm that our training and test sets are completely separated, with no risk of data leakage. To further demonstrate the robustness of VeriThinker, we conducted two additional experiments. \n\nFirst, we built a small CoT verification dataset using only PRM12K and GSM8K problems for training, and then evaluated the fine-tuned model on the much harder AIME24 and AIME25 datasets. As shown in Table 2, even with training data limited to PRM12K and GSM8K, our method effectively reduced token usage while maintaining or even improving accuracy on these more challenging benchmarks.\n#### *Table 2 Finetuned on PRM12K and GSM8K, evaluated on the much more difficult AIME Datasets*\n| Model| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B | 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| **+VeriThinker**  | **95.0% (2534 tokens)**|**56.4% (10302 tokens)** | **39.8% (11270 tokens)**|\n| R1-Distill-14B| 95.2% (3529 tokens)| 69.0% (11724 tokens) | 49.6% (13409 tokens)|\n| **+VeriThinker**| **95.2% (2505 tokens)**| **68.7% (8425 tokens)** | **49.2% (10580 tokens)**|\n\nSecondly, to further illustrate this point, we evaluated our model (finetuned exclusively on mathematical problems) on the GPQA Diamond dataset. GPQA Diamond is a multiple-choice benchmark covering diverse disciplines (chemistry,physics, biology......) and significantly differs in both format and domain from our training data.  As shown in Table 3, our method achieved substantial CoT compression while maintaining accuracy on this challenging benchmark.\n#### *Table 3 Cross-Domain Performance on GPQA-Diamond*\n| Model| GPQA-Diamond |\n|--|--|\n| R1-distill-7B | 51.01% (7407 tokens)| \n| **+VeriThinker**  | **50.00% (4984 tokens)**|\n| R1-distill-14B | 60.1% (6996 tokens)| \n| **+VeriThinker**  | **60.6%  (4309 tokens)**|\n\nThe above results demonstrate that our method still achieves strong performance even when there is a domain gap between the training and test sets. This cross-domain generalization is also a key strength of our approach.\n\n> **Q4: redundancy in paper:**\n\n**A:** Thanks for the valuable and insightful comments. We truly appreciate your feedback and will make sure to address this issue thoroughly in the next version of our paper. Your comments are very helpful in improving the quality of our work.\n\n### Reference\n[1] \"Phi-4-mini-reasoning: Exploring the limits of small reasoning language models in math.\" arXiv preprint arXiv:2504.21233 (2025)."}, {"review_id": "w1hpMbHeDE", "reviewer": "Reviewer_gTAt", "summary": "This paper introduces VeriThinker, a method designed to mitigate the \"overthinking\" issue in Large Reasoning Models (LRMs) which leads to excessively long reasoning chains and high inference costs. The core idea is Supervised Verification Finetuning (SVFT), where an LRM is finetuned on an auxiliary task of verifying the correctness of Chain-of-Thought (CoT) solutions. The authors posit that by learning to accurately assess CoT solution correctness, the LRM becomes more adept at deciding when self-reflection is truly necessary, thereby compressing the reasoning chain while aiming to maintain or even improve accuracy. The paper presents experimental results on several mathematical reasoning benchmarks to support VeriThinker's efficacy in reducing token count and its potential in applications like solution-wise speculative reasoning (SSR) and for enhancing short CoT LLMs.", "questions": "See above", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**strengths**\n- Intuitively, I think the proposed VeriThinker method, which uses an auxiliary verification task to help models discern when to stop or continue thinking, makes sense. The idea of training a model to verify solutions to indirectly improve its reasoning efficiency is quite an original approach to the \"overthinking\" problem in LRMs. The experimental results presented, such as significant token reduction on benchmarks like MATH500 and AIME while maintaining or even slightly improving accuracy, also look promising and suggest the method has practical value.\n\n**weaknesess/questions**\n- The paper mentions that the SFT baseline uses \"synthesized concise CoT chains as targets\", but I feel there's insufficient detail on how these concise CoTs were generated. If the quality of these synthetic CoTs for the SFT baseline was not particularly high, it might make VeriThinker's relative performance appear more favorable than it would be against a stronger, well-optimized SFT baseline. More transparency and better quality on the SFT target data generation and its finetuning setup would be beneficial for a more complete assessment of fairness.", "was_revised": true, "final_justification": "I had no major concerns about the core intuition or overall motivation of the paper. However, my primary issue was with the choice of baseline and the lack of clarity around the dataset construction, which I believe weaken the empirical evaluation. Reading other reviewers' comments further reinforced these concerns.\n\nI did not raise expectations around model scale or training cost, considering the resource constraints common in the current research landscape. Given this, I believe my current borderline accept rating is already a fairly generous evaluation.", "rebuttal": "Thanks for the thoughtful and valuable feedback. Please find our responses below, we hope they adequately address your concerns. If you have any further questions or need additional clarification, we’d be happy to discuss them with you. Thanks again for your time and efforts.\n\n> **Q1: The paper mentions that the SFT baseline uses \"synthesized concise CoT chains as targets\", but I feel there's insufficient detail on how these concise CoTs were generated.** \n\n**A:** Thanks for the insightful comments. We would like to clarify this point.\n\nTo synthesize concise reasoning chains for the SFT baseline, we follow CoT-Valve [1] by merging the base and reasoning models at a 0.2:0.8 ratio to generate concise reasoning chains on PRM12K and GSM8K. Only correct CoT solutions are retained, and the average length of these concise chains is about 60% of the original. Both SFT and our VeriThinker method are finetuned using LoRA with same configuration.\n\nTo ensure a fair comparison, we also created a small verification dataset using only PRM12K and GSM8K problems and trained our SVFT method with this restricted data. As shown in Tables 1 and 2, our approach still outperforms SFT, especially on the more difficult AIME benchmark.\n\nIt’s also important to highlight that generating data for SFT is much more expensive than for our method. SFT relies on a merged long-CoT model to produce training data. In contrast, our method only needs a short-CoT model to generate solutions for verification, making the process much more efficient. For example, using the vLLM framework on the same 4 × A5000 GPUs, a 7B short-CoT model achieves 10× higher throughput than the merged long-CoT model used for SFT.\n\n#### *Table 1 Performance comparison with SFT on the same training dataset (R1-Distill-7B).*\n| Method| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-7B | 94.0% (3791 tokens)| 54.1% (13108 tokens) | 38.7% (14321 tokens)|\n| +SFT (PRM12K+GSM8K) | 91.2% (2064 tokens)| 49.1% (8843 tokens) | 32.1% (9686 tokens)|\n| +VeriThinker(PRM12K+GSM8K)| 95.0% (2534 tokens)| 56.4% (10402 tokens) | 39.8% (11270 tokens)|\n| +VeriThinker (Complete Verification Data) | 94.8% (2125 tokens)| 56.5% (9381 tokens) | 40.8% (10287 tokens)|\n\n#### *Table 2 Performance comparison with SFT on the same training dataset (R1-Distill-14B).*\n| Method| MATH500 | AIME24 |AIME25 |\n|--|--|--|--|\n| R1-Distill-14B | 95.2% (3529 tokens)| 69.0% (11724 tokens) | 49.6% (13409 tokens)|\n| +SFT (PRM12K+GSM8K) | 92.8% (2226 tokens)| 58.3% (9021 tokens) | 43.3% (10644 tokens)|\n| +VeriThinker (PRM12K+GSM8K)| 95.2% (2505 tokens)| 68.7% (8425 tokens) | 49.2% (10580 tokens)|\n| +VeriThinker (Complete Verification Data) | 95.0% (2255 tokens)| 73.0% (7423 tokens) | 54.8% (9304 tokens)|\n\n### Reference\n[1] CoT-Valve: Length-Compressible Chain-of-Thought Tuning. In Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics."}]

Author rebuttal:

Meta-review: Reviewers agree the paper is clearly written, the method is intuitive and potentially useful, and results show reduced computation with maintained or slightly improved accuracy. The main concerns are about experimental completeness, dataset construction details, and limited model diversity. The rebuttal clarified several of these points, alleviating major doubts. Overall, I consider the paper technically solid and recommend acceptance.
Decision: Accept (poster)