Thoughts Are All Over the Place: On the Underthinking of Long Reasoning Models
Authors: Yue Wang
Qiuzhi Liu
Jiahao Xu
Tian Liang
Xingyu Chen
Zhiwei He
Linfeng Song
Dian Yu
Juntao Li
Zhuosheng Zhang
Rui Wang
Zhaopeng Tu
Haitao Mi
Dong Yu
Venue: NeurIPS 2025 spotlight ()
Keywords: Reasoning
Long COT
o1
Primary area: deep_learning

Abstract: Long reasoning models (LRMs) such as OpenAI's o1 and DeepSeek's R1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where LRMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source LRMs, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty (Tip)  that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in LRMs and offer a practical solution to enhance their problem-solving capabilities. Our code is open-source and available at https://github.com/wangyuenlp/underthinking.

Thoughts Are All Over the Place: On the Underthinking of Long Reasoning Models
Yue Wangh
Qiuzhi Liu
Jiahao Xu
Tian Liang?*
Xingyu Chen Zhiwei He
Linfeng Song²
Dian Yu²
Juntao Li
Zhuosheng Zhang* Rui Wang*
Zhaopeng Tu
Haitao Mi?
Dong Yu²
Soochow University
Tencent
Shanghai Jiao Tong University
Correct Respanse
Incorrect Response
18000
60
$13
100
Generated Tokens
Number of Thoughts
12,206
43.1
12000
6000
5,22
5.515
20
919
977957
Math- 72B
Liama3 3 70B
Qu Preview
Deepstaat R Previeew
DeepSieck- R1 R1-6718
Chv Bwo--3B--Prvviees Preview
Deepstek RI Previcw
DeepSickk RR 161-671B
Owan- Owon-Matth
(a) Generaled Tokens
(b) Number o'Thoughis
Figure 1: Illustration of the underthinking issue the challenging AIME2024 testset: In LRMs (e.g.. A-Q--2B--rreveee and PrepSeek-R167111 incorrect answers often switch reasoning strategies more frequently than correct ones (Figure b), leading to longer responses without improved accuracy (Figure a). In contrast, conventional LLMs (e.g., Qwen-Math-72BB and Llama3.3-77BB show no significant difference in response length between incorrect and correct answers.
Abstract
Long reasoning models (LRMs) such as OpenAl's ol and DeepSeek's RI have demonstrated remarkable abilities in complex reasoning tasks by scaling test- time compute and exhibiting human-like deep thinking. However, we identify a phenomenon term underthinking, where LRMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, conduct experiments three challenging test sets and two representative open-source LRMs, revealing that frequent thought switching correlates with incorrect responses. We introduce novel metric quan- tify underthinking by measuring token efficiency in incorrect answers. To address underthinking. we propose decoding strategy with thought switching penalty (TTP) that discourages premature transitions between thoughts, encouraging deeper explo- ration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning.
"Equal Contribution. The work done when Yue, Xingyu and Zhiwei were interning Tencent. "Correponndence to: Zhaopeng Tu <>ptu@teencnt.ccom
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Our findings contribute to understanding reasoning inefficiencies in LRMs and offer a practical solution to enhance their problem-solving capabilities. Our code is open- source and available at https: https://githhb. http://ww.....oooggggaaa//////aa
1 Introduction
Long reasoning models (LRMs) (OpenAl 2024; DeepSeek] 2025 Qwen 2024; Kimi 2025 have
revolutionized artificial intelligence by enabling models tackle increasingly complex tasks. LRMs, known for their deep reasoning capabilities, exemplity the potential of large language models (LLMs) exhibit human-like deep thinking by scaling test-time computation during problem-solving. These models aim to explore diverse reasoning strategies, reflect on their decisions, and iteratively refine solutions, closely mimicking human cognitive processes.
Despite their successes, a critical yet underexplored question remains: Are long reasoning models thinking deeply enough? This study provides an initial exploration of this problem. In this work, we investigate a phenomenon we term underthinking, which refers to the tendency of LRMs to prematurely abandon promising lines of reasoning, leading to inadequate depth of thought. To systematically analyze underthinking. we conduct experiments on three challenging test sets (e.g.. MATH500, GPQA Diamond, and AIME2024) and two open-source LRMs with visible long chains of thought (e.g.. QwQ-32B-Previee and DeepSSek-RR167111 Through extensive analyses, we found that underthinking manifests in the following patterns: (1) occurs more frequently on harder problems, (2) it leads to frequent switching between different thoughts without reaching a conclusion in each, and (3) it correlates with incorrect responses due insufficient exploration of reasoning paths. For example, Figure D compares the token usage and number of thoughts of correct and incorrect responses. On average, LRMs consume 225% more tokens incorrect responses than in correct ones due to 418% more frequent switghin behaviors.
To quantify this phenomenon, introduce a novel underthinking metric that measures token effi- ciency in incorrect responses by evaluating the proportion of the response that contributes to reaching correct thoughts. Combining the widely-used accuracy metric with the proposed underthinking metric provides more comprehensive assessment of LRMs models: accuracy measures how often the model can produce correct responses, while the underthinking metric evaluates the token efficiency within incorrect responses that contributes to reaching correct thoughts.
In response these findings, we propose decoding strategy with thought switching penalty (TIP) that discourages premature transitions between thoughts during the generation process. By adjusting decoding penalties for tokens associated with thought switching, the model is encouraged to thoroughly develop each line of reasoning before considering alternatives. Experimental results show that employing TIP improves accuracy across challenging test sets without requiring additional model fine-tuning.
Our study makes the following contributions:
1. We formally define and characterize the underthinking issue in long reasoning models, where models frequently abandon promising reasoning paths prematurely, leading to inadequate depth of reasoning on challenging problems.
2. We introduce novel metric to evaluate underthinking by measuring token efficiency in incorrect responses, providing a quantitative framework to assess reasoning inefficiencies.
3. We propose a decoding approach with thought switching penalty (TIP) that encourages models to deeply explore each reasoning thought before switching, improving accuracy without additional model fine-tuning.
2 Observing Underthinking Issues
In this section, we present a comprehensive analysis of outputs from LRMs on challenging math problems. We begin by illustrating the frequent thinking switch phenomenon observed in responses to these problems, as shown in Figure 2 highlighting how this behavior differs significantly between correct and incorrect answers (Section2..) We then show that this phenomenon leads to an inadequate depth of reasoning, causing models to abandon promising reasoning paths prematurely (Section 2.2

---

Les a, b, and be real nambers with 4-44 and bo-1 such that (a 2/ 21a22y22 Q:
-froocff (ooofff--0j210000 20622/622111 (racf6-117 2//22/1- 2)-1. Find the least porsible value a
Thoughti 41l zoloou
So I've gut this problem here that involves some equations with variables u, b, x, and y. and I need to find the least possible value of'a b given some conditiuns. Pertups I can think of this as sysiem of equations and iry sulve for x and y temms of'a and b.
Thought2
Alternatively, muybe there's geometric interpretation. Since both equations represent ellipses, perhups the cundition is that these allipses tangent each other.... So, unless there's some transfomrationn something, they don't seam he the same cilipse.
588 tokens
Thought3
Atrernativcly, perhaps the problem is that for some (x.y), both equations hold simultanenusly. and I need to find a and is such that this possible.... solive the first equation fory of and substicute the second equation. But that messy.
109 tokens
Solnion
Thought4
Alternatively, perhups I can consider this optimication problem where need minimize + subject the condition that the up algebraically.
sokens
equatioos have solution...
Thought5
Atternatively, perhaps consider the distanee
their (y 11y2 y 22y 121. However, only have y*2, not y. maybe isn't way to substitute.
of ellipses
613 toliens
20 More Thoughts Averaged tokous
Given that, perhaps need to accept that this pooblem beyond my current ability and seek help or look for different problem.
**iinal Answer*::
{[ (15
An example of underthinking issue for Bo-Q-32B-Previeee 's output that consists of 25 reasoning thoughts within single solution. The final correct answer for this example is 23. Thoughts # #1,3,4,5 are promising and can lead to the correct answer if explored sufficiently, As intermediate cognitive steps, reasoning thoughts typically does not engage in thorough deduction to get a answer.
Figure 2:
Based on this observation, we propose a metric to empirically assess the underthinking issues and present empirical results in Section 2.3 We conclude that LRMs often underthink when they fail to tackle challenging math problems.
2.1 Frequent Thinking Switch of LRMs
We conduct experiments on three widely-used challenging testsets: MATH500 (Hendryeks et al., 2021), GPQA Diamond (Rein et al. 2023). and AIME 2022-2024 (MAA Committees). We mainly investigate two widely recognized open-source LRMs featuring visible long CoT: QwQ-32B-Prrr Preview and DeepSeek-R1-671 IB. We also include DeepSeek-R1 11-Rreiievv to show the development of R1 series models. Given DeepSeek-R PertSeekkR--Peviiie -r-eviiss''s s daily message limit of via web interface, we evaluated this model solely on the MATH500 and AIME test sets.
Definition of Reasoning Thoughts In this paper, we define thoughts as the intermediate cognitive steps within a reasoning solution produced by the model. LRMs often switch reasoning thoughts using terms like "alternatively". For instance, as shown in Figure 2 the problem-solving process involves multiple reasoning thoughts, shifting from algebraic manipulation to geometric interpretation and optimization strategies. The ability to switch between different reasoning strategies allows for broader exploration of potential solutions and demonstrates the flexibility of the model in tackling complex problems. In this study, we provide a comprehensive analysis of the side effects associated with this ability to switch reasoning thoughts.
We utilize the Llama--33-77B model to automatically segment a response into reasoning thoughts due to its superior capabilities in both instruction following and mathematical reasoning. Initially, manually analyzed responses from the QwQ-32B-Previie model to gather expressions indicative of shifts in thought. We then tasked the Lllama-3.37005 model with scanning the entire response to identify all occurrences of such expressions. Furthermore, we asked the model to determine whether these expressions truly signify change thought or merely reflect a stylistic pattern in the response. Only the expressions indicating a genuine thought shift were used as separators for reasoning processes.
3 LRMs Switch Thinking More Frequently on Harder Problems Figure 3 shows the averaged thoughts and tokens in generated responses across various difficulty levels in the MATH500 test set. Clearly, all models generate more reasoning thoughts with the increase of difficulty level, which is
3

---

12
Thoughts Tokens
12
Thoughts Tokens
12
Thoughts Tokenss
10
#Thoughs
#Thoughs
Thoughss
#Tokons (K)
HTokeen
HTokons
3.1
2.7
1.9
2.5 4.0
2.1
3
Level (Difficulty))
Level (Dificulyyy))
Lovel (Difliuulty))
(a) M--Q-32B-Previen
(b) DeepSeek-R R1-Preview
(c) DeepScck-RI R1-61BB
Figure 3: Average number of thoughts and tokens across different difficulty levels on MATH500.
Correct Response
Response
Correct Response
Incorrect Response
14000
40
8000
15
263
7271
Generated Takens
12000
Number of Thoughss
Generated Tokens
Number Thoughss
10000
21.
10
20
4000
6000
4000
2.44
10
2000
2000
QuQQPPey
RI-Prev
R1-6718
RI-Prew
R1-671B
QuQ-Prev
R1-671B
QuQ.Prevv Prev
R1-671B
Qu
(a) Math500-Hard
(h) GPQA Diamond
Figure 4: LRMs switch thinking more frequently incorrect responses, thus expend more tokens
without contributing to accuracy.
consistent with the growth of generated tokens. This observation suggests that as the complexity of the problems increases, the models tend to switch thoughts more frequently. This behavior implies that LRMs are able to dynamically adjust their reasoning processes to tackle more challenging problems. The following experiments focus on Level in the MATH500 test set (MATH500-HaR Hardd.
Increased Thought Switching in LRMs during Incorrect Responses When examining the behavior of LRMs, we observe a distinct pattern how they handle incorrect responses. As depicted in Figures [nd these models exhibit significant increase the frequency of thought switching while generating incorrect answers across all test sets. This trend suggests that although the models designed to dynamically adjust their cognitive processes solve problems, more frequent thought switching does not necessarily lead to higher accuracy. Essentially, the models may be expending additional computational resources evidenced by an increase in generated tokens without achieving more accurate solutions. These insights are crucial because they highlight the need not only to explore additional cognitive pathways when faced with challenges but also to operate in a more targeted and efficient manner, thereby improving accuracy even when complex reasoning is required. In the following sections, we empirically validate the inefficiencies associated with frequent thought switching in incorrect responses.
2.2 Existence of Underthinking
The behavior of frequent thinking switch incorrect responses could stem either from (1) genuine underthinking, where the model succeeds in finding promising strategies but fails to stick with them, or from (2) lack of understanding. prompting it to explore diverse but ineffective approaches. To disentangle these possibilities, we propose assessment framework that evaluates whether abandoned reasoning path is actually sufficient to derive a correct answer. By focusing on whether the model can persistently follow and deepen single, promising line of thought, we can identify instances of underthinking.
Assessing Thought Correctness In the example presented in Figure we observe that some early thoughts may lead to the correct answer. For instance, Thought initiates correct interpretation

---

by recognizing that the given equations resemble those of ellipses centered at (0,0) and (20. 1). Setting the two expressions equal a valid approach to finding common points (z. y) that satisfy both equations. Instead of concentrating on thoroughly exploring the plausible thought with further algebraic manipulation and optimization techniques, the model frequently shifts its focus and uses approximately 7,270 additional tokens without arriving at a correct answer. Ultimately, it concludes with a guessed answer that lacks support from the extended COT process.
We leverage LLMs to assess whether each thought leads to a correct answer using the prompt detailed in Appendix Specificall we use two models distilled from DeepSeek-R1-67111 based on Llama and Qwen- DeepSeek-RR Biieeekk-RRDDD- RI-Distill-Llan
70B and DeepSeek- RI RI-Dissill--Qenn-22222 Qwen-32B, which achieve new -f-te-of-the--e art results for dense models across various reasoning benchmarks. If at least one model generates a confidence score of 2 for a thought, we regard it as correct thought.
We evaluate the accuracy of assessment approach using responses generated by Qwen-32B- Preview for 90 instances from the AIME 22-24 test sets. We utilize the final thought in each response as the test example and its correctness as the ground-truth label. To ensure fair comparison, we randomly streamline correct thoughts to match the average length of incorrect thoughts. Ultimately, we have 35 correct thoughts with an average length of 1 tokens and 55 incorrect thoughts with an average length of 278.3 tokens. Our assessment approach achieves accuracies of 82.9 % for correct examples and 81.8 % for incorrect examples, demonstrating its effectiveness.
Early-Stage Thoughts Are Correct but
50%
DeepSeek RI -6188
A Abandoned in Incorrect Responses Fig- ure [ depicts the ratio of correct thoughts each indxx in incorrect responses on the three challenging test sets. The analysis highlights critical insight into the phenomenon of un- derthinking. Specifically, a notable proportion of initial thoughts across various models were correct but were not pursued to completion. This tendency to abruptly shift away from these promising thoughts indicates an inad- equate depth of reasoning, where potentially correct solutions are prematurely abandoned before being thoroughly explored. This ob- servation suggests a need for enhancing the models' ability to persistently explore specific line of reasoning deeply and accurately before opting to switch to alternative thought processes.
DaepSack- RI-Preview
40%
Qu@--1BePreviie 34.3%
Correctness Ratio
30.6%
30%
33
9%
25.0%
31.4%
31.4%
20.0%
20g4
2 :
%%
20%
1 3.3%%
13.3%
10%
0%
2
3
4
5
6
7
8
9
210
Index of Thought
Figure 5: The ratio of correct reasoning thoughts at each index in incorrect responses.
Most Incorrect Responses Contain Correct
100%
DespSeck- R1-67BB
Thoughts Figure the thought correct- ness ratios in incorrect responses from vari-
34 24%%
R1 Preeview
80%
166
QwQ) 32B Breview
ous models. We observe that over 70% of
Distribution
63.25 256
60%
incorrect responses contain at least one cor- rect thought. Furthermore, in more than 50% of these responses, over 10% of the thoughts are correct. Combined with observations from Figure [5] this suggests that while LRMs can initiate correct reasoning pathways, they may struggle to continue these pathways to reach the correct conclusion. This highlights the im- portance of encouraging models to maintain and expand their initial correct thoughts to synthesize them into accurate final answers. These insights lead us to propose an underthinking metric based on the presence of the first correct thought in the subsequent section.
59.5%
17.4%
40%
16.85%
36.97
32.4%
20%
22.2%
10.0
11.1%
0%
>00
20.1
20.2 20.3 20.4 20.5
20.6 20.7
20.8
20.9
Ratio of Correct Thoughts
Figure 6: The distribution of thought correctness ratio in incorrect responses.
5

---

2.3 Empirical Underthinking Results
In this section, we propose a metric for empirically assessing underthinking issues based on token efficiency, complementing the widely used accuracy metric.
Underthinking Metric Intuitively, if model generates correct thought early stage and then switches to other thoughts without reaching a correct answer, the tokens generated thereafter do not contribute to reaching a correct solution and are considered inefficient due underthinking. The underthinking score, denoted as ÉUT, is defined as:
N Σ ==1
SUT -
T
Here, N represents the number of instances in given test set where the evaluated model generates incorrect responses. T; is the total number of tokens in the i-th incorrect response, and 7; is the number of tokens from the beginning of that response up to and including the first correct thought. there no correct thought in the i-th response. 7; = T, indicating that the model lacks an understanding of this problem, leading it to explore diverse but ineffective approaches. Therefore, it cannot be considered underthinking. Consider Figure 2 as an example: the first reasoning thought 411
can reach a correct answer if fully explored, with = 411. Consequently, &ur = which can be considered extremely inefficient, reflecting high underthinking score.
0.946,
7681
The metric fuT complements the accuracy metric by quantifying the extent underthinking by measuring the token efficiency in generating effective content within an incorrect response:
lower value of {ur indicates higher token efficiency, meaning that greater proportion of tokens in incorrect responses contribute towards reaching correct thought before switching to another thought. This suggests that the model more efficient in token utilization even when it fails to provide a correct answer.
A higher value of fuT signifies lower token efficiency, indicating that a larger number of tokens do not contribute effectively towards generating correct thought. This reflects greater underthinking. where the model generates redundant or irrelevant tokens by frequently switching thoughts.
Empirical Results Table pro-
Table 1: Underthinking scores on challenging testsets. Models
vides insights into model performance across challenging test sets, evaluat- ing both accuracy and underthinking (UT) scores. Clearly, all LRMs suffer from significant underthinking issues, although there are considerable differ- ences across models and test sets. The results reveals that the relationship be- tween model accuracy and underthink- ing varies across different datasets. On the MATH500- Hard and GPQA Diamond datasets, higher accuracy achieved by the superior DeepSeek- R1-671B model accompanied by higher UT Scores, indicating more underthinking in incorrect responses.
Accuracy(t) UT Score (L)
MATH500-Hard (Level 5)
QwQ-32B -reeiee
84.3
58.2
DeepSeek-Re -I-Peeeww
83.6
61.5
DeepSeek-R1-677
92.5
65.4
GPQA Diamond
1-Q--2B-Preeviee DeepSeek-R1-6711
59.6
48.3
73.2
58.8
AIME2024
QwQ-32B-Prewve
46.7
65.0
DeepSeek-R1-B Ri--eevwww
46.7
75.7
DeepSeck-R1-611
73.3
37.0
This suggests that while the model is more capable overall, it may produce longer but less effective reasoning when uncertain, possibly due to exploring multiple incorrect reasoning paths without efficiently converging the correct solution. Conversely, on the AIME2024 test set, the DeepSeek- R1-671B model not only attains higher accuracy but also exhibits a lower UT score, reflecting less underthinking and greater token efficiency. This implies that the model's reasoning remains focused and effective even when it does not arrive at the correct answer, perhaps due to better alignment with the problem types and reasoning processes required by the AIME2024 task.
These findings illustrate that underthinking behavior sensitive to the nature of the dataset and the tasks involved. The larger model's superior capabilities do not uniformly translate to less

---

Table 2: Underthinking scores of Qwen3 Family on AIME24. We report the average number of
thought-switching tokens (V in Equation 3.1 and the average interval between them.
Accuracy (1)
Switching Tokens
Weighted
Models
Pass @ 1
Pass Pass@8 Pass 16
Number Interval
UT Score (L)
Qwen3-4B
65.6
79.5
81.6
83.3
27.6
372.1
15.0+18.5
Qwen3-8B
64.6
78.0
81.6
83.3
20.3
561.4
16.8+20.6
Qwen3-14B
70.8
82.3
86.6
90.0
18.2
506.6
13.4420.1
Qwen3-32B 73.8
87.5
90.0
93.3
13.7
681.3
10.6+115
underthinking across all tasks. In some cases, increased model capacity leads to more elaborate but inefficient reasoning in incorrect responses, while in others, it enhances both accuracy and reasoning efficiency. Understanding the underthinking phenomenon is crucial for developing models that not only provide correct answers but also exhibit effective reasoning processes.
Furthermore, due to different training strategies, models across different families may differ funda- mentally: some reach correctness intuitively (low UT score), while others do so through iterative refinement (higher UT score). Since both approaches can achieve high accuracy, this observation explains the weak correlation between UT score and accuracy shown in Table [ Nevertheless, within specific model families, UT scores show clearer correlation with accuracy. This trend may result from similar training strategies that reduce behavioral variance, supported by the results in Table 2 Within the Qwen3 family, for instance, we observed a clear trend where the severity of underthinking decreases as model size increases.
3 Mitigating Underthinking Issues
In this section, we propose a lightweight mechanism that mitigates underthinking issues without requiring any model fine-tuning.
3.1 Decoding with Thought Switching Penalty
Aforementioned findings show that LRMs prioritize exploring many solutions over deeply investi- gating one. Inspired by the success of the coverage penalty in neural machine translation (Tu et al. 2016 Wu et al. 2016), we propose novel decoding algorithm with thought switching penalty to encourage the model to explore potential thoughts more thoroughly before moving on to new ones.
Standard Decoding In standard decoding, the probability of each token at position / is computed using the softmax function over the logits 2, [V| ((V) is the vocabulary size) in the output layer:
exp (Zt,w)
P(z, = v/sre)) Evev exp (2t,0r)
where 2t, E Z, is the logit for token By repeating this step for each position in the sequence, the model generates sequences of tokens, computing probabilities for each possible continuation.
Thought Switching Penalty (TIP) To encourage the model delve deeper into current thoughts before switching, we introduce a penalty on tokens that are associated with thought transitions. A key consideration in designing this penalty is to distinguish between unproductive, rapid thought- switching and deliberate, strategic shifts in reasoning (e.g.. backtracking) (Gandhi et al.) 2025). Therefore, TIP is designed to be selective: specifically targets and penalizes thought-swittcing tokens only when they appear with high frequency within a recent context, pattern indicative of shallow exploration. This ensures that isolated or intentional shifts in thought remain unpenalized, preserving the model's ability to employ effective complex reasoning strategies like backward chaining, Let V. C V be the set of tokens associated with thought switching (e.g.. "alternatively"). modify the logits as follows:
21,0 - a, if E E and t < 1 +
21,0
21,00
otherwise
7

---

Table 3: @ass@k performance of the proposed TiP method. We report the average number of thought- switching tokens (V in Equation 3.1 and the average interval between them in the generated samples.
Accuracy (1)
Switching Tokens
Weighted
Models
Pass @1
Pass@4 Pass@8 Pass 16
Number Interval UT Score (1)
MATH500-Hard (Level 5)
DwQ-32B-Previn
83.1
92.4
94.4
95.8
12.6
445.6
11.7=20.5
+ TIP
83.7
93.2
95.3
96.4
5.7
517.6
11.0=19.5
R1-Distifl S1-Diisill-Qeen-325
Qwen-22en-3
88.3
94.5
96.1
97.6
6.7
792.5
3.3
TIP
89.4
94.6
96.1
97.0
2.7
964.0
3.0
GPQA Diamond
TwQ--2B-Prrevie
57.6
78.5
85.3
90.3
21.1
356.8
25. +/2.9
TTP
59.1
78.9
85.8
91.2
7.3
432.5
23.2
11-Distill-Qwen--33
61.6
78.1
83.6
86.9
13.4
548.6
22.3
TIP
61.7
80.2
86.6
90.4
4.6
747.1
23.1 225.
AIME2024
QwQ-32B-Previe
38.3
53.7
58.5
62.7
16.1
459.7
40.6+28.1
+ TIP
44.1
61.6
68.3
74.0
13.9
515.7
35.8+27.8.
RI-Distifl
61.4
75.9
79.7
BI.7
8.2
819.5
19.6-20.6
+ TIP
64.1
79.0
81.7
83.0
4.5
1018.0
17.7=20.6.
DeepSeek-RI
73.8
86.2
88.8
89.8
13.8
580.1
14.6
+ TIP
74.8
86.4
88.8
89.8
5.7
941.6
13.0
where
2 0 (Penalty Strength) a parameter controlling the strength the penalty applied to thought- switching tokens. A larger a results in greater reduction of the logits for these tokens, making them less likely to chosen.
Z (Penalty Duration) specifies the number of positions from the start of a thought at V, during which the penalty is active. A larger 3 extends the penalty over more positions, further discouraging early thought switching.
When 0 or 3 0 the penalty is effectively disabled, and the decoding process reduces to the standard decoding algorithm. The adjusted logits &,, reduce the probability of generating thought-switching tokens within specified window, encouraging the model to continue expanding on the current thought before moving on. The new probability distribution becomes:
exp (λt,v)
P(e. = = x(xxe)= = Ever exp (2),))
3.2 Experimental Results
For reliable evaluation, we report Pass@1 1 computed from 32 samples per problem with a temperature of 0.7 and top p value of 0.95. We tuned {3, 5, 10, 20. 30) and [300, 400, 500, 600, 700) on the AIME 2022-2023 development set using MMVQ-3B-Preevve
selecting the best pair a = 3 600 for all models and benchmarks. Please refer Appendix B.2 for details.
Standard Decoding 3 that our TIP method consistently improves performance in all cases by mitigating the underthinking issues. On AIME-24, Pass@) improves by 5.8% on QwQ 32B-Pr,, 2.7% on -1-Distill-wwen and 1.0% on ReepSeek-R1, while the underthinking (UT) score drops across the board. Observing the indicators, we see fewer thought-switching larger intervals when using TIP, confirming that our method encourages models to explore individual reasoning paths more thoroughly and mitigates underthinking. For example, when applying TIP to DeepSeek-R1 on AIME2024, the average thought-switching tokens decreased (13.8 +13.8+5577), and the average interval between switches increased (580.1 1-991.6). These changes reflect fewer premature transitions, resulting in more focused and hluaa--lik- exploration of reasoning paths.
tokens and

---

Table 4: Results of TiP for best-of-N sampling on AIME2024. We conducted 10,000 trials by randomly sampling from the samples and reported the average results. "(Averaged)" denotes the average performance over 32 samples.
4 Samples
8 Samples
16 Samples
Models
Acc.(t)
UT (L)
Acc.(1)
UT (1)
Acc.(t)
UT (J)
QwQ (Averaged)
38.4
40.5
38.3
40.6
38.3
40.6
+ TIP (Averaged)
44.1
35.8
44.0
35.9
44.0
35.9
QwQ + Self-Consistencc
43.7
35.4
44.3
34.0
44.6
31.9
+ TTP
51.4
26.6
53.4
24.3
53.9
24.1
QwQ Laconic Decoding
47.0
28.2
47.0
25.5
45.1
24.0
+ TiP
50.3
26.7
51.6
23.3
50.9
20.8
R1 R1-Distill-Qwen (Averaged)
61.4
19.2
61.3
19.2
61.3
19.1
+ TIP (Averaged)
64.1
17.8
64.0
17.7
64.1
17.7
31-Distill-Qwer Self Saff-Consistency
67.0
13.4
67.8
11.4
68.9
8.9
+ TIP
69.9
12.5
71.4
11.0
72.3
9.1
+ Laconic Decoding
71.1
11.3
74.4
8.7
77.5
7.4
+ TIP
75.4
9.8
78.0
7.3
77.9
6.5
RI (Averaged)
73,9
14.5
73.7
14.6
73,8
14.5
TIP (Averaged)
74.8
13.0
74.8
12.9
74.8
13.0
RI + Self-Consistency
79.3
10.1
79.8
9.8
79.7
9.3
+ TIP
81.3
7.5
82.2
6.4
82.1
5.8
R1 + Laconic Decoding
81.4
8.1
82.6
6.2
83.2
5.1
+ TIP
83.1
7.4
83.8
6.6
83.3
6.7
To further assess TIP, we combined it with two widely used best-of-N sampling methods: (1) Self-Consistency (Wang et al.) 2023). selecting the most consistent answer from multiple samples; (2) Laconic Decoding (Raoof & Dimakis 2025). selecting the shortest of multiple generated answers, based the observation that correct responses often have fewer tokens.
Best-of-N Sampling
Table indicates that using TIP consistently boosts accuracy across all model-method combinations. For instance, applying TIP to Self-Consistency with QwQ-32B-Prent Preview (4-sample setting) signifi- cantly raises accuracy (43.7% -51.4% and reduces UT scores (35.4-266.6) Similarly, combining Laconic Decoding with TIP yields consistent gains, particularly pronounced for stronger models samples). These results clearly demonstrate that the TIP method successfully complements existing sampling strategies, encouraging more thorough reasoning and reliably mitigating underthinking issues in challenging mathematical reasoning scenarios.
(e.g., EI--DitilllQween
74.4%%>78..l
Overall, the TIP approach represents a significant step toward addressing the underthinking problem in LRMs. Although the hyperparameters tuned the AIME 2022 and 2023 test sets using the QwQ-32B-Pree
model, the consistent improvements observed across various test sets and models with the same hyperparameters validate the generalizability of the method. Our findings also suggest that the TIP method synergizes well with best-of-N sampling strategies, leading to further improvements in accuracy and reductions in underthinking scores. This indicates that encouraging more thorough exploration of individual reasoning paths complements the diversity introduced by sampling methods.
4 Related Work
Scaling Test-Time Compute Recent advancements in deep reasoning models, such OpenAl's ol, have emphasized scaling test-time compute improve complex problem-solving capabilities. One approach focuses expanding the search space by considering multiple candidate solutions during decoding, exemplified by self-consistency (Wang et al.) 2023), best-of-n decoding, and minimum Bayes risk decoding (Lightman et al., 2024 Li et al. 2023 3 Khanov et al. 2024 Heineman al. 2024 Wu al., 2024). Another influential direction involves promoting human-like deep
thinking, beginning with Chain-of-Thougle (Wei al. 2022) where models mimic human reasoning

---

processes Cesista 2024 Pfau et al. 2024). Recent models, such as QwQ (Qen 2024), DeepSeek- RI (DeepSeek) 2025), and Kimi-1.5 (Kimi 2025). leverage reinforcement learning (RL) to enable
strategic, reflective reasoning and improve accuracy in complex tasks.
Efficient Thinking Efficient reasoning matters as much for language reasoning models (LRMs) as does for human cognition. Models sometimes suffer overthinking, wasting resources on trivial paths (Chen et al., 2024). In contrast, we focus on the less-explored issue of underthinking, where models prematurely abandon promising reasoning directions, limiting performance on challenging problems. Along this direction, recent research has begun exploring methods to enhance reasoning efficiency. For instance, Laconic decoding implements shortest-of-n decoding strategies to minimize error-prone lengthy responses (Raoof & Dimakis 2025), while Muennighoft al. (2025) propose techniques to optimize test-time computation through dynamic termination signals.
Manipulating Decoding Penalties
Penalty mechanisms in NLP decoding have become increas- ingly relevant to addressing shortcomings in traditional search methods. Length normalization
penalties (Jean et al., 2013 Koehn & Knowles 2017] Tu et al. 2017] Murray & Chiang, (011)) encourage appropriate translation lengths, improving fluency and adequacy. Additionally, coverage penalties (Tu et al. 2016) Wu et al. (0166) reduce textual redundancies by ensuring comprehensive attention over source tokens. (See et al. (2017) also applied these ideas summarization tasks. In this work, we introduce specific decoding penalties to mitigate underthinking, prompting models to sustain deeper reflection rather than superficial or frequent strategy shifts. To our knowledge, we are the first to investigate decoding penalties to address the underthinking problem.
Conclusion
In this work, we identified underthinking as key limitation for LRMs performing challenging reasoning tasks, highlighting how premature abandonment of promising paths reduces efficiency and accuracy. We developed new metric to quantify underthinking based on token efficiency in incorrect responses, and introduced a decoding strategy thought switching penalty (TIP) to encourage deeper exploration before shifting reasoning directions. Empirical evaluations show that TIP significantly reduces underthinking and improves performance on difficult reasoning benchmarks, without requiring additional model training.
This work contributes to deeper understanding of reasoning processes in LRMs and provides a practical approach align their problem-solving capabilities. Future directions include explor- ing adaptive mechanisms within models to self-regulate thought transitions and further improving reasoning efficiency.
References
Cesista, F. L. Multimodal structured generation: Cvpr's 2nd mmfmm challenge technical report. arXiv preprint arXiv:2406. 1/ 11403, 2024.
Chen, X., Xu, J., Liang, T., He, Z., Pang, J., Yu, D., Song. L., Liu, Q., Zhou, M., Zhang, Z., Wang, R., Tu, Z., Mi, H., and Yu, D. Do not think that much for 2+3=? the overthinking of ol-like 1lms, 2024. URL/https: //axxii////xx arriv..iiiivv.iii http:///axxvv..../bbbbb
DeepSeek. Deepseek-rl: Incentivizing reasoning capability in llms via reinforcement learning. 2025. wwt.eaaww......a....ooooorraaaaa wttg///rrpss.:22777799555
URL httth:://pppii semanticscooolrrr
Gandhi, K., Chakravarthy, A., Singh, A., Lile, N., and Goodman, N. Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective stars. arXiv preprint arXiv:2503.01300 307 2025.
He, C., Luo, R., Bai, Y., Hu, S., Thai, Z., Shen, J., Hu, J., Han, X., Huang, Y., Zhang, Y., et al. Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual multimodal scientific problems. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 3828 18588,8800000 2024.
10

---

Heineman, D., Dou, Y., and Xu, W. Improving minimum bayes risk decoding with multi prompt. In Proceedings of the 2024 Conference on Empirical Methods Natural Language Processing, pp- 22525-2265 22545, 2024.
Hendrycks, D., Burns, C.,, Kadavath, S., Arora, A., Basart, S., Tang, E., Song, D., and Steinhardt, J. Measuring mathematical problem solving with the MATH dataset. In NeurIPS, 2021.
Hong. W., Yu, W., Gu, X., Wang, G., Gan, G., Tang, H., Cheng, J., Qi, J., Ji, J., Pan, L., et al. Glm-4.1 v-thinking: Towards versatile multimodal reasoning with scalable reinforcement learning. arXiv e-prints, pp. arXiv-2507, 2025.
Jean, S., Firat, O., Cho, K., Memisevic, R., and Bengio, Montreal neural machine translation systems for wmn' 15. In Proceedings of the tenth workshop statistical machine translation, pp. 134-140, 2015.
Khanov, M., Burapacheep, J., and Li, Y. Args: Alignment as swrard-giided search. In The Twelfth International Conference on Learning Representations. 2024.
Kimi. Kimi k1.5: Scaling reinforcement learning with llms. 2025.
Kochn, P. and Knowles, R. Six challenges for neural machine translation. In Proceedings of the First Workshop on Neural Machine Translation, pp. 28-39, 2017.
Li, Y., Lin, Z., Zhang, S., Fu, Q., Chen, B., Lou, J.-G., and Chen, W. Making language models better reasoners with step-aware verifier. In Rogers, A., Boyd-Graber, J., and Okazaki, N. (eds.), Proceedings of the 6l Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 5315 5333,, Toronto, Canada, July 2023. Association for Computational Linguistics. doi: 10.18653/v
URL httppss://aalaathhoooooo ////a/rr////aallaaaoooooooo////g org/
acl acl- 291
Lightman, H., Kosaraju, V., Burda, Y., Edwards, H., Baker, B., Lee, T., Leike, J., Schulman, J., Sutskever, I., and Cobbe, K. Let's verify step by step. In The Twelfth International Conference on Learning Representations, 2024. URL
MAA Committees. Aime problems and solutions. and_Solutions
http://arrooprooleesolvii.gg...
index, Mhdex.php/AIME.Be. Awtp:ppppAAAEEeoooeeeeeeeo
Muennighoff, N., Yang. Z., Shi, W. Li, X. L., Fei-Fei, L., Hajishirzi, H., Zettlemoyer, L.,, Liang, P., Candès, E., and Hashimoto, sl: Simple test-time scaling. arXiv preprint arXiv:2501,19393 2025.
Murray, K. and Chiang, Correcting length bias in neural machine translation. In Proceedings of the Third Conference on Machine Translation: Research Papers, pp. 212-223, 2018.
OpenAL. Learning
reason with llms.
https://oppeai.comm http:/pppaaicccmiinnieeee index/
learning- teee--torreeoooo wwtt- 11ms, 2024.
Pfau, J., Merrill, W., and Bowman, S. R. Let's think dot by dot: Hidden computation in transformer language models. arXiv preprint arXiv:2404.15758. 2024.
Qwen. Qwq: Reflect deeply on the boundaries of the unknown, November 2024. URL https 7/qwenlm. git.in.itttuu..... 10/ wws.io//lloggoo qwq-ppqp3b330 1oogg-3bbppeee preview/
Raoof, N. and Dimakis, A.
Laconic decoding. 1885447830120362099 February 2025.
httts::/xx.com//eexxxiiiiiis
Rein, D., Hou, B. L., Stickland, A. C.,, Petty, J., Pang, R. Y., Dirani, J., Michael, J., and Bowman, S. R. Gpqa: A graduate-level google-proof q&a benchmark. arXiv preprint arXiv:2311.12022. 2023.
See, A., Liu, J., and Manning, C. D. Get to the point: Summarization with pointer-generato networks. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics ( (Voluee I: Long Papers), pp. 1073-1083, 2017.

---

Tu. Z., Lu. Z., Liu, Y., Liu, X., and Li, H. Modeling coverage for neural machine translation. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume I: Long Papers), pp. 76-85, 85, 2016.
Tu, Z., Liu, Y., Shang, L., Liu, X., and Li, H. Neural machine translation with reconstruction. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 31, 2017.
Wang, X., Wei, J., Schuurmans, D., Le, Q. V., Chi, E. H., Narang, S., Chowdhery, A., and Zhou, D. Self-consistency improves chain of thought reasoning in language models. In The Eleventh International Conference on Learning Representations, 2023, URL https: net/ #orum/1d=11L1NINMMr
Wei, Wang, X., Schuurmans, D., Bosma, M., Xia, F, Chi, E., Le, Zhou, D., al. Chain-of- thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824 24837, 2022.
Wu, I., Fermandes, P., Bertsch, A., Kim, S., Pakazad, S., and Neubig, G. Better instruction-folloving through minimum bayes risk. arXiv preprint arXiv:2410.02902, 2024.
Wu, Y., Schuster, M.. Chen, Z., Le, Q. V., Norouzi, M. Macherey, W., Krikun, M., Cao, Y., Gao,
Q., Macherey, K., Klingner, J., Shah, A., Johnson, M., Liu, X., Kaiser, E.,, Gouws, S., Kato, Y., Kudo, T., Kazawa, H., Stevens, K., Kurian, G., Patil, N., Wang, W., Young, C., Smith, J., Riesa, J., Rudnick, A., Vinyals, O., Corrado, G., Hughes, M., and Dean, J. Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. arXiv, 2016.
Xiaomi, L.-C.-T. Mimo-vl technical report, 2025, URL
org/ abs 03569
12

---

A Assessing Thought Correctness
In the example presented in Figure 2 we observe that some early thoughts may lead the correct answer. For instance, Thought 1 initiates a correct interpretation by recognizing that the given equations resemble those of ellipses centered at (0,0) and (20,11). Setting the two expressions equal is valid approach to finding common points (z. y) that satisfy both equations. Instead of concentrating on thoroughly exploring the plausible thought with further algebraic manipulation and optimization techniques, the model frequently shifts its focus and uses approximately 7,270 additional tokens without arriving at a correct answer. Ultimately, it concludes with a guessed answer that lacks support from the extended COT process.
We leverage LLMs to assess whether each thought leads to a correct answer using the following prompt:
Problem P= [problem]
Solution Draft S (split solutions} Correct Answer A (expected answer)
1. Please analyze the relevance between the solution S and the problem P, and conduct some verifications to check the correctness of the solution itself. Please think step by step to give an explanation **EXPLANATION"
2. If you think the solution draft S can lead to the correct answer of the problem P. please stick the line of thinking without deviation and carry it through completion. If you think it cannot yield the correct answer or you' re not sure, don't 't force yourself to give an answer and generate ***
3. Please tell me honestly how confident you are that you can solve the problem P correctly based on the the solution draft S. Out of 2, please generate your confidence score **CONFI- DENT SCORE**
Please output "EXPLANATION*** and SONNFIDENTSSCRRFEE according to the following format:
EXPLANATION: \boxed()
CONFIDENT SCORE: \boxed[]
Specifically, we use two models distilled from DeepSeek-R1-4 based on Llama and Qwen DeepSeek-R R/ Rel--isiill-Lamate -lama--00 and PrrpSSek--I-Diisee RI-DDisttlll---wee32B which achieve new state-of- the-art results for dense models across various reasoning benchmarks. If at least one model generates confidence score of 2 for a thought, we regard it correct thought.
We evaluate the accuracy of our assessment approach using responses generated by Qwen-32B- Preview for 90 instances from the AIME 2022, 2023, and 2024 test sets. We utilize the final thought in each response as the test example and its correctness as the ground-truth label. To ensure fair comparison, we randomly streamline correct thoughts to match the average length of incorrect thoughts. Ultimately, we have 35 correct thoughts with an average length of 278. 1 tokens and 55 incorrect thoughts with an average length of 278.3 tokens. Our assessment approach achieves accuracies of 82.9% for correct examples and 81. 8% for incorrect examples, demonstrating its effectiveness.
B Experimental Details of TIP
B.1 Selection of Thought-Switching Tokens
A key component of our TIP decoding strategy is the use of predefined set of thought-switching tokens that signal a potential switch in the reasoning path. The selection of these tokens treated as a task-specifee hyperparameter. For our experiments, they were chosen empirically based on qualitative analysis common thought-switching patterns observed the model's outputs. Specif- ically, we select alternative and messy as thought-switching tokens in our implementation. This approach provides a simple yet effective mechanism that can be adapted to different tasks or model behaviors without extensive tuning. Besides, since LLM tokenizers can split single word into
13

---

Table 5: Accuracy on AIME2022-23 with respect to different values of a and B3.
Pass@1 1
Cx
Accuracy
5
10
20
300
35.2
37.0
39.0
39.4
400
39.3
37.1
37.1
38.4
B
500
38.5
38.7
39.1
39.2
600
39.8
39.4
38.0
38.0
700
37.1
39.4
39.0
38.3
multiple subword tokens, the switching penalty is applied exclusively to the first subword token of designated thought-switching word.
B.2 Grid Search of and
To ensure robust conclusions, we report Pass@) results computed from 32 samples per instance. We calculate the weighted underthinking score for each instance over its 32 samples:
32
1
ÉOUT
(s))
32
where s; the i-th sample of the instance, and (ET((;)) = 0 when 8; is correct.
By adjusting a and 3, we can control the model's behavior to achieve the desired level of thought exploration. We performed grid search with a values in [3, 10, 20, 30] and 3 values in [300, 400, 500, 600, 700] using development set that included the AIME 2022 and 2023 test sets. 5ists the impact of varying the penalty strength a and penalty duration 8 on the model's accu- racy. We observe that increasing the penalty strength generally leads to an improvement in accuracy up to certain threshold, after which the benefits plateau even diminish. Adjusting the penalty duration 3 also significantly affects performance: At lower penalty strength (a = 3), increasing from 300 600 results in accuracy gains from 35.2% 39.8%, the highest observed accuracy in our experiment. Conversely, at higher penalty strengths (a 20), extending 3 beyond 300 leads to decrease in accuracy, indicating that too long a penalty duration can hinder performance when combined with strong penalty. We selected 3 and B 600 for our subsequent experiments.
C Generalization to Multimodal Reasoning
To investigate underthinking extends beyond text-only domains, we evaluated two vision-language (Hong)
Table 6: Underthinking scores challenging testsets.
Models
Accuracy(t)
UT Score (L)
models,
MiMo- MiMo-VL-7B-B VL-7B-RL GLM-4. V-Thnnking
56.7
4.8
et al. 2025) and MiMo-VL. 7B-RL (iiaomi 2025). on the
58.7
17.1
OE_MM maths en_ COMP subset of OlympiadBench (He al. 2024). This benchmark contains competition-level mathematics problems that require synthesizing information from both text and images. As shown in Table 6 both models exhibit underthinking. This finding leads two implications: first, our framework can be adapted to analyse multimodal reasoning. and second, it suggests that underthinking is a general reasoning failure not confined single modality.
14

---

NeurIPS Paper Checklist
1. Claims
Question:
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: this paper, we define the underthinking issue in long reasoning models, introduce novel metric and propose decoding approach with thought switching penalty.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as is clear that these goals attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification: In Section 2.3 we claim that underthinking behavior is sensitive to the nature of the dataset and the tasks involved. The larger model's superior capabilities not uniformly translate to less underthinking across all tasks, which needs further exploration.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "I "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect the scope of the claims made, e.g., if the approach was only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and prool's
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
15

---

Answer:
[NA]
Justification:
The paper does not include theoretical results.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proof's can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided not)?
Question:
Answer: [Yes]
Justification: We elaborated in detail on the implementation details of the proposed metric and decode strategy.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, descríbing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily new model architecture, the paper should describe the architecture clearly and fully.
(c) the contribution is a new model (e-g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should possible for other researchers to have some path to reproducing verifying the results.
5. Open access to data and code
16

---

Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, as described in supplemental material?
Question:
Answer: [No]
Justification:
We will make our code publicly available soon.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.co cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (c.g., for a new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https
//nips //ips.cc//pil wttp:ccppppcccceeeeeeeeee..c.ett httaa//gguudeee/eeeeabiiissssss /Cc////oddiiisssseeeeeee ssiisssiiciiiyyyycc for more details.
The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Question:
Answer: [Yes]
Justification: We have provided a detailed description of the backbone model used in the experiment, the generation details, and the hyperparameter grid search result of TIP.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification:
We present the pass@k results for various backbone models.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by error bars, confi-
dence intervals, statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for
example, train/test split, initialization, random drawing of some parameter, or overall with given experimental conditions).
17

---

The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
should be clear whether the error bar is the standard deviation or the standard error of the mean.
It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not to show in tables figures symmetric error bars that would yield results that are out range (c.g. negative emror rates).
If error bars reported in tables plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables the text.
8. Experiments compute resources
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes]
Justification:
We report related information in appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't 't make it into the paper).
9. Code ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics
Answer: [Yes]
Justification: In this paper, we adhere strictly to the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special cireumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification:
This work is foundational research and not tied to particular applications.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
18

---

The conference expects that many papers will be foundational research and not tied particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms monitor how system learns from feedback over time, improving the efficiency and accessibility of MI..
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [NA]
Justification: In this paper, no data models were released.
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Lieenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper. properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: We have complied with the license for using the dataset.
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (c.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (c.g., website), the copyright and terms of service of that source should be provided.
If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswi thcode. com com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
19

---

If this information is not available online, the authors are encouraged to reach out to the asset's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: The paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/mmoel as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsoureing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well details about compensation (if any)?
Answer: [NA]
Justification: The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question:
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA]
Justification:
The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Depending the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
20

---

Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology. scientific rigorousness, or originality the research, declaration is not required.
Answer: [NA]
Justification: The core method development in this research does not involve LLMs any important, original, or non-standard components.
Guidelines:
The answer NA
that the method development in this research does involve LLMs as any important, original, or non-standard components.
Please refer to our LLM policy for what should or should be described.
21


Reviews:
[{"review_id": "lDkxBYcQfh", "reviewer": "Reviewer_Po39", "summary": "The paper identifies underthinking in long-reasoning LLMs (LRMs)—a tendency to hop between reasoning threads without sufficiently exploring promising ones. It (i) formalises an underthinking score that captures token-efficiency in incorrect answers \n, (ii) shows the prevalence of the phenomenon across three maths-reasoning benchmarks, and (iii) proposes Thought-switching-penalty (TIP), a decoding modification that down-weights tokens signalling a strategy switch. TIP improves Pass@1 by up to +5.8 pp without fine-tuning and synergises with self-consistency and laconic decoding", "questions": "See the weakness part.", "limitations": "yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n\n1. To the best of my knowledge, this is the first paper that systematically characterise the \"underthinking\" in reasoning LLMs.\n\n2. Therefore this is also the first paper that proposed the SUT score, a valid metric for quantifying the underthinking behaviours.\n\n3. This paper really expanded my understanding of the LLMs' limitations beyond the simple accuracy metrics.\n\nWeakness\n\n1. The correct thought score is judged by the distilled LLMs, which may introduce bias.\n\n2. Rather than saying as a weakness point, I am a little bit curious that if this kind of analyse toolkit could be easily adapt to coding and multi-modal reasoning problems?", "was_revised": true, "final_justification": "I will maintain the original score, in my opinion this paper should be accepted.", "rebuttal": "Thank you for your positive assessment (rating 5) and for highlighting the novelty of our systematic characterization of underthinking in LRMs, our proposed SUT score (which you called a \"valid metric\"), and how it expands understanding beyond simple accuracy metrics. We appreciate your curiosity about extensions and are glad our work resonated with you.\n\n---\n> Q1: The correct thought score is judged by the distilled LLMs, which may introduce bias.\n> \n\nA1: We agree this is a critical aspect and have already quantified the classifier's reliability in the paper. As detailed in Lines 131-137, we validated our LLM-based classifier on a manually annotated set. It achieves **82.9% accuracy on correct thoughts and 81.8% on incorrect thoughts.** While not perfect, this level of accuracy is sufficiently high to reliably identify the trends central to our paper's claims, such as the correlation between frequent thought-switching and incorrect final answers.\n\nWe believe this establishes a strong baseline for this novel analysis task. We fully agree that developing more robust, model-independent evaluation methods is a valuable direction for future work, and we will emphasize this in the limitations section of the revised paper.\n\n---\n\n> Q2: Rather than saying as a weakness point, I am a little bit curious that if this kind of analyse toolkit could be easily adapt to coding and multi-modal reasoning problems?\n> \n\nA2: Thanks for suggesting we explore the applicability of our findings beyond math reasoning. Inspired by your feedback, we conducted new experiments on a multimodal benchmark.\n\n**Our analysis toolkit generalizes well to multimodal reasoning.** We evaluated two multimodal LRMs (QVQ-72B-Preview, GLM-4.1V-Thinking) on the OE_MM_maths_en_COMP subset of OlympiadBench, which requires reasoning over both text and images. The results clearly show that the underthinking phenomenon persists in this more complex, multimodal setting.\n\n| Models | Accuracy (↑) | UT Score (↓) |\n| --- | --- | --- |\n| QVQ-72B-Preview | 46.0% | 33.6 |\n| GLM-4.1V-Thinking | 58.7% | 17.1 |\n\nThis confirms that underthinking is a broad challenge not limited to text-only math problems. We will add these new results and a discussion to the final manuscript to strengthen the paper's general applicability."}, {"review_id": "t7ZHjRy8z9", "reviewer": "Reviewer_4W6S", "summary": "This work investigates the phenomenon of underthinking in current LRMs, where models frequently switch to different reasoning thoughts without fully exploring the path. It designs token efficiency metrics to measure such behaviors in QwQ-32B-Preview and Deepseek-R1-671B. To mitigate underthinking issues, this work develops Thought Switching Penalty to decrease the logit values during inference. The approach is evaluated on AIME-24 demonstrating that TIP reduces underthinking and improves accuracy .", "questions": "1. The TIP method works by penalizing the logits of certain keywords (like “alternatively”) that indicate thought switching. But some of these keywords might also reflect other useful cognitive behaviors, as discussed in a related work [1]. Do you think TIP might unintentionally suppress those behaviors too? Any insight or analysis would be helpful.\n\n[1] Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs.", "limitations": "The authors briefly mention limitations in Section 2.3, but a separate section outlining them more clearly would be helpful.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. This paper is well-written and content is clear and straightforward.\n2. The underthinking is an interesting concept to study the reasoning behaviors, providing a useful perspective in understanding LRMs.\n3. The work presents a thorough analysis of the correctness of intermediate thoughts and provides convincing empirical evidence to validate the presence of underthinking.\n\nWeaknesses:\n1. Table 2 is missing results for R1-Distill-Qwen-32B and Deepseek-R1 on MATH500-hard and GPQA Diamond. Also, from the table,  the results suggest that TIP yields more substantial accuracy improvements for models with lower baseline performance (such as QwQ on GPQA and AIME-24). Do you have any insight on this?\n\n2. (minor) The paper does not clearly explain why underthinking behavior appears in LRMs. A further discussion of its possible causes would help improve understanding.", "was_revised": true, "final_justification": "I have carefully read the authors' responses and encourage the authors to incorporate these results and clarifications into the revision. I've noted that some of the clarifications rely on hypotheses without concrete evidence, which is the main reason I am hesitant to provide a higher score. From the empirical side this paper makes a timely and valuable contribution.", "rebuttal": "Thank you for your supportive review and for praising the paper's clarity, the interesting concept of underthinking as a lens on LRMs, and our thorough analysis with convincing evidence. We're grateful for your detailed questions, which helped us refine our insights.\n\n---\n\n> Q1: Table 2 is missing results for R1-Distill-Qwen-32B and Deepseek-R1 on MATH500-hard and GPQA Diamond. Also, from the table, the results suggest that TIP yields more substantial accuracy improvements for models with lower baseline performance (such as QwQ on GPQA and AIME-24). Do you have any insight on this?\n> \n\nA1: Thank you for pointing this out. We have updated Table 2 with new results.\n\n1. **New Results:** We have added results for **R1-Distill-Qwen-32B** on MATH500-hard and GPQA Diamond. These results reinforce our claims: the model exhibits underthinking, and our TIP method successfully mitigates it to improve accuracy. Due to the limited rebuttal period and high computational cost, we were unable to complete the runs for DeepSeek-R1 but will ensure they are included in the final camera-ready version.\n2. **Insight on Performance Gains:** That’s a sharp observation. **We hypothesize that models with lower baseline accuracy (like QwQ on GPQA) may have been trained on data that inadvertently encourages underthinking, or were simply less optimized against this specific failure mode.** Consequently, TIP, which directly targets this issue, provides a larger relative boost. However, we emphasize that TIP consistently improves performance across *all* tested models, demonstrating its broad utility.\n\n| Models | **Accuracy (Pass@1) (↑)** | **Thought Number**| **Thought Interval**|**Weighted UT Score (↓)** |\n| --- | --- | --- | --- | --- |\n| **MATH500-Hard (Level 5)** |  |  |  |  |\n| QwQ-32B-Preview | 83.1 | 12.6 | 445.6 | 11.7±20.5 |\n| + TIP | 83.7 | 5.7 | 517.6 | 11.0±19.5 |\n| R1-Distill-Qwen-32B | 88.3 | 6.7 | 792.5 | 3.3±8.8 |\n| + TIP | 89.4 | 2.7 | 964.0 | 3.0±8.5 |\n| **GPQA Diamond** |  |  |  |  |\n| QwQ-32B-Preview | 57.6 | 21.1 | 356.8 | 25.1±23.9 |\n| + TIP | 59.1 | 7.3 | 432.5 | 23.2±23.2 |\n| R1-Distill-Qwen-32B | 61.6 | 13.4 | 548.6 | 22.3±25.0 |\n| + TIP | 61.7 | 4.6 | 747.1 | 23.1±25.3 |\n| **AIME2024** |  |  |  |  |\n| QwQ-32B-Preview | 38.3 | 16.1 | 459.7 | 40.6±28.4 |\n| + TIP | 44.1 | 13.9 | 515.7 | 35.8±27.8 |\n| R1-Distill-Qwen-32B | 61.4 | 8.2 | 819.5 | 19.6±20.6 |\n| + TIP | 64.1 | 4.5 | 1018.0 | 17.7±20.6 |\n| DeepSeek-R1 | 73.8 | 13.8 | 580.1 | 14.6±19.1 |\n| + TIP | 74.8 | 5.7 | 941.6 | 13.0±18.0 |\n\n---\n\n> Q2: The paper does not clearly explain why underthinking behavior appears in LRMs. A further discussion of its possible causes would help improve understanding.\n> \n\nA2: Thank you for asking for clarification. We hypothesize that underthinking is an unintended byproduct of training LRMs to mimic complex, multi-path human reasoning. The causal chain is likely:\n\n1. To enable deep reasoning, models like OpenAI's o1 demonstrated the value of exploring multiple reasoning paths.\n2. This influenced the creation of supervised fine-tuning (SFT) datasets, which likely over-represented examples with frequent thought-switching to encourage this exploratory behavior.\n3. As a result, models learn to switch paths too readily, even when a current path is promising. This leads to the premature abandonment of good ideas that we term \"underthinking\".\n\nWe will add this explicit explanation to the paper to provide better context.\n\n---\n\n> Q3: The TIP method works by penalizing the logits of certain keywords (like “alternatively”) that indicate thought switching. But some of these keywords might also reflect other useful cognitive behaviors, as discussed in a related work. Do you think TIP might unintentionally suppress those behaviors too? Any insight or analysis would be helpful.\n> \n\nA3: That's a great question. **No, we designed TIP specifically to avoid this.** TIP does not penalize all thought-switching, only behavior indicative of *underthinking*: frequent, rapid, and unproductive switching.\nSpecifically, TIP applies a penalty only when a switching keyword (e.g., \"alternatively\") appears with high frequency in a short span (in our work, ≥2 times within 600 tokens). An isolated, deliberate switch to a new strategy (like backtracking or reflection, as in [1]) would not be penalized. Therefore, TIP complements, rather than suppresses, productive reasoning strategies. We will clarify this important nuance in the revised manuscript.\n\n[1] Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs."}, {"review_id": "toERnrjYsT", "reviewer": "Reviewer_Ffc3", "summary": "The paper investigates a phenomenon called “underthinking” in long reasoning models (LRMs)—a tendency to prematurely switch between different lines of reasoning rather than fully developing promising thoughts that could lead to correct answers. The authors observe that frequent thought-switching correlates with incorrect responses across three challenging mathematics benchmarks (MATH500-Hard, GPQA-Diamond, AIME 2024) and two open-source LRMs (QwQ-32B-Preview and DeepSeek-R1). Notably, many incorrect solutions still contain at least one early correct insight, which the models fail to pursue, instead expending large numbers of tokens on unproductive reasoning paths. To quantify this behavior, the authors introduce a novel metric called the underthinking score. To mitigate the issue, they propose a decoding strategy called TIP (Thought-switching Penalty), which requires no fine-tuning and consistently improves performance across the benchmarks.", "questions": "Please provide some details about generalization to new domains.", "limitations": "Yes the authors have discussed some limitations.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "1) Strengths\n\n1a) Frequent Thought Switching in LRMs: The paper begins with an insightful observation: long reasoning models (LRMs) often switch between multiple solution strategies without fully committing to promising ones, even when such paths could lead to correct answers. This erratic behavior results in significant computational waste—incorrect answers tend to consume far more tokens than correct ones due to excessive idea-switching. This sheds new light on inefficiencies in tasks that demand long-term reasoning.\n\n1b) Underthinking Metric: To quantify this behavior, the authors introduce the underthinking score—a simple yet effective ratio that captures how many tokens are used after the first correct thought in failed solutions. This metric complements traditional accuracy by offering a way to measure reasoning inefficiency across models and datasets, enabling more fine-grained evaluations and tracking of future improvements.\n\n1c) TIP Decoding for Efficiency: Motivated by these findings, the authors propose TIP (Thought-switching Penalty) decoding, a method that discourages frequent shifts in reasoning. TIP requires no retraining and not only cuts token usage by more than half but also improves accuracy. Given the high computational costs of LRM-based reasoning, this offers a practical and impactful advance for improving efficiency and reducing latency.\n\n1d) Effective Qualitative Insights: In addition to quantitative results, the paper includes compelling qualitative examples that clearly illustrate the underthinking phenomenon. These case studies reinforce the paper’s central claims and enhance its overall effectiveness and clarity.\n\n2) Weaknesses\n\n2a) Limited Model-Size Coverage: The paper’s findings are based on two very large LRMs—QwQ-32B-Preview and DeepSeek-R1-671B (plus a preview variant)—tested on three math-focused benchmarks. However, the study does not explore whether the observed “underthinking” behavior persists in smaller models from the same families or in other widely used model series (e.g., LLaMA 2 models ranging from 7B to 70B). Including a more model sizes would help assess whether underthinking is a general phenomenon or one that primarily emerges at large scales.\n\n2b) Restricted Evaluation Scope: All experiments are limited to math reasoning and GPQA, with no investigation into whether the findings, the proposed underthinking metric, or the TIP decoding method generalize to other domains such as commonsense reasoning, dialogue, code generation, or multimodal tasks. Expanding the evaluation to diverse reasoning settings would significantly strengthen the broader applicability of the approach.\n\n2c) Evaluation Pipeline Limitations: The underthinking score relies on an auxiliary LLM-based classifier to determine whether intermediate thoughts are “correct.” However, this classifier achieves only ~82% accuracy on a small validation set, introducing uncertainty into the core metric. Increasing the size and robustness of this evaluation could enhance the credibility of the results and reduce measurement noise.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your encouraging review (rating 4) and for emphasizing strengths like our insightful observation of underthinking, the novel UT metric, TIP's practical efficiency gains, and our qualitative examples. We value your suggestions for broader coverage — they've pushed us to expand our analysis.\n\n---\n\n> Q1: Limited Model-Size Coverage\n> \n\nA1: This is an excellent point. To investigate whether underthinking is specific to very large models, we ran new experiments on a range of smaller models from the Qwen3 family (4B, 8B, 14B, 32B) on the AIME24 benchmark.\n\nOur findings are twofold and very insightful:\n\n1. **Underthinking is a general phenomenon:** It occurs consistently across all tested model sizes, not just the largest ones.\n2. **Underthinking severity correlates with model scale:** Within the Qwen3 family, smaller models exhibit *more* severe underthinking than their larger counterparts. For instance, the 4B model has a much higher UT Score than the 32B model.\n\nThis new analysis significantly strengthens our paper by demonstrating the broad relevance of our work across model scales. We will add a new section with these results.\n\n| Models | Accuracy (Pass@1) (↑) | UT Score (↓) |\n| --- | --- | --- |\n| Qwen3-4B | 65.6% | 15.0 |\n| Qwen3-8B | 64.6% | 16.8 |\n| Qwen3-14B | 70.8% | 13.4 |\n| Qwen3-32B | 73.8% | 10.6 |\n\n---\n\n> Q2: Restricted Evaluation Scope\n> \n\nA2: Thank you for the valuable suggestion. Inspired by your feedback, we conducted new experiments on a multimodal benchmark.\n\n**Our analysis toolkit generalizes well to multimodal reasoning.** We evaluated two multimodal LRMs (QVQ-72B-Preview, GLM-4.1V-Thinking) on the OE_MM_maths_en_COMP subset of OlympiadBench, which requires reasoning over both text and images. The results clearly show that the underthinking phenomenon persists in this more complex, multimodal setting.\n\n| Models | Accuracy (↑) | UT Score (↓) |\n| --- | --- | --- |\n| QVQ-72B-Preview | 46.0% | 33.6 |\n| GLM-4.1V-Thinking | 58.7% | 17.1 |\n\nThis confirms that underthinking is a broad challenge not limited to text-only math problems. We will add these new results and a discussion to the final manuscript to strengthen the paper's general applicability."}, {"review_id": "6tedpwXyOp", "reviewer": "Reviewer_MhYP", "summary": "This paper studies underthinking, a phenomenon where a LRM frequently switches between reasoning thoughts before fully exploring promising paths. The authors found that incorrect responses often have a significantly higher number of thoughts, even though many of those thoughts could have led to correct answers. They further propose a UT score to quantitatively measure this issue. Based on these findings, the paper proposes a decoding strategy TIP that uses a thought-switching penalty. Experiments show that this simple strategy leads to improved performance for both standard decoding and best-of-N sampling while maintaining high token efficiency.", "questions": "- The TIP decoding strategy requires a predefined set of thought-switching tokens. How are these tokens selected? What if a word is tokenized into multiple tokens?\n- The legend for Figure 5 is confusing. There are dots in the figure that look different from the rest. What is the difference between these dots and the others?", "limitations": "The authors briefly discuss the limitations in Section 2.3 (as stated in the checklist). I would suggest that the authors explicitly discuss this in a \"Limitations\" section to make things clear.", "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- This paper is well-motivated. It tackles an important problem in LRMs and provides insights into model performance and token efficiency.\n- The experiments and analysis are clean and easy to follow.\n- The proposed strategy, TIP, effectively mitigates the identified issues without significant overhead.\n\nWeakness\n- My main concern with this paper is the proposed UT score. If I understand correctly, the score measures the percentage of tokens required to achieve the first correct thought, but not how frequently the model switches between thoughts. It is still possible for a model to quickly reach the first correct thought (therefore having a low UT score), but then switch between different thoughts afterward. Therefore, I’m not sure if the UT score correctly captures what the authors intended to measure.\n- Additionally, based on Table 1, there is not a clear correlation between accuracy and the UT score, so it is unclear if the proposed metric can provide useful insights on the relation between underthinking issues and model performance. Instead, I think the \"switch tokens\" number and the interval measure in Table 2 would be more informative.", "was_revised": true, "final_justification": "Overall, I think it's a solid paper that studies an important problem in reasoning models. The experimental results could provide some insights for future research. There were some points of confusion in the paper, which were clarified in the rebuttal.", "rebuttal": "Thank you for your strong endorsement (rating 5) and for noting our clean motivation, experiments, and TIP's effectiveness in improving performance and efficiency. We appreciate your detailed questions on metrics and implementation — they've helped clarify key aspects.\n\n---\n\n> Q1: My main concern with this paper is the proposed UT score. If I understand correctly, the score measures the percentage of tokens required to achieve the first correct thought, but not how frequently the model switches between thoughts. It is still possible for a model to quickly reach the first correct thought (therefore having a low UT score), but then switch between different thoughts afterward. Therefore, I’m not sure if the UT score correctly captures what the authors intended to measure.\n> \n\nA1: Thank you for the opportunity to clarify. **The UT score is intentionally designed to measure the *inefficiency* caused by switching *after* a correct path has been found, not just the raw frequency of switching.**\nA model that quickly finds a correct thought (low initial token use) but then switches away from it frequently will receive a high UT score, as many tokens are \"wasted\" after the first point of success. Conversely, a model that finds a correct thought and develops it to the final answer will have a UT score near zero. This design directly operationalizes our definition of underthinking: prematurely abandoning a promising path. We apologize if this was not perfectly clear and will refine the description in Section 2.3.\n\n---\n\n> Q2: Additionally, based on Table 1, there is not a clear correlation between accuracy and the UT score, so it is unclear if the proposed metric can provide useful insights on the relation between underthinking issues and model performance. Instead, I think the \"switch tokens\" number and the interval measure in Table 2 would be more informative.\n> \n\nA2: This is a very insightful observation. You are correct that there isn't a simple, universal correlation *across different model families* in Table 1, and for good reason.\n\n1. **UT Score vs. \"Switch Tokens\":** As you note, other metrics like \"switch tokens\" are informative, and we include them for this reason. However, switching itself is not always bad; abandoning an incorrect path is a feature of good reasoning. The UT score is more nuanced because it specifically penalizes abandoning *correct* paths.\n2. **Cross-Family vs. Intra-Family Correlation:** Different model families may use fundamentally different strategies (e.g., some are trained for iterative refinement, others for more direct solutions). This can lead to high accuracy with either high or low UT scores, masking a direct correlation. However, as shown in our new results for **Reviewer-Ffc3**, **within a single model family (Qwen3), there is a clear negative correlation between model size/accuracy and the UT score.** This strongly suggests that for a given architecture and training style, reducing underthinking (lower UT score) is aligned with better performance. We will add this crucial discussion to the paper.\n\n| Models | Accuracy (Pass@1) (↑) | UT Score (↓) |\n| --- | --- | --- |\n| Qwen3-4B | 65.6% | 15.0 |\n| Qwen3-8B | 64.6% | 16.8 |\n| Qwen3-14B | 70.8% | 13.4 |\n| Qwen3-32B | 73.8% | 10.6 |\n\n---\n\n> Q3: The TIP decoding strategy requires a predefined set of thought-switching tokens. How are these tokens selected? What if a word is tokenized into multiple tokens?\n> \n\nA3: That's a great practical question.\n\n1. **Selection:** The tokens (e.g., `alternatively`, `messy`) were selected empirically by observing common phrases that preceded a strategy switch in the models' outputs. While they function as tunable hyperparameters, we found these general terms worked well across tasks without extensive tuning.\n2. **Tokenization:** When a switching keyword is split into multiple subwords, our implementation penalizes **only the first subword token** of that keyword. This ensures the penalty is applied once per intended switch.\n\nWe will clarify these implementation details in the paper.\n\n---\n\n> Q4: The legend for Figure 5 is confusing. There are dots in the figure that look different from the rest. What is the difference between these dots and the others?\n> \n\nA4: Thank you for pointing this out, and we apologize for the confusion. The dots in Figure 5 represent individual thoughts, plotting their position in the reasoning chain against the probability of being abandoned. **The visually distinct dots are simply statistical outliers and do not represent a different category of data.** They do not change the overall trend shown by the regression line. We will revise the figure caption in the final version to explicitly state this and improve clarity for the reader."}]

Author rebuttal:

Meta-review: This paper proposes a novel decoding strategy and provide experimental results to demonstrates that the proposed method can improve accuracy across challenging datasets without requiring model fine-tuning. The paper is well written and the proposed idea is innovative. However, the analyses done to evaluate the technique are questionable (scoring, further discussion of causes, model-size coverage, limitations). It is suggested that the authors further revise the paper and address the issues raised by the reviewers. We recommend accepting this paper.
Decision: Accept (spotlight)