Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning
Authors: Wenkai Yang
Shuming Ma
Yankai Lin
Furu Wei
Venue: NeurIPS 2025 poster ()
Keywords: test-time scaling
LLM reasoning
Primary area: deep_learning
TL;DR: We find that excessively scaling Chain of Thought (CoT) length can impair the model's reasoning performance in certain domains, and we propose a Thinking-Optimal Scaling strategy to achieve more effective and efficient test-time scaling.

Abstract: Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with the teacher model QwQ-32B-Preview that produces the seed data.

Towards Thinking-Optimal Scaling of Compute for LLM Reasoning
Wenkai Yang' Shuming Ma', Yankai Lin Furu Wei?
Gaoling School of Artificial Intelligence, Renmin University of China
"iicoooott Research
(wenkaiyang, Lankailin)@ruc. edu.c..eddcc.
(shuming.mg ma, fuwei] emicrosoot.com
Abstract
Recent studies have shown that making model spend more time thinking through longer Chain of Thoughts (CoTss enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs certain domains. Moreover, discover that there exists optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking- Optimal Scaling strategy. Our method first uses small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-In -nns-uuutt outperform other distillation-be based 32B ol-like models across various math benchmarks, and achieve performance on par with the teacher model QwQ-32B-Prent that produces the seed data 3
Introduction
Recently, System-2 thinking has become an important research area for enhancing the reasoning capabilities of Large Language Models (LLMs). Unlike previous System-1 thinking systems [45] 35
that perform fast thinking. such slow thinking system aims to increase the test-time compute of LLMs make them think more thoroughly before responding
question. OpenAl' ol model 2 has demonstrated a promising potential in this direction. By incentivizing the model to employ longer internal Chain of Thoughts (CoTs)) 42 for thinking, ol shows human-like reasoning capabilities, including searching, reflecting, backtracking, and re-exploring in its reasoning process, and achieves outstanding performance on complex reasoning tasks 33
Subsequently, a series of follow-up studies (30 36
have been proposed to imitate and explore ol-like thinking systems. These studies try to scale the number of reasoning tokens of LLMss either
by distilling from existing ol-kike models [14] 25 26 or reinforcement learning [6] [5], and gain
significant improvements compared earlier reasoning models [45 35
WWork done during an internship at Microsoft Research.
t Cooresponniig Author
1 Code, data and models are available at htttps://github..omm//tt
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Behind the promising paradigm of test-time scaling, there is few concurrent studies B 22 high- lighting an efficiency issue of overthinking in existing ol llkeike models, where they tend to generate an excessive number of tokens, even for simple questions that could be answered correctly with just a few tokens. However, we are concerned about a more critical issue that could the excessive pursuit of longer CoT's have negative impacts on the model's 's reasoning performance? That is, besides the efficiency issues, we aim to explore and study whether and how overly test-time scaling could potentially impair the reasoning performance of LLMs, typically in the math domain.
To study the problem, we first calculate and compare the accuracies and used reasoning tokens of several ol-like models and their corresponding System-1 I thinking models on MATH500 [20] and AIME2024 (see Figure Li. We find that subsequent ol -like models, S-QQ-32-PPreieee [3] as an typical example, generate much more tokens but gain only limited improvements in model performance. This preliminary exploration indicates that scaling to more reasoning tokens might not consistently lead to better performance. Then, to fairly investigate the performance comparison of the same base model after scaling with different lengths of Co'Ts, we conduct additional experiments on LLaMA3. --SB-Instruct [24] and Qwen2.5-333 -
Instrrctt [29] Specifically, we utilize QwQ-32B-
Preview (30 to generate and filter three types of reasoning paths with different lengths for the same set of prompts. Then, we teach the base model to use different reasoning efforts (i.e., different numbers of reasoning tokens) to solve a given problem based on learning on different subsets. Surprisingly, we find that training with longer reasoning paths leads to worse performance especially in easier tasks, and there exists an optimal reasoning effort that varies across tasks of different difficulty levels. Our further analysis reveals that longer CoTs may contain more erroneous steps. Though including certain incorrect steps and subsequent reflective steps can teach the model how to correct errors in inference, training excessive erroneous steps can have negative impact.
Based on the above findings, we propose a Thinking-OPtimin Scaling strategy (TOPS) that allows LLMs to decide by themselves how many tokens are needed to solve a given problem. The motivation is, if an LLM can already answer a question correctly under the given reasoning effort, increasing the response length with additional tokens may have adverse effects as longer responses are more likely to include erroneous steps. On the other hand, encouraging LLMs to spend more time thinking brings benefits to tackling more challenging problems. Therefore, we first responses under different reasoning efforts (i.e., of varying lengths) to train a "tag" model, which is used to generate responses for large set of math problems under different reasoning efforts. Then, we select the shortest correct response generated across all reasoning efforts given the same problem create thinking-optiine model. Our self-improved model based on Qwen2.5-32BBInssie than existing distillation-bass based 32B ol-like models in various benchmarks with varying levels of difficulty, including GSM8K A MATH500 and AIME2024. Furthermore, we perform iterative self-improvement and obtain reasoning model that achieves comparable performance to QwQ-32B- Preview.
small set of ol-kike
dataset, which is used for the self-improvement of the base
achieves better performance
2 Related work
LLM Reasoning Leveraging the Chain-of-Thought (CoT) technique
LLMs have 42
CoT enables LLMs to decompose the entire problem into several sub-goals and then reason step-by-step to achieve a more reliable answer. Among various LLM reasoning tasks, mathematical reasoning has become one of the most widely studied and important tasks. Current work on LLM math reasoning primarily
demonstrated impressive performance on various reasoning tasks 34
33
35
focuses on: synthesizing large-scale and diverse math data [49 48 17 constructing challenging math reasoning benchmarks & 19, training powerful process reward models (PRMs) 220 39 (3)]
and designing more effective algorithms to improve math reasoning capabilities of LLMSs [1, 12 5
Test-Time Scaling Recently, scaling test-time compute of LLMs has shown significant potential for further improving their reasoning performance [1].. Existing test-time scaling studies can be divided into several categories: (1) Sampling-
scaling aims to increase the number of individual reasoning paths of LLMs when solving a given problem. Then the most reliable answer is selected from all the generated options using mechanisms such as majority voting [4), weighted majority
voting 18] or best-of-N selection 20 (2) Tree search- scaling expands reasoning paths by
2

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100
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s00
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(a) Results MATH500
(b) Results AIME2024
Figure 1: The accuracy and the average number of tokens for each model on MATH500 and AIME2024. To ensure a fair comparison, we tokenized model outputs using the Qwen2.5 tokenizer.
constructing tree-like trajectories, allowing LLMs to explore diverse options each state and continue reasoning along the most promising directions. Tree-of-Thougeee (ToT) [47] and Monte Carlo Tree Search (MCTS) 43 50 37 (52 are typical tree search-based test-time scaling methods. (3) In-context search- based scaling enables LLMs to learn to search, backtrack and re-explore within one single CoT path 77. Recently, OpenAl's ol model (28 have made significant breakthrough in this line. It leverages reinforcement learning to scale the lengths of CoT to enable LLMSs to perform thorough thinking through reflection, verification and re-exploration when solving problems. Following the same line, a series of studies (36 6 30 11 25 [4 19 46) have been proposed to scale CoT lengths during inference time. Our work also primarily focuses on the scaling properties of ol-like models.
We notice that there is few concurrent studies 3 22
highlighting that existing ol-like models exhibit overthinking issues, often generating an excessive number tokens for simple problems with minimal benefit. Thus, they aim shorten the CoT lengths of ol-like models while preserving their performance. However, our work differs in that we aim to uncover a deeper and more critical issue: scaling with more tokens can, in some cases, even degrade the model's performance. Thus, our work focuses on achieving optimal test-time scaling from base models in both aspects of effectiveness and efficiency.
3
The impact of scaling efforts on the effectiveness of test-time scaling
3.1 Preliminary analysis on existing -l-like models
Though ol-like models has proven be much more effective on reasoning tasks than previous System- 1 thinking models, we are curious about the scaling process behind the these ol-like models. That is, we want to explore that: How effective has their scaling achieved compared their corresponding System-l thinking models(e.g., QwQ-32B -eer-ie v.s. Qwen2.5-22 5-22255--BB-mmee 2-B--tsttcc))
We first conduct preliminary analysis on several existing typical ol-like models along with their corresponding System-1 thinking models. Specifically, we choose -1-mini 28 v.s. gpt-4o/4o-
mini (27 2o-minni.0--Fash-- Thinking-nniiiiiie
[11] Geemini..0-Flash-EB Preview 30 v.s. Swven..5-32B-Instruue (29). and DeepSeek-R1
(10), QwQ-32B-
6 v.s. DeepSeek- V3 21 as our
experimental models. We calculate the accuracy and the average number of generated tokens of each model on two typical benchmarks: MATH500 (00]: 500 high school math competition problems
across various subjects, sampled from MATH benchmark [13: AIME2024: 30 challenging problems from the American Invitational Mathematics Examination (AIME). To address the issue of token counts not being directly comparable due to the different tokenizers used by different models, we standardize by using Qwen2.5 tokenizer to tokenize the reasoning completions of different models
'Note that ol -mmii and 4o/4o mini do not have equivalent number of parameters, but we make a rough comparison here.
3

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Table 1:
Data statisties (number of problems and average number of tokens in responses for each type of reasoning effort) of three types of data samples under different reasoning efforts for training each tag model.
#Tokens
Model
#Problems
Low
Medium
High
LLaMA3.1-8B-1 Tag
1256
1532.32
2460.07
3647.50
Qwen2.5-32B-Tag
1312
1588.23
2535.65
3767.92
and then calculate the number of tokens. As the internal CoT of o1-mini is not available to users, we use an estimation strategy based on the summary part, the number of reasoning tokens and total number of completion tokens returned from the ol-mini model to estimate the number of tokens of hidden CoT tokenized by Qwen2.5 tokenizer. Details and further discussions are in Appendix B We set the maximum number of generation tokens to 16,384 for each model in all evaluations.
We put the visualization results in Figure [ As we can see, subsequent ol-like models (QwQ- 32B-Preview and Gemini2.0-Fun 1---0--F--Thhinnkee Thinking) show less effective scaling effects compared with ol-mini, as they generate much more tokens but gain less improvements when scaling from their corresponding System-1 thinking models. BwQ-32B-Prreve This preliminary analysis suggests, to some extent, that excessively scaling to longer CoT's does not maximize test-time scaling effects.
has the most severe issue in this regard.
3.2 Deeper explorations on the scaling process of CoT length
The above analysis still faces a problem that the base models of different ol-like models are not identical, making it unfairly to compare the impacts of scaled CoT lengths on test-time scaling effects of different models. Therefore, we conduct experiments on ILaMA3. 1--.MA...---BBB. -ns-Instruct (24] and Qwen2.5-32B-Innttee
[29] to fairly investigate the impact of the scaling efforts on the effectiveness
of test-time scaling. Specifically, we first use three system prompts (refer to Figure corresponding to different levels of reasoning effort ("Low", "Medium" and "High"), to prompt JWWQ-3B--Previce to generate solutions of different numbers of tokens for the same set of math problems sampled from NuminaMath [7]. We then filter out the problems that can be answered correctly under all three reasoning efforts, along with the corresponding three reasoning paths of different lengths. However, we find that MMQ-32B-Previin
has relatively poor instruction-following abilities, reflected in that the length distributions of the generated responses for the same question does not closely match the specified system prompts (refer to the empirical evidence in Appendix G). Therefore, for given problem, further reorder the three responses based their lengths and keep them if their pairwise length difference consistently exceeds 300 tokens. The length is determined either by LLaMA3.1 tokenizer or Qwen2.5 tokenizer depending on the chosen experimental model. Finally, a set of 1.3K problems, each accompanied by three ol-like responses of varying lengths. The data statisties of each set for each model is shown in Table I We assign different system prompts (the same in Figure 7 to each type of responses and train the base model on all three types of samples. By doing so, we ensure the consistency between the base model and the training problems, allowing for a fair comparison on the impacts of different scaling efforts on the effectiveness of test-time scaling, We refer to the fine-tuned model as the "tag" model (LLaMA3.1-8P) During inference, we can use different system prompts to guide the tag model in applying varying levels of reasoning effort to answer the questions.
curate
and Qwen2.5-32B-IT -agg))
The detailed training settings are put in Appendix AIME2024 introduced before, we further include GSM8K [4] that contains 1319 grade school math word problems. In the following, unless otherwise specified, we set the decoding temperature to 1.0 for all ol-like models, by following the recommended setting for ol model For System-1 thinking models LLaMA3.1 1-B.1-8B-Inaa -ns-rutt and Qwen2.5 - we report the results for both decoding temperatures with 1.0 and 0.0 for comprehensive comparison. Each result under 1.0 temperature averaged over 5 random seeds. The full results on 1-LMA...--B-InSSS
E. For evaluation, besides MATH500 and
and Qwen2.5-32B-Insttee are shown in Figure and Figure 3 respectively. We also display the performance of QwQ-32B-
hattps://platoore: http://laaffrr..opea.... wttp://tttttooccco//oooooooocce/ hatpaa/aoono/c//ggug/////eeaaaan

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Accurio 55-
Accuacy (N)
Acomey (i0
Laba beaer
75
300
1083
2000
200
1090
2006
3000
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2006 4000
6000
1900
10009
Average Number of Tokens
Auerage Number of Tokens
Average Number of Tokens
Results GSM8K
(b) Results MATH500
(c) Results on AIME2024
Figure 2: The accuracy and the average number of tokens of LLaMA3. I-8B-Instruct Instruct and LLaMA3.1 1- 8B-Tag under different reasoning efforts ("Low", "Medium" and "High") on different benchmarks with varying levels of difficulty.
Acsinyy (N)
Accrney
Accmmty
Omedl 1:20 Reaen (hep
wnwuttitonni Th
Ceeds ca8 Dhrprih
Unail
CoN Tgr
Creda cak Ag
55
1069
3500
2000
4000
Average
Average
Average
(a) Results on GSM8K
(b) Results on MATH500
(c) Results on AIME2024
Figure 3: The accuracy and the average number of tokens of Qwen2.5-32B 1aee225-32B----seeee Instruct and Qwen2.5- 32B-Tag under different reasoning efforts ("Low", "Medium"" and "High") different benchmarks with varying levels of difficulty.
Preview on all evaluation benchmarks when directly prompted with different prompts in Appendix H for reference. We can draw several interesting conclusions from these results: (1) A small number ol-like responses already highly effective in enhancing the reasoning performance LLMs. This is also consistent with the previous findings [25] 14.. (2) Scaling with longer CoTs can bring negative effects to the model's reasoning performance in certain domains, especially on easy tasks. For example, both LLaMA3.1 1-.......--BB..... -88-TTag and Qwen2.5-33B--TH reasoning effort compared to the other two reasoning efforts, while consuming significantly more tokens, particularly that varies across different tasks of varying difficulty levels. As we can see, low reasoning effort consistently works best GSM8K, while medium and high reasoning efforts
perform worse under high
GSM8K and MATH500. (3) There exists an optimal reasoning efforts
more beneficial for harder question. Furthermore, we display the breakdown results of each model on MATH500 categorized by different problem levels in Appendix F and the results also show the consistent conclusions on the negative effect of excessively scaling CoT lengths. We also conduct additional experiments general reasoning tasks beyond mathematical reasoning to demonstrate that the above findings hold true in other tasks as well. The detailed results and discussions are in Appendix [
To further investigate the impact of scaling with varying CoT length distributions, we calculate the distributions of answers of reasoning effort-conditioned models under different reasoning efforts. Specifically, we calculate the average number of distinct answers in 5 samples per prompt under each reasoning effort. The results are in Table 2 We also display the accuracy on each benchmark for reference. We find a very interesting phenomenon. Generally, the reasoning effort that achieves the best performance on certain benchmark also leads the lowest average number of distinct answers per prompt. This indicates that, under the optimal thinking effort, the model can generate the most consistent answers across multiple samplings without either underthinking or overthinking.
3.3 Analysis on the adverse effects of excessive length scaling
Here, we take deeper step to explore why training on longer CoT's leads to decline in model's reasoning performance. We randomly selected 100 problems from the tag model's training set along
5

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Table 2: The distribution of distinct answers under different reasoning efforts along with the average accuracy. We highlight the best accuracy and the lowest average number of distinct answers per prompt.
GSM8K
MATHO00
AIME2024
Model
Accuracy
#Answers
Accuracy
#Answers
Accuracy
#Answers
LLaMA3.1 models
LLaMA3. 1-B.--8--Taag -ow
87.26
1.37
59.00
2.34
7.33
4.27
LLaMA3.1-8 -------T--edduuuee
87.06
1.42
61.12
2.54
4.27
-aMAA.J-8B-Tag-HH
86.89
1.47
59.36
10.00
4.00
Qwen2.5 models
Qwen2.5-322 5-32B-Tag-LLoo
95.53
1.33
90.60
1.39
34.67
3.20
Qwen2.5-322 TarB--TT--Meiiue
94.33
1.14
91.48
1.36
42.00
3,13
93.31
1.15
90.56
1.40
41.33
3.30
Ary, Namter Reasoing Kounds
5000
Are Namborr ef Resonin, Rounds Centaniing Eranoao Skyo
Ratto Trand
$2.0
0.20
F77
LLaMAd. XS lestrcc:
Namber of Reasoning Rounds
MATTI500 Accuracy
51.0
LEaMA3.1 KB Long CoT (wic los makking)
Oil
0.15
Rabbo Value
0.10
49.0
48.0
0.05
0.5
0.0
Low
Medium
High
0.00
46.0
Model
Reasoming Effort
Figure 4: The statistics of responses under differ- Figure 5: Empirical results loss masking on ent reasoning efforts for training the tag models. erroneous steps. Evaluation temperature is 0.0.
with their responses under three different reasoning efforts. We first follow the existing study [3] to use go to determine the total number of reasoning rounds contained in each response. Each reasoning round defined as complete reasoning process or verification process that contains final answer. Besides, we further use gpt-4o to determine the number of reasoning rounds that contain erroneous steps or wrong final answers. The utilized prompt is shown Appendix [ We visualize the average number of reasoning rounds, the average number of erroneous reasoning rounds, and the average ratio of erroncous reasoning rounds, on each problem under each reasoning effort Figure Note that all evaluated responses have correct final answers.
First, we can see that the number of reasoning rounds consistently increases from low reasoning effort to high reasoning effort. It could lead to the overthinking issue in reasoning models (3]. where redundant tokens are used answer the question through repetitive verification. This, however, should not affect the accuracy if all reasoning rounds are correct. Unfortunately. we observe pattern that the number and proportion of erroneous reasoning rounds also increase when the reasoning effort becomes higher. Training the model on more wrong steps would bring adverse effects to the model's s reasoning abilitics, which can explain why scaling with high reasoning effort leads to conclude that while including certain incorrect and reflective steps
worse results. Therefore, can help the model learn to correct errors during inference, an excess of erroncous steps can have detrimental impact on model's learning.
To further validate the above claim, we conduct controlled validation experiments about training the model on erroneous reasoning steps with subsequent error corrections. Specifically, we first construct long CoT's with reflection and correction from seratch. obtain initial CoTs with incorrect answers generated by critique them (i.e., identify the erroneous step and generate suggestions for correction). Then, we enable LLaMA3.1 1-B Instruct to generate self-reflections and corrections based on the critiques, and
MATH training prompts, and use Dwwen2.5-72B-IIntiie Instrrcct to

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Seed Data Under Different Reasoning Effects
Additiona Problems
Qm
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Format
Reasoning
Self- Improvement
Imitation
Effort-
Conditioned
Generation
Figure 6: The illustration of our Thinking- Opttimll Scaling method. Our method includes three stages: Format Imitation enables the base model to learn how to adopt different levels of reasoning effort Coofot-Condiiioned
& to perform System-2 thinking, using a small set of seed data. Reasoning Generation requires the model to apply System-2 thinking to large set of problems under different reasoning efforts. eelf-Improvementt select the shortest correct response for each problem among all responses to fine-tune the base model to achieve thinking thinking-optimal test-time scaling.
merge these with the initial responses to form long COT's. We fine-tune LLaMA3. 1.3.1-888-Insttue on the created long CoTs. In the results shown in Figure 5 can observe that if we apply loss masking to the tokens in the identified wrong steps (i.e., not calculating loss on these erroneous steps), the performance is better compared to calculating loss all steps/tokens. This further validates our claim that training on erroneous steps can negatively impact model performance. Additional experiments and empirical analysis are Appendix
4 Thinking-optimal test-time scaling
The above analysis reveals that excessively increasing the response lengths of LLMs can result in negative consequences. This motivates us that an optimal approach achieve test-time scaling is allowing the model to determine by itself the number of tokens needed to solve each problem. Specifically, for a simple question, if the model can provide a correct answer within certain number of tokens, further extending the CoTss becomes suboptimal, as it may introduce unnecessary overthinking or even additional erroneous steps into the reasoning process. Conversely, the model should be encouraged to use more tokens for difficult problems if additional reasoning effort can help it to obtain a more reliable and accurate answer.
Thus, we propose a Chinking-OPtingg Scaling (TOPS) strategy aiming to achieve more effective and efficient test-time scaling for LLM reasoning. We define System-2 thinking-optimal response as the shortest correct response that the model can generate using System-2 thinking: fewer tokens may lead to wrong answer while more tokens causes overthinking. Then, our method includes three stages: Format Imitation, Reasoning Cefoit-Condiioooeed Generation, and self-Improvement. The illustration of our method is shown in Figure
Format Imitation First, we require a small set of ol-like responses for a cold start, enabling the model learn the format of System-2 thinking patterns, including searching, reflecting, verification, backtracking, etc. Preliminary results in Section 3.2 and previous studies [25] [4] have shown that small number of ol-kiee responses are sufficient for the model to effectively learn the format of System-2 reasoning. Such small set of seed data can be manually human-
or generated by existing oikei models. However, different from previous studies 225 26 that use a fixed length distribution of seed samples (i.e.. directly generated by existing ol like models), which may not be manking--ppiman distribution for our base model, we instead create the seed data containing responses under different reasoning efforts (i.e., different length distributions). Specifically, we define a small number of seed problems as P., and our goal is to curate seed dataset D. D., U... D..., where D.; {(e,, x, ye: [z P.} represents the responses seed problems under specific
7

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reasoning effort eç. This follows the same procedure as data curation for the tag model in Section 3.2] Then, we train the base model on this dataset to obtain the tag model that can apply different levels of reasoning effort to perform System-2 thinking on a given problem:
arg max Bee,, )nD, (P(ye 20 0)]
sag
(1)
Reasoning Effort-Conditioned Generation We then use the tag model generate the solutions on a large number of additional math problems Pa under different reasoning efforts e;:
ye, T(le,, 2; Orag), 2 Pa.
where T-1(0tz) denotes the output distribution of the tag model. We select the shortest correct solution Yee among all generations {Ve...... , Ve,, } as the thinking-optimal response for problem z, and obtain a thinking-optimal self-improve sef-impprvvemet dataset Drop {(z, ysc) x ~ Pa)).
Self- reff--mprovementt After obtaining the thinking-optimat dataset determined by the model itself, we can use it to train the base model, enabling the base model to achieve better celf-improvement on System-2 thinking. Specifically, we perform Supervised Fine-Tuning (SFT) to the base model on Drop:
OTOP- = arg max ((e...e)-Pror !P(yse (r, 0)]-
5 Experiments and analysis
5.1 Experimental settings
Base Model We mainly display and compare the results of performing Selnkingg-ptiiman Scaling on Qwen2.5-32B-Instruce as it serves as an appropriate base model for exploration on test-time scaling according previous works (30 25 26) To validate the generalizability of our approach, also
perform additional experiments on LLaMA3.1 1-A..1--BB 1-88---sstttrc and put the results in Section 5.4
Datasets First. directly use the model Qwen2.5-32B --me2.---2---ag--- Tag created in Section 3.2 as the tag model for reasoning dffort-conditions seed data that contains 1.3K problems from subset of NuminaMath, and totally 3.9K responses under three types of reasoning efforts generated by Mio--3BB-Previee We then use this tag model to additional subset of NuminaMath containing extra 50K problems under different reasoning efforts. On each problem, we sample only 1 response for each reasoning effort, though we believe that performing multiple samplings could further enhance effectiveness. For each problem, we select the shortest correct response among all three responses to the problem as the thinking-optimal response. Finally, we incorporate the responses corresponding to low reasoning effort from the seed data into the above generated dataset, resulting in thinking-optimal dataset of about 26K samples for self-impres eeff-improvement. We denote the self-improved model created by our We then evaluate the performance of our model on three typical math reasoning benchmarks: GSM8K. MATH500, and AIME2024. The additional results on general reasoning tasks can be found in Appendix !
generation. As mentioned before, this tag model is trained on the
generate responses
method as Fren2.5--2B-TOFF
Training and Evaluation Details In the SFT stage, the learning rate is 1 x 10-5 the batch size is 96, and the number of epochs is 2. In inference, the decoding temperature is 1.0, the maximum generation length is 16.384. We report the average accuracy across 5 random seeds in each experiment. The standard deviation results are in Appendix K In the evaluation of MATH500, we also use gpt-4o to assist in identifying missed cases caused by format issues (8].
Baselines Besides the base model Qwen2.5-32B 3-B--nnttu we compare our self-improved model with several existing ol-like models that are based on the same base model: (1) QwQ-32B-Preeveew: One
of the most popular ol-like reasoning models developed by Qwen Team. (2) STILL-2-32B [25]
A System-2 thinking model trained on 3.9K challenging math examples generated by QwQ-32B-
[6]: The reasoning model trained on 17K examples generated by QwQ-32B--review, including 10K math examples. (4) Qwen2.5-32B- Random: After the reasoning effort-based generation, we randomly select a correct solution on each problem rather than the shortest one form thinking-subooptmaa dataset, and train the base model
Preview and SeepSeek-Rl-Liinne (3) Sky-T1-32B-Previeee
on this dataset.
https::/appis docs. wwtpp/ppeeee.eeeeeeeeeeeeeeeeeee

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Table 3: The results of our self self-improved (Qwen2.5-32B-TOO)) and further iteratively self-improvee models 2ww.------TOSS----- compared to existing ol-like models using the same base model on GSM8K, MATH500, and AIME2024. In each setting, the underlined value represents the best result for System-1 thinking models, while the bold value indicates the best result for System-2 thinking models.
GSM8K
MATHO00
AIME2024
Model
Accuracy
#Tokens
Accuracy
#Tokens
Accuracy
#Tokens
System-1 thinking models
Owen2.5-32B-Instrucl (Temp. 0.0)
95.91
295.01
84.20
576.89
16.67
1407.43
Qwen2.5-32B-Inse (Temp. 1.0)
95.30
296.98
82.84
555.65
14.67
855.62
System-2 thinking models
QwQ-32B-Preview
95.23
761.01
92.02
2416.23
45.33
7636.63
STILL-2-32B
95.47
570.64
91.40
2005.28
45.33
6656.11 11
Sky-TI-32B-Prees
94.82
695.66
89.48
2022.07
35.33
5351.29
Qwen2.5-32B- 5-32B-Random
95.00
938.45
90.16
2670.19
39.33
7691.30
Swen2.5-32B-TTD (ours)
95.82
412.24
91.48
1883.29
43.33
7260.26
Qwen2.5-32B 1-----------SPSS -SFT (ours)
95.45
366.14
90.76
1701.11
44.00
6611.89
Qwen2.5-32B-TOOL
(ours)
95.80
384.81
91.60
1731.72
46.00
6426.62
Main results
The results of each model are displayed in Table 3 Besides the accuracy, we also report the number of CoT tokens used by each model on each dataset
First, we can see that the model trained under thinking-optingg samples (Qwen2.5-32BB- TOPS) consistently performs better than the model trained under bhinking-subopting samples (Qwen2.5- (2B-Random) This helps to revalidate our motivation that scaling with shortest correct responses, as determined by the base model itself using System-2 thinking, the most effective approach to achieve optimal test-time scaling. Second, compared to distillation-ann baased models STILL-2-32B and model Swen2.5-33BBTOS.
Sky-T1-32B- Nky-T1-32B-Preview our seff-improvement-beeee
achieves better results across the board, except for AIME2024, where it slightly underperforms STILL-2-32B. However, note that STILL-2-32B uses greater number of high-quality distilled samples (3,9K) including more challenging problems from AIME1983-208
whereas our model achieves comparable performance using only 1.3K seed samples and effective self- self-improvement strategy.
Regarding the reasoning efforts (i.e., the number of reasoning tokens) used by each model to solve different difficulty levels of tasks, observe that 5-322.5--3BS uses fewer tokens easier tasks like GSM8K compared to other models, effectively mitigating the issue of overthinking [ On the other hand, it tends to spend more time thinking on harder problems such as AIME2204. The comparison of reasoning tokens used by different models across various domains reflects our model's ability to exhibit adaptive reasoning depths.
5.3 Results of iterative self-improvement
To further enhance the reasoning performance of our model on challenging problems, perform iterative eef--improeeeett on Sreen2.5-32B-TOR Specifically, we select additional 4500 MATH problems [3] (which have not appeared in the previously used problems) and the problems from RMME198-20223 On each problem, we sample 8 responses from Dwee2.55-3BBTOOm select the shortest correct response among 8 responses as the chosen response. One iterative self-improvement approach is to further supervised fine-tune Dwven..5-32B-TT composed of all chosen responses (shortest correct responses), resulting in Qwen2.5-32B-TTOPS Iter-SFT. Besides, we can also perform preference optimization. Specifically. if there are responses with incorrect final answers, we select the longest incorrect response the rejected response to improve reasoning capability. Additionally, we include preference pairs where the rejected response the shortest wrong response there exists wrong response that shorter than the shortest correct
Then,
on the dataset
For STILL-2-32B and Sky-TI-32B do not include the tokens in the summary part.
we only calculate the number of tokens in the thought part and

---

Table 4: The ceff-improvement results on LLaMA3.1 1---B-Instttcttt In each setting, the underlined value represents the best result for System-1 thinking models, while the bold value indicates the best result for System-2 thinking models.
GSM8K
MATH500
AIME2024
Model
Accuracy
#Tokens
Accuracy
#Tokens
Accuracy
#Tokens
System-1 thinking models
LLaMA3.1-88 --B-sttre-- (Temp. 0.0)
82,18 76.21
262.23
47.00
1801.76
6.67
5506.30
LLaMA3.1-8B ---nstruuct (Temp. 1.0)
233.08
39.60
733.56
4.67
1691.88
System-2 thinking models
I.LMM33 --8--------ao------
87.94
1051.05
60.52
3627.23
4.67
8165.69
-LaMAS.1-BB-TOSS..
88.54
571.10
61.28
3254.01
8.00
7392.59
response, to avoid causing the model to underthink. After obtaining the preference dataset, we perform Direct Preference Optimization (DPO) [32] on Qwen2.5-32B-TOLL TOPS-Iter-PO. Detailed experimental settings are in Appendix
to get Qwen2.5-32B-
The results of iterative self-improvement are in Table 3 As we can observe, further SFT is mainly effective in shortening the CoT lengths but does necessarily improve reasoning performance. Preference optimization improves both the efficiency and the effectiveness, resulting in a reasoning model that is comparable to WwW--2B-Prreiees
5.4 Results on
Here, we display the results of performing our Thinking-Opiin Test- Best-Time Scaling strategy on 1-A.AA3.-8B-Insttie in Table The experimental setups are consistent with that in the main experi- ments above. The results demonstrate the generalizability of our method on other model architectures.
6 Conclusion
In this work, we aim to explore a potential issue under current pursuit of test-time scaling. Through empirical analysis on mathematical reasoning tasks, we first demonstrate that overly long CoTs can negatively impact the model's reasoning performance in certain domains, emphasizing the need for optimal CoT length scaling. To tackle this, we propose Thinking- which first leverages small set of seed data to teach LLMs to adopt varying levels of reasoning effort to perform System-2 thinking. Then, our approach allows models to identify the shortest correct response for self-improvement, leading to more efficient and effective System-2 thinking. Experimental results show that our self-improved and iteratively self-improved models, based on Qwen2.5-32B-Inse Innstruuct,, outperform existing distillation- ol ol-like models and achieve comparable performance with QwQ-32B- 32B-Previww across various math benchmarks.
Scaling strategy,
7 Limitations
There are some limitations in the current work: (1) Our analysis mainly focuses on the math reasoning domain, because math tasks offer relatively accurate and reliable performance verification. However, we believe investigating the potential impact of long CoT's in other domains important, which can be promising direction future work. We also provide some preliminary results in the general reasoning domain in Appendix [ (2) This work primarily focuses on the SFT setting. While investigating effective SFT and distillation very important and practical-as highlighted in concurrent studies [5] 38 exploring the impact of CoT length in the reinforcement learning (RL) setting is another compelling direction. We believe that our findings can be extended RL-based scaling. Specifically, since RL assigns positive rewards (e.g., 1.0) to all solutions with correct final answers, shorter correct solutions with fewer erroneous reasoning steps should be preferred over longer correct ones with more errors. Over-rewarding the latter may encourage the model to generate incorrect intermediate steps first and rely on its imperfect self-correction ability to correct erroneous steps, rather than producing the correct answer in one go.
10

---

Acknowledgements
We sincerely thank all the anonymous reviewers and (S)ACs for their valuable comments and thoughtful suggestions. This work was supported by The National Natural Science Foundation of China (No. 62376273 and No.U2436209) and Beijing Natural Science Foundation (L253301).
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Table 5: CoT token count returned from ol-mini API and estimated by Qwen2.5 tokenizer.
Method
MATH500
AIME2024
o1-mini API
1122.07 1110.88
4861.87
Qwen2.5 Tokenizer
4972.08
A Impact statement
This work aims to explore the effectiveness and limitations of ol-like test-time scaling. Our goal is to enhance both the efficiency and effectiveness of test-time scaling in more thinking-optimn way. These findings highlight importance of adaptive reasoning efforts and provide promising direction for more effectively enhancing L.M reasoning capabilities.
B Details on estimating the number of tokens in hidden CoT of ol o1-mini by Qwen2.5 tokenizer
In the preliminary analysis in Section 3.1 we use Qwen2.5 tokenizer to calculate the number of tokens the CoTs generated by each model for fair comparison. However, ol ol-mini does not expose the internal CoTss to users, but only shows the summary parts S, along with the number of reasoning tokens nel and total number completion tokens ngt (the sum of reasoning tokens and summary tokens) measured by ol-mini tokenizer. Therefore, we choose to estimate the number of tokens in its hidden CoT's measured by the Qwen2.5 tokenizer using S, nęl and n Specifically, we denote the number of tokens of the summary part measured by Qwen2.5 tokenizer ngwen then the estimated
number of tokens of hidden CoT by Qwen2.5 tokenizer can be calculated as ngwen X nol
We also display the comparison results on the COT token count returned by the ol-mini API and the number of tokens we estimated using the Qwen2.5 tokenizer in Table As we can see, the numbers do not differ significantly. Thus, we use the estimation results from the Qwen2.5 tokenizer in the main text in order to make fair comparison of the number of reasoning tokens used by different models.
C Prompts for generating reasoning responses under different reasoning efforts
We put the system prompts for QwQ-32B-Preview to generate responses under different reasoning efforts in Figure 7
D User prompt for gpt-4o to determine the number of (erroneous) reasoning rounds
We display the user prompt for go to help determine the number of total and erroneous reasoning rounds in Figure g
E
Experimental settings
E.1 Training settings for tag models
When creating two tag models, the learning rate is 1 x 10-3, the batch size is 32. The number of epochs is for Qwen2.5-32B-Tia and 5 for I.LMM3..1 1-8B-Tag. The training performed on 8 8XNVIDIA H100 80G.
22

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System Prompts for S-0--32B-Previeee under Different Reasoning Efforts
Low Reasoning Effort: You have extremely limited time think and respond the user's query, Every additional sorond
processing and reasoning incurs a significant resource enst, which could affect efficiency and effectiveness. Your task la to prioritize speed without sacrificing essential clarity or accuracy. Provide the most direct and concise refinements UNL.ESS ABSOLUTELY NECESSARY. correct respouse.
possible. Avoid unnecessary steps, reflections, verification,
primary goal
deliver a quick, clear and
Medium Reasoning Effort: You have sufficient time think and respond the user's query. allow- iug for a more thoughtful and in-depth answer. However, be aware that the longer you take to reason and process, the greater the associated resource costs and potential consequences. While you should not rush, aim balance the depth of your response, but analysis. Use your reasoning time wisely, focusing on what is essential for delivering an accurate response without unnecessary delays and overthinking.
well-thonghh-out overextend your thinking with efficieccy. Prioritize providing ressonable answer can provided
of
High Remsoning Eifart: You have unlimited time to think and respond to the user's question. There is no need to worry about reasoning time of sasociated costs. Your only goal la to arrive at a reliable, correct final answer. Feel free explore
problem from multiple angles, and try various methods your reasoning. This includes reflerting on reasoning by trying different approaches. verifying steps from different sspects, and rethinking your conclusions needed. You are encouraged to take the time to analyze the problem thoroughly, reffect your after a deep, comprebensive thought process should you provide the final answer, ensuring is correct and well-supported by your reasoning.
promptly and test all possible solutions. Only
Figure 7: System prompts for QwQ-32B-Previes with varying levels of reasoning effort.
User Prompt for gpt-4o to Determine the Number of (Erroncous) Reasoning Rounds
You will be provided with math problem and solution generated reasoning model.
The model's response may consist of multiple reasoning rounds.
One reasoning round is a part the full model generation and is defined as a complete reasoning procrss verification process that explicitly contains the final answer.
Your
determine the number reasoning rounds contains, and identify how many of these solutions contain erroncous steps, including intermediate erroneous steps erroneous final answer that is different from the ground truth answer.
carefully analyze the response
After you reasoning process, please give your final conclusions "## #### Number of rounds: <aumber>' and #f # ## Number of wrong rounds: <number>".
Problem: {question)
Solution: (solution)
Ground Truth Answer: [auswer]
Figure 8: User prompt for got-4o to determine the number reasoning rounds.
E.2 Training settings in format imitation
In the format imitation stage, we perform SFT on the base model Srren..5-32BInnstrue on a small subset of seed data containing 1.3K problems sampled from NuminaMath along with responses with varying lengths for each problem. The statistics of the seed data is shown in Table In SFT stage, the learning rate is 1 x 10-5, the batch size is 32, the number of epochs is 3. The training is performed on 8XNVIDIA H100 80G.
E.3 Training settings in self-improvement
In the self-imppovemmet stage, we perform SFT on Wwven255-32B-Instruue the curated thinking- optimal dataset for 2 epochs. The learning rate is 1 x 10-5, and the batch size is 96. The training is performed on 4xNVIDIA H100 S0G.
E,4 Training settings in iterative self-improvement
In the iterative self imfroveneee stage, for Qwen2.5-322 1-02255--2B--O-- TOPS-IterSSS the learning rate is 1 1x10 the batch size is 32, and we set the training epoch to For ----------TO-S--- learning rate is 5 x 10-7, the batch size is 32, the training epoch is 3. The training is performed on 8VNIIA H100 80G.
the
F.5
Evaluation settings
For all ol models, we set the decoding temperature to 1.0 and average the results over 5 random seeds for each evaluation experiment. The maximum generation length 16,384. All evaluations are conducted on 4 x NVIDIA A100 80G.
23

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Table 6: Breakdown results of tag models on MATH500 categorized by problem difficulty levels.
Level-1
Level-2
Level-3
Level-4
Level-5
Model
Acc.
#Tokens
Acc.
#Tokens
Acc.
#Tokens
Acc.
#Tokens
Acc.
#Tokens
LLaMA3.1-8B -LaMA3.J--B-Tag-LLoo
Tag-Low
92.09 1415,00 78.89 1702.68 68.38 2238.64 54.22 3386.63 32.24 4719.16
87.44 2123.17 17 79.11 2775.34 72.19 3541.26 57.81 4467.70 35.07 6267.16
87.44
2924.74
78.67
3561.78
71.62 4447.92
54.22
5242.71 32.69 6735.32
Bren2.5-32B-Tag-Lo0
97.67 673.82 95.33 987.61
97.14 1098.93
90.31 1802.25
80.30 3330.60
Been2.-33B--agg 1e0-TT---Meuum
96.74
1757.15 96.22 1761.37
97.14 1983.42
90.94
2692.74
82.69 4344.62
Qwen2.5-32B-Tai Ta----Taggghh
96.74
2077.88 95.33 2291.11
95.43 2479.56
89.84 3223.67
82.24 4659.30
Table Raw length distributions (response length rankings) of different reasoning- prompted responses QwQ-32B- -2e-Pre
Effort
Longest %
Middle %
Shortest
Low
15.2
18.3
66.5
Medium Hight
36.4
45.4
18.2
48.4
36.2
15.4
F Breakdown results of tag models on MATH500
We display the breakdown results of tag models MATH500 under different difficulty levels in Table 6 The results also validate the claim that continuously increasing the reasoning effort can indeed bring adverse effects, especially on lower-level problems (c.g., 92.09 (Low) -> 87.44 (Medium/High) and 97.67 (Low) -> 96.74 (Medium/High) on Level problems for LLaMA3.1-8B. Tag and Qwen2.5-32B Tag separately).
G Response length distribution of QwQ-32B-Preview under different reasoning effort-based system prompts
We put the initial response length distribution of different reasoning-effor prompted responses on QwQ-32B-Previee in Table 7 As we can see, in nearly 15% of cases, the low reasoning- effort prompted responses are even the longest among three responses. This indicates that only using direct prompting is unreliable to explore the impact of CoT length on reasoning performance. Therefore, when training tag models, for each training problem, we reorder the responses to ensure that the response lengths under different reasoning efforts follow an consistently increasing order from low medium to high. In such a controlled setting, we can fairly observe the impact CoT length on reasoning performance.
H Performance of QwQ-32B-Prees and QwQ-32B when directly prompted with different reasoning effort-based prompts
Here, we display the performance of QwQ-32B 3--e-eiee 30 and QwQ-32B 31 on all three evaluation benchmarks when directly prompted with different reasoning effort-based prompts. Since QwQ-32B includes both reasoning and summary components its responses and typically generates much longer CoTS, we extended its max_seq_ len to 32K to allow for sufficient reasoning and summarization. The full results are T These results re-validate our main claim: longer CoTs may not necessarily lead to better performance.

---

Table 8: The performance of QwQ-32B- 3----Peeview and QwQ-32B on three benchmarks when directly prompting the model with various reasoning effort-based prompts.
GSM8K
MATH500
AIME2024
Reasoning Effort
Accuracy
#Tokens
Accuracy
#Tokens
Accuracy
#Tokens
QwQ-32B-Preview
Low
93,95
418.26
90.24
1592.29
42.00
5152.97
Medium
93.56
844.32
89.16
2356.29
44.00
6413.97
High
92.78
1112.97
88.36
2684.87
41.33
6678.50
QwQ-32B
Low
96.56
568.49
95.76
2532.82
74.00
11390.70
Medium
96.50
1152.86
96.08
3708.79
78.00
12969.53
High
96.36
1752.29
95.80
4198.67
80.67
13194.29
Table 9: The performance of the model trained on data with high reasoning effort after filtering out all solutions that identified contain erroncous steps.
GSM8K
MATH500
AIME2024
Model
Accuracy
#Tokens
Accuracy
#Tokens
Accuracy
#Tokens
Dwen2.5-32B-Taag 3ag---B------ae High
93.31
1820.17
90.56
3185.75
41.33
8753.87 8049.29
Swen2.5-32B-Tag TTg--HighFilttred Filtered
94.87
1478.10
90.00
2783.98
36.33
I Results of fine-tuning on samples after filtering out solutions with erroneous steps
We conduct additional experiments supporting the claim that including erroneous rounds in the training stage can lead to greater adverse effects. Specifically, we filter out those solutions that contain erroneous steps (identified by GPT-4.1) 1) under the high reasoning effort, and fine-tune Qwen2.5-32B-Insstee Instruttt on the filtered data, which yields Qwen2.5-32B.
The results
in Table g
have some interesting findings: (1) After removing samples containing erroneous rounds, the trained model produces much shorter CoTss The reason is that the solutions removed are usually very lengthy as they contain more self-reflections and celf-corrections, thus the average length of the dataset after removing these samples is much shorter. (2) Removing samples containing erroncous rounds brings significant performance improvement on GSM8K, while causing certain performance degradation harder benchmarks MATH500 and AIME2024. The reason is that after removing those samples, the model cannot learn to effectively perform deeper thinking such as correcting the errors it could make in previous rounds. GSM8K is relatively simple, the model does not need to engage in excessive reflection and correction. Therefore, removing these behaviors actually improves model performance. On more challenging datasets, the advantages of longer reasoning chains that include reflections and corrections become apparent. Moreover, by comparing with the results in Figure 5 in the main text, we find that instead of directly removing correct solutions that contain erroneous steps, a more effective approach is to apply loss masking specifically to the wrong steps. The latter strategy allows the model retain the ability learn how correct previous mistakes. without explicitly learning from the erroncous steps themselves.
Results on general reasoning tasks
Here, we additionally prompt QwQ-32B-Pree Preview to generate responses under different reasoning effort-based prompts on a subset of the Weblnstrruct-eerffied dataset (23), and curate a seed general reasoning dataset that contains correct responses with varying reasoning efforts. We then fine-
tune Qwen2.5-7B -B-Inntrutt [29] the seed dataset to get Qwen2.5-7B Geggeerrra,, and evaluate
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Table 10: The performance of Qwen2.5-7B-bun --sed models MMLU-Pro and GPQA-Diamond
MMLU-Pro
Model
Accuracy
#Tokens
Accuracy
#Tokens
System-1 thinking models
Dwen2.5--7-Instrucc (Temp. 0.0)
52,46
401.38
34.85 33.84
592.73
Owen2.5-7B-Instruct (Temp. 1.0)
51.49
379.84
537.41
Tag models
Bwen2.5-BB-Tag-GGeee General-Loo
56.00
1674.60
31.82
2808.88
Owen2.5-7B-TT
---7--Ta--Genraal Geeneaal-Mddium
55.92
2341.27
36.87
3931.13
Qwen2.5-7B-TH. (ren2.5-7B-Tag-Geeeeer Tag-Generall-iie High
55.81
2632.05
32.83
4238. 11
System-2 thinking models
Bren2.5-7B-RRndon--eeees
55.86 56.50
1960.87
34.34
3385.70
Qwem2.5-7B-TTOPS-Geerrrl (ours)
1788.74
38.38
3083.76
Table 11: The detailed standard deviation results on LLaMA3.1-8D-Imstuuee.
Model
GSMSK
MATH500
AIME2024
System-1 thinking models
(Temp. 0.0)
82.18 (# 0.00)
47.00 (#: 0.00)
6.67 (+ 0.00)
1aaMAA.1-BB-Inttree (Temp. 1.0)
76.21 (# 0.66)
39.60 (#: 0.84)
4.67 (#: 2.98)
System-2 thinking models
LLaMA3.1-88 SB-Random SFT
87.94 (# 0.33) 88.54 (# 0.26)
60.52 (# 1,38) 61.28 (# 0.73)
4.67 (# 1.83) 8.00 (#: 1.83)
LLaMA3.1 ------OPPS
its performance on MMLU-Pro [4] and GPOA-Diamond 33 using the same reasoning effort-
conditioned prompting strategy in Section 3.2 We only sample once for each prompt considering the evaluation cost. The results are displayed in Table [1] The findings are consistent with the results in the math reasoning domain that excessive scaling with longer CoTs can bring negative effects to the model's performance in general reasoning tasks. Also, the model needs more reasoning effort to perform well on more challenging task GPQA-Diamond.
Following the above setup, we then perform our thinking-optime scaling General and perform random scaling get
held-out set of the
Weblnstruct--errffie dataset to get Qwen2.5-7B-TOPS. T-P---rrPP-aenrrlll 5ren2.5-7B-Random -eneral.. The evaluation results in Table [0 show that our method can also work well for general reasoning tasks.
K Standard deviation results
We put the detailed standard deviation results in Table
II and Table 12 for reference.
26

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Table 12: The detailed standard deviation results on Qwen2.5-32B-Inssie
Model
GSMSK
MATH500
AIME2024
System-1 thinking models
Qwen2.5-32B-Instreee (Temp. 0.0)
95.91 (t 0.00)
84.20 (#: 0.00)
16.67 (# 0.00)
Qwen2.5-32B-Instte (Temp. 1.0)
95.30 (t: 0.36)
82.84 (# 0.65)
14.67
(#: 5.06)
System-2 thinking models
QwQ-32B-Preview
95.23 (:: 0.39)
92.02 (:: 0.87)
45.33 (d: 3.80)
STILL-2-32B
95.47 (+ 0.26)
91.40 (# 0.80)
45.33 (# 6.06)
Sky-T1-32B-Pree
94.82 (# 0.33)
89.48 (# 0.78)
35.33 (# 2.9))
Qwen2.5-32B-Randomm
95.00 (t 0.31)
90.16 (# 0.95)
39.33 (+ 2,79)
Owen2.5-32B-TOWP (ours)
95.82 (1: 0.15)
91.48 (1 0.59)
43.33 (:: 2.36)
20022---2B-TOPSSIeee (ours)
95.45 (t: 0.14)
90.76 (:: 0.71)
44.00
(:: 3655
Dwen2.5-32B-TOOP TTOpS-IterDDP (ours)
95.80 (4: 0.13)
91.60 (1: 0.62)
46.00 3.65)
27


Reviews:
[{"review_id": "YfnPZjs0Gs", "reviewer": "Reviewer_CZmU", "summary": "- This paper presents an analysis and a new algorithm to modulate the amount of reasoning effort (length of CoT) for language models.\n - First, the paper studies the observation that training on longer reasoning paths hurts accuracy on easier problems because empirically (as judged by GPT-4o), additional reasoning processes increaess the probability of error.\n - Then the authors propose a strategy, TOPS, that varies the amount of reasoning effort based on the problem. In particular, they train a model to condition on the amount of reasoning effort, and then learna model to allocate fewer tokens to easier problems and more tokens to harder problems (for each problem, they determine the shortest reasoning trace that yields the correct answer).\n - In the end, they produce a model that performs comparably to QwQ-32B-Preview on GSM8K, MATH500, AIME2024.", "questions": "- Figure 4 shows that the number of erroneous reasoning steps increases with length. What's the mapping from this to whether the final answer is correct or not? Is it that one erroneous step is enough to kill the solution or is there some robustness (e.g., at least two have to be wrong)? Fundamentally though, it seems like the metric at the end is more of an \"and\" rather than a \"sum\" (almost everything has to be right).\n - How are the length distributions of the reasoning effort-conditioned model? Does the model actually generate reasoning chains of the appropriate length?\n - I would have liked to see a bit more qualitative discussion of what modulating the reasoning effort does to the reasoning chain? Does the model just skip steps if asked to make it shorter or are there fundamentally different strategies?\n - As one changes the amount of reasoning effort, what happens to the distribution of answers (I think it's always helpful to think about the whole distribution, acknowledging that there is an increased computation cost)?", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "- Trying to get models that vary the amount of reasoning effort based on the problem is a very sensible goal.\n - Training a model to condition on the amount of reasoning effort is good too (this reduces the number of potential confounders).\n - Using the shortest one reasoning trace seems problematic conceptually. For each amount of reasoning effort, one really has a probability of correctness. So then what does the \"shortest reasoning trace\" mean? Practically speaking, the dataset that's collected by (2) might be quite noisy.\n - The actual accuracies are not particularly noteworthy (AIME2024 is in the 40s, but there are 32B models now that are in the 70s - e.g., QwQ-32B).", "was_revised": true, "final_justification": "I increased my score by 1 based on the rebuttal.", "rebuttal": "We sincerely thank you for your great efforts on reviewing our paper and your helpful questions. We are glad that you think our target is a sensible goal and our method is good. We make the following response to address your questions.\n\n**Q1:** Regarding the question \"what does the \"shortest reasoning trace\" mean\" and the comment \"the dataset that's collected by (2) might be quite noisy\".\n\n**A1:** The \"shortest reasoning trace\" refers to the **correct solution with the minimal response length that can be generated by the target model across all levels of reasoning effort**. This trace represents the most efficient path the model can take to reach the correct final answer. As analyzed in Section 3.3, other longer responses are more likely to contain additional erroneous steps, even if their final answers are correct, and training on such responses can degrade model performance.\n\nBased on these findings, we propose constructing thinking-optimal datasets using Eq. (2) to enable more effective test-time scaling. We agree with you that datasets collected via Eq. (2) may be noisy, because it is nontrivial to precisely define and find the truly shortest correct response. However, we believe that increasing the number of samples for each prompt under each reasoning effort can help mitigate this noise and improve the reliability of the thinking-optimal dataset.\n\n\n**Q2:** Regarding the comment \"the actual accuracies are not particularly noteworthy\".\n\n**A2:** **The main scope of our work is to reveal the potential side effects of scaling with excessively long CoTs and to propose a more efficient and effective self-improvement strategy.** Our self-improved model achieves comparable performance to QwQ-32B-Preview with more efficient and adaptive thinking modes using only 1.3K seed data, and consistently outperforms other direct distillation-based models which rely on more high-quality distillation data in both effectiveness and efficiency. Also, our thinking-optimal model significantly outperforms random scaling (Qwen2.5-32B-Random) under the same constraints, validating our initial motivation. Finally, we believe **our method is also applicable when using other models such as QwQ-32B to curate seed data for self-improvement**.\n\n**Q3:** Regarding the question \"What's the mapping from the number of erroneous reasoning steps to whether the final answer is correct or not?\"\n\n**A3:** **For Figure 4, all candidate responses have correct final answers.** The purpose of Figure 4 and Figure 5 is to elucidate the empirical findings presented in Figure 2 and Figure 3: although all training solutions ultimately yield correct answers, scaling with longer CoTs can adversely affect the model’s reasoning performance in certain domains. This is because longer CoTs are more likely to include additional erroneous reasoning steps, and excessive training on such responses may degrade the model’s overall reasoning ability.\n\n**Q4:** Regarding the length distributions of the reasoning effort-conditioned model.\n\n**A4:** **Figure 3 displays the length distributions of the reasoning effort-conditioned models (i.e., tag models).** As we can see, the reasoning effort-conditioned models achieve the best reasoning performance on GSM8K under the low reasoning effort with fewer than 500 average tokens, and achieve promising performance on AIME2024 under the high reasoning effort with more than 8000 average tokens. **This helps to validate that the reasoning effort-conditioned models can actually generate reasoning chains of the appropriate lengths.**\n\n**Q5:** Regarding the qualitative discussion of what modulating the reasoning effort does to the reasoning chain.\n\n**A5:** Thank you for your constructive question. We follow your suggestion to manually analyze the reasoning chains under different reasoning efforts. We find that in the vast majority of cases, responses under low reasoning efforts use fewer complete reasoning rounds compared to responses under higher reasoning efforts (consistent with Figure 4). This property manifests differently in simple and difficult problems:\n\n(1) For simple problems (about 40% samples we checked), higher reasoning effort leads to **overthinking**, where the model continuously adopts alternative strategies to re-solve the problem. This causes the model to initially answer correctly but subsequently obtain incorrect answers through re-solving, and then become misled by these wrong answers, ultimately leading to incorrect responses.\n\n(2) For some difficult problems, the property of engaging in continuous reflection, correction, and exploration under higher reasoning efforts enables the model to solve problems that cannot be addressed by lower reasoning efforts due to **underthinking**.\n\n**Q6:** Regarding the question \"As one changes the amount of reasoning effort, what happens to the distribution of answers?\"\n\n**A6:** We follow your suggestion to calculate the distributions of answers of reasoning effort-conditioned models under different reasoning efforts. Specifically, we calculate the average number of distinct answers in 5 samples per prompt under each reasoning effort. We also display the accuracy on each benchmark in the following table for reference. We find some very interesting phenomena: **Generally, the reasoning effort that achieves the best performance on a certain benchmark also leads to the lowest average number of distinct answers per prompt.** This indicates that, **under the optimal thinking effort, the model can generate the most consistent answers across multiple samplings without either underthinking or overthinking.** Your question is helpful for better understanding of empirical findings in Section 3.2 and we will add it into the revision.\n\nTable 1: The distribution of answers under different reasoning efforts along with the average accuracy. We highlight the best accuracy and the lowest average number of distinct answers per prompt.\n\n|Reasoning Effort|GSM8K||MATH500||AIME2024||\n|-|-|-|-|-|-|-|\n| | Avg. # Distinct Answers | Accuracy |Avg. # Distinct Answers | Accuracy |Avg. # Distinct Answers | Accuracy |\n|***Qwen Models***|\n|Qwen2.5-32B-Tag-Low|**1.13**| **95.53** | 1.39| 90.60 | 3.20|34.67 |\n|Qwen2.5-32B-Tag-Medium|1.14|94.33 |**1.36** | **91.48** | **3.13** | **42.00** |\n|Qwen2.5-32B-Tag-High|1.15| 93.31 | 1.40| 90.56 | 3.30| 41.33| \n|***LLaMA Models***|\n|LLaMA3.1-8B-Tag-Low|**1.37**| **87.26** | **2.34** | 59.00 |4.27|7.33| \n|LLaMA3.1-8B-Tag-Medium|1.42|87.06 | 2.54| **61.12** |4.27|7.33 |\n|LLaMA3.1-8B-Tag-High|1.47| 86.89| 2.59 |  59.36 |**4.00**| **10.00**|\n\nWe hope the above clarifications address your concerns. We are glad to have further discussions if you have any further questions."}, {"review_id": "3P2hYxyD2u", "reviewer": "Reviewer_EPhU", "summary": "This works makes a very important and timely observation that if an LLM can already answer a question correctly under the given reasoning effort, increasing the response length with additional tokens may have adverse effects as longer responses are more likely to include erroneous steps. However, encouraging LLMs to think more is beneficial to tackle more challenging problems. This work proposes a method that use a small set of o1-like responses under different reasoning efforts (i.e., of varying lengths) to train a “tag” model, which\nis used to generate responses for a large set of math problems under different reasoning efforts. Then, it selects the shortest correct response generated across all reasoning efforts to create a thinking-optimal dataset, which is used for the self-improvement of the base\nmodel.", "questions": "1. Only three math data is provided for reasoning task. Will the observation hold for other reasoning tasks like commonsense reasoning, coding etc ?\n2. Will the method work for these new reasoning task ?", "limitations": "N/A", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The work is very insightful and relevant to the community. \n2. The work is very well motivated with analysis on state of the art LLM models.\n3. The insights provided on \"the impact of scaling efforts on the effectiveness of test-time scaling\" is very useful, timely and a big novelty of the this. \n\nWeakness:\n\n1. The improvement is not a lot. Hence it's important to see statistical significance results. Both for table 6 and table 2. \n2. 3 dataset are not enough to evaluate.\n3. Only math reasoning task is studied.\n4. The method is not backed by theory or a justification/intuition on how the method works.", "was_revised": true, "final_justification": "I think the paper is timely and present interesting insights for the community. The rebuttal also addressed all my issues. However after looking at other rebuttal, I decided to keep my score.", "rebuttal": "We sincerely thank you for your positive review and your constructive comments. We are glad that you think our paper is well-motivated and very insightful. We are encouraged that you find our insights very useful. We make the following response to address your remaining concerns.\n\n**Q1:** Regarding the statistical significance results.\n\n**A1:** We have displayed the statistical significance results of Table 2 (self-improvement results on Qwen2.5-32B-Instruct) in Table 7 in Appendix I. Here, we show the standard deviation results of Table 6 (self-improvement results on LLaMA3.1-8B-Instuct) in the following table for your reference. We will add it into the revision.\n\nTable 1: Standard deviation results of self-improvement results on LLaMA3.1-8B-Instuct.\n\n|Model|GSM8K|MATH500|AIME2024|\n|-|-|-|-|\n|LLaMA3.1-8B-Instruct (Temp=0.0)|82.18|47.00|6.67|\n|LLaMA3.1-8B-Instruct (Temp=1.0)|76.21(±0.66)|39.60(±0.84)|4.67(±2.98)|\n|LLaMA3.1-8B-Random|87.94(±0.33)|60.52(±1.38)|4.67(±1.83)|\n|LLaMA3.1-8B-TOPS (ours)|88.54(±0.26)|61.28(±0.73)|8.00(±1.83)|\n\n**Q2:** Regarding the observations on more datasets and other reasoning tasks.\n\n**A2:** We follow your suggestion to perform the same empirical validation in the general reasoning domain as we did in Section 3.2. Specifically, we prompt QwQ-32B-Preview to generate responses under different reasoning effort-based prompts on a subset of the WebInstruct-verified dataset [1], and curate a seed general reasoning dataset that contains 3.6K correct responses with varying reasoning efforts. We then finetune Qwen2.5-7B-Instruct on the seed dataset to get Qwen2.5-7B-Tag-General, and evaluate its performance on MMLU-Pro and GPQA-Diamond using the same reasoning effort-conditioned prompting strategy as in Section 3.2 (only sample once for each prompt and set max_seq_length to 8K considering the huge evaluation cost). The results are displayed in the following table. **The findings are consistent with the observations in the math reasoning domain that excessive scaling with longer CoTs can bring negative effects to the model’s performance in general reasoning tasks.** Also, we can find that the model needs more reasoning effort to perform well on the more challenging task GPQA-Diamond.\n\nTable 2: The performance of Qwen2.5-7B-Tag-General on MMLU-Pro and GPQA-Diamond.\n\n|Model|MMLU-Pro||GPQA-Diamond||\n|-|-|-|-|-|\n| |Acc. | #Tokens|Acc. | #Tokens|\n|Qwen2.5-7B-Instruct (Temp=0.0)|52.46|401.38|34.85|592.73|\n|Qwen2.5-7B-Instruct (Temp=1.0)|51.49|379.84|33.84|537.41|\n|Qwen2.5-7B-Tag-General-Low|**56.00**|1674.60|31.82 | 2808.88|\n|Qwen2.5-7B-Tag-General-Medium|55.92|2341.27|**36.87**|3931.13|\n|Qwen2.5-7B-Tag-General-High|55.81|2632.05|32.83|4238.11|\n\n\n\n\n**Q3:** Regarding the performance of TOPS on other reasoning tasks.\n\n**A3:** Following the setup in A2, we then perform our thinking-optimal scaling strategy on a held-out set of the WebInstruct-verified dataset to get Qwen2.5-7B-TOPS-General and perform random scaling to get Qwen2.5-7B-Random-General. The evaluation results in the following table show that **our method can also work well for general reasoning tasks**.\n\nTable 3: The self-improvement results on MMLU-Pro and GPQA-Diamond.\n\n|Model|MMLU-Pro||GPQA-Diamond||\n|-|-|-|-|-|\n| |Acc. | #Tokens|Acc. | #Tokens|\n|Qwen2.5-7B-Instruct (Temp=0.0)|52.46|401.38|34.85|592.73|\n|Qwen2.5-7B-Instruct (Temp=1.0)|51.49|379.84|33.84|537.41|\n|Qwen2.5-7B-Random-General|55.86|1960.87|34.34|3385.70|\n|Qwen2.5-7B-TOPS-General (ours)|**56.50**|1788.74|**38.38**|3083.76|\n\n\n**Q4:** Regarding the intuition on how the method works.\n\n**A4:** **Our method is backed by the empirical analysis in Section 3.2 and Section 3.3.** As shown in Figure 2 and Figure 3, even though all the trainings are performed on solutions that are all ultimately correct, scaling with longer CoTs can adversely affect the model’s reasoning performance in certain domains, and there exists an optimal reasoning effort that varies across different tasks of varying difficulty levels. Figure 4 and Figure 5 help to explain such phenomenon: longer responses are more likely to contain more erroneous steps, and excessive training on such responses can degrade the model’s reasoning performance. Based on these intuitions, we propose to create a thinking-optimal dataset that contains the shortest correct response of the model on each prompt across all reasoning efforts, because this is the most efficient and effective trace that needs to be learned.\n\n\nWe hope the above clarifications address your concerns. We are glad to have further discussions if you have any further questions.\n\n[1] Ma, Xueguang, et al. \"General-reasoner: Advancing llm reasoning across all domains.\" arxiv 2025"}, {"review_id": "Yol2Sr8axU", "reviewer": "Reviewer_AhwA", "summary": "This paper studies how the length of Chain-of-Thought affect model’s reasoning abilities. The authors found that excessively scaling the Chain-of-Thought length can impair the reasoning performance of LLMs. They further found that there exists some optimal length depending on the difficulty of the problems. Based on those findings, they proposed a Thinking-Optimal Scaling strategy to finetune the system-1 models and demonstrate the effectiveness through experiments.", "questions": "I will update the score once either or both of the weakness points I raised in the previous section is addressed. Additionally, the authors study the problem in the supervised finetuning setup, and it remains a question whether the same finding is relevant and can generalize to models trained with RL like o1 and Deepseek r1. This may be interesting to include but I understand if this is outside the scope of the paper.", "limitations": "The authors have included a limitation section.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Overall, the paper is well-written. The findings that excessively longer CoT may harm the reasoning performance contribute to the understanding of test-time scaling. However, there are a few weaknesses.\n\n1.\tOne potential issue of the method is the usage of system prompt to control the CoT length. Specifically, the authors admit in line 138-140 that QwQ-32B-Preview model they use to generate the responses has relatively poor instruction following abilities. This questions the validity of using system prompt as a way to control the CoT length. Specifically, the results they found may just be because of the poor alignment. What is the performance of QwQ-32B-Preview on the benchmark when prompting the model with different reasoning efforts? Does prompting them for different reasoning efforts affect their performance? The authors should include this result as well.\n\n2.    The author finds that the number of erroneous reasoning rounds also increase when reasoning effort becomes higher in Fig. 4. However, the ratios of erroneous reasoning rounds make more sense than the absolute number of erroneous reasoning rounds. Although erroneous rounds increase, the correct reasoning rounds also increase. Additional experiments are needed if the author wants to claim that including more erroneous rounds in the training stage can lead to greater adverse effects. For example, the authors can filter out those with erroneous steps and finetune and check if the performance of the model trained on data with high reasoning effort degrade or not. I appreciate that the authors conduct controlled experiments and include the results in Fig. 5. However, the dataset is different. Why not just using the same data presented in Fig. 4 and masking out the loss with erroneous steps to demonstrate the point? The dataset generated for this controlled experiment is different from the SFT data the authors use for all other experiments. This raises concerns for consistency.", "was_revised": true, "final_justification": "Overall, this is an interesting paper addressing a timely and relevant topic. The authors have adequately responded to all my concerns and questions. While some arguments provided during the rebuttal are not entirely supported by experimental evidence, the overall quality of the paper has improved. As a result, I have raised my score to 5.", "rebuttal": "We sincerely thank you for your positive review and your thoughtful suggestions. We are encouraged that you believe our paper is well-written and that our findings contribute to the understanding of test-time scaling. We make the following response to address your remaining questions.\n\n**Q1:** Regarding the usage of system prompts to control the CoT length.\n\n**A1:** Your concern is exactly what we have considered. **To solve this issue, and as explained in Lines 141-143, we do not use the responses from QwQ-32B-Preview under different prompts directly. Instead, we filter and reorder the correct responses from QwQ-32B-Preview under the three reasoning efforts to ensure that, for the same problem, the lengths of the three corresponding responses increase sequentially and significantly from low to medium to high.** This makes the length distributions of the responses under different reasoning efforts clearly distinguishable. Then, we set different system prompts for different subsets of responses under the three reasoning efforts, and merge all subsets to train tag models. By doing so, **the fine-tuned tag models can follow the system prompts strictly and generate different lengths of CoTs when given different system prompts in the inference stage.**\n\n\n**Q2:** Regarding the performance of QwQ-32B-Preview on the evaluation benchmarks when prompting the model with different reasoning efforts.\n\n**A2:** We also follow your suggestion to evaluate the performance of QwQ-32B-Preview on 3 evaluation benchmarks when prompting the model with different reasoning efforts. The evaluation parameters are the same as those used in our main experiments. **The following results are consistent with the results on the tag models and re-validate our main claim: longer CoTs may not necessarily lead to better performance.**\n\n\nTable 1: The performance of QwQ-32B-Preview on 3 benchmarks when prompting the model with different reasoning efforts. \n\n|Reasoning Effort|GSM8K||MATH500||AIME2024||\n|-|-|-|-|-|-|-|\n| |Acc.|#Tokens|Acc.|#Tokens|Acc.|#Tokens|\n|Low|**93.95**|418.26|**90.24**|1592.29|42.00|5152.97|\n|Medium|93.56|844.32| 89.16|2356.29|**44.00**|6413.97|\n|High|92.78| 1112.97|88.36|2684.87|41.33|6678.50|\n\n**Q3:** Regarding the comment \"the ratios of erroneous reasoning rounds make more sense than the absolute number of erroneous reasoning rounds.\"\n\n**A3:** We follow your suggestion to display the ratios of erroneous reasoning rounds in responses under different reasoning efforts. As the following table shows, **the ratio of erroneous reasoning rounds also consistently increases as the reasoning effort increases**.\n\nTable 2: The statistics of responses under different reasoning efforts for training the tag models.\n\n|Reasoning Effort|Avg. Rounds|Avg. Erroneous Rounds|Ratio of Erroneous Rounds|\n|-|-|-|-|\nLow|1.64|0.11|0.067|\nMedium|2.28|0.20|0.088|\nHigh|2.81|0.32|0.114|\n\n**Q4:** Regarding additional experiments on supporting the claim that including more erroneous rounds in the training stage can lead to greater adverse effects.\n\n**A4:**  We follow your suggestion to filter out those solutions that contain erroneous steps (identified by GPT-4.1) under the high reasoning effort, and finetune Qwen2.5-32B-Instruct on the filtered data, which yields Qwen2.5-32B-Tag-High-Filtered.\n\nTable 3: The performance of the model trained on data with high reasoning effort after filtering out all solutions that are identified to contain erroneous steps.\n\n|Model|GSM8K||MATH500||AIME2024||\n|-|-|-|-|-|-|-|\n| |Acc. | #Tokens|Acc. | #Tokens|Acc. | #Tokens|\n|Qwen2.5-32B-Instruct (Temp=0.0)|95.91 |295.01 |84.20 |576.89 |16.67| 1407.43|\n|Qwen2.5-32B-Instruct (Temp=1.0)|95.30| 296.98| 82.84| 555.65|14.67|855.62|\n|Qwen2.5-32B-Tag-High|93.31|1820.17| 90.56| 3185.75|41.33|8753.87|\n|Qwen2.5-32B-Tag-High-Filtered|94.87 (+1.56)| 1478.10 (-342.07)|90.00 (-0.56)|2783.98 (-401.77)|36.33 (-5.00)|8049.29 (-704.58)|\n\n\nWe have some interesting findings: (1) After removing samples containing erroneous rounds, the trained model produces much shorter CoTs. The reason is that the solutions removed are usually very lengthy as they contain more self-reflections and self-corrections, thus the average length of the dataset after removing these samples is much shorter. (2) Removing samples containing erroneous rounds brings significant performance improvement on GSM8K, while causing certain performance degradation on harder benchmarks MATH500 and AIME2024. The reason is that after removing those samples, the model cannot learn to effectively perform deeper thinking such as correcting the errors it could make in previous rounds. GSM8K is relatively simple, so the model does not need to engage in excessive reflection and correction. Therefore, removing these behaviors actually improves model performance. On more challenging datasets, the advantages of longer reasoning chains that include reflections and corrections become apparent. These findings are consistent with the main claim of our paper.\n\nMoreover, by comparing with the results in Figure 5 in the main text, we find that instead of directly removing correct solutions that contain erroneous steps, a more effective approach is to apply loss masking specifically to the wrong steps. The latter strategy allows the model to retain the ability to learn how to correct previous mistakes, without explicitly learning from the erroneous steps themselves.\n\n\n**Q5:** Regarding the question that \"Why not just using the same data presented in Fig. 4 and masking out the loss with erroneous steps to demonstrate the point?\"\n\n**A5:** The reason we do not use the responses for training tag models in the loss masking experiment is that **it is very difficult to accurately locate which specific steps are erroneous in those responses, due to the informal nature of o1-like outputs**. We have tried prompting LLMs to locate the exact erroneous steps, but found the results to be highly unreliable. In contrast, **when we construct our own long CoT data, we can precisely segment the reasoning traces step by step during the generation process, and then apply loss masking to the specific erroneous steps as needed**. We will include this clarification into the revision.\n\n**Q6:** Regarding future work on explorations in the RL setting.\n\n**A6:** **The primary scope and contribution of our work is to uncover the potential negative effects of scaling with excessively long chains of thought (CoTs).** Through comprehensive empirical analysis, we propose an efficient and effective self-improvement strategy, and demonstrate its effectiveness primarily in the SFT/DPO setting. We agree that **investigating the impact of CoT length in the RL setting is a valuable direction for future research, but it is out of the scope of this work**. As discussed in the Limitations section, our findings are also applicable to RL-based scaling. In particular, since RL typically assigns positive rewards (e.g., 1.0) to all solutions with correct final answers, it is preferable to favor shorter correct solutions with fewer erroneous reasoning steps over longer correct ones that contain more errors. Over-rewarding the latter may inadvertently encourage the model to generate incorrect intermediate steps and rely on its imperfect self-correction ability, rather than producing the correct answer directly.\n\nWe hope the above clarifications address your concerns. We are glad to have further discussions if you have any further questions."}, {"review_id": "SGxQABBdeD", "reviewer": "Reviewer_B8YC", "summary": "This paper investigates the impact of test-time compute scaling via Chain of Thoughts (CoT) length on Large Language Model (LLM) reasoning. The authors challenge the common assumption that longer CoTs always improve performance, demonstrating through mathematical reasoning tasks that excessive CoT length can harm accuracy, particularly in easier problems. They identify an optimal CoT length distribution varying by task difficulty and propose the Thinking-Optimal Scaling (TOPS) strategy. TOPS trains a \"tag\" model on diverse reasoning efforts to generate responses of different lengths, then selects the shortest correct response for self-improvement. Experiments on Qwen2.5-32B-Instruct show that TOPS outperforms distillation-based models on math benchmarks (GSM8K, MATH500, AIME2024) and matches QwQ-32B-Preview's performance. The approach addresses overthinking by adapting reasoning effort to task difficulty, reducing token usage on easy tasks while maintaining effectiveness on hard ones.", "questions": "Please see the Weaknesses above.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n- Thoroughly evaluates performance on multiple mathematical reasoning benchmarks, showcasing the method's effectiveness.\n- The structure of the paper facilitates easy understanding.\n\n\nWeaknesses\n- TOPS relies on QwQ-32B-Preview for seed data generation. Performance may vary with weaker base models. And there is no analysis of model-agnostic generalization (e.g., applying TOPS to non-Qwen architectures).\n- While limitations note RL as future work and can be extended (Section 7), TOPS is only tested in SFT settings. The training dynamics of the RL-based reasoning models can be very different from SFT models.", "was_revised": true, "final_justification": "This paper focuses on an important topic of LLM reasoning and is interesting. The authors have addressed some of my concerns, even though the empirical evidence is not strong. I have read the reviews and responses, including reviews from other reviewers. The quality of the revised paper, based on the rebuttal, can be improved. As a result, I have raised my score.", "rebuttal": "We sincerely thank you for your great efforts on reviewing our paper. We are glad that you think our experiments are thorough and our method is effective. We make the following response to address your questions.\n\n**Q1:** Regarding the performance on weaker base models and the generalization to non-Qwen architectures.\n\n**A1:** Thank you and your question is what we have considered. We have performed our method on LLaMA3.1-8B-Instruct, which is an non-Qwen weaker base model. The results are already put in Table 6 in Appendix I. And we also display in the following Table 1 for your reference. Furthermore, we perform additional experiments on Qwen2.5-7B-Instruct in general reasoning domain (the training data is from WebInstruct-Verified [1], and the evaluation data includes MMLUPro and GPQA-Diamond), and show the self-improvements in the following Table 2. **The results show that thinking-optimal scaling can also consistently improve the performance of weaker base models compared with random scaling in diverse domains, demonstrating the generalizability of our method.**\n\n\nTable 1: The self-improvement results of LLaMA3.1-8B-Instruct.\n\n|Model|GSM8K|MATH500|AIME2024|\n|-|-|-|-|\n|LLaMA3.1-8B-Instruct (Temp=0.0)|82.18|47.00|6.67|\n|LLaMA3.1-8B-Instruct (Temp=1.0)|76.21|39.60|4.67|\n|LLaMA3.1-8B-Random|87.94|60.52|4.67|\n|LLaMA3.1-8B-TOPS (ours)|88.54|61.28|8.00|\n\nTable 2: The self-improvement results of Qwen2.5-7B-Instruct on MMLU-Pro and GPQA-Diamond.\n\n|Model|MMLU-Pro|GPQA-Diamond|\n|-|-|-|\n|Qwen2.5-7B-Instruct (Temp=0.0)|52.46|34.85|\n|Qwen2.5-7B-Instruct (Temp=1.0)|51.49|33.84|\n|Qwen2.5-7B-Random-General|55.86|34.34|\n|Qwen2.5-7B-TOPS-General (ours)|**56.50**|**38.38**|\n\n**Q2:** Regarding future work on explorations in the RL setting.\n\n**A2:** **The primary scope and contribution of our work is to uncover the potential negative effects of scaling with excessively long chains of thought (CoTs).** Through comprehensive empirical analysis, we propose an efficient and effective self-improvement strategy, and demonstrate its effectiveness primarily in the SFT/DPO setting. We agree that **investigating the impact of CoT length in the RL setting is a valuable direction for future research, but it is out of the scope of this work**. As discussed in the Limitations section, our findings are also applicable to RL-based scaling. In particular, since RL typically assigns positive rewards (e.g., 1.0) to all solutions with correct final answers, it is preferable to favor shorter correct solutions with fewer erroneous reasoning steps over longer correct ones that contain more errors. Over-rewarding the latter may inadvertently encourage the model to generate incorrect intermediate steps and rely on its imperfect self-correction ability, rather than producing the correct answer directly.\n\nWe hope the above clarifications address your concerns. We are glad to have further discussions if you have any further questions.\n\n[1] Ma, Xueguang, et al. \"General-reasoner: Advancing llm reasoning across all domains.\" arxiv 2025"}]

Author rebuttal:

Meta-review: This paper focus on inference time compute optimization. It shows that overly long reasoning paths on easy problems can actually hurt the model performance. Motivated by this, it proposed a strategy of adaptively selecting optimal thining budget to address this issue. The proposed method is shown to be effective at reducing overthinking on easy problems while maintaining the effectiveness on difficult problems. 

The research topic is timely given the current trends of scaling test time compute in LLMs. However, the paper received borderline ratings due to some limitations. For examples, there are some arbitrary design choices such as using the "shortest reasoning traces" that could benefits from more analysis; and it would be useful to try to experiment on baseline models with close-to-SoTA performance on some dataset such as AIME24. Nethertheless, this paper has improved noticeably during the rebuttal with additional results and clarifications that could be improved. We generally agreed that the paper is a valuable contribution to the field despite some of the limitations and recommend acceptance. We recommend the authors to still try to address some of the questions and suggestions raised by the reviewers in the final revision to produce a solid publication.
Decision: Accept (poster)