Don’t Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models
Authors: Sohyun An
Ruochen Wang
Tianyi Zhou
Cho-Jui Hsieh
Venue: NeurIPS 2025 poster ()
Keywords: Reasoning
Large Language Models
Efficiency
Primary area: deep_learning

Abstract: While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to *overthinking*—characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance.
We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed *thinking patterns* at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length.
Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Don't Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models
Sohyun An', Ruochen Wang', Tianyi Zhou?, Cho-Jui Hsieh
University of California, Los Angeles
2 University of Maryland, College Park
sohyun84238cs www.. edu tianyi@umd. edu chohsieh@cs.ucla edu
Abstract
While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using rein- forcement learning, they may also drastically increase the output length due cetttiinkknn-chhaactrtiieee by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMss' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns the right position. To investigate this hypothesis, we propose dynamic optimization framework that segments moder--genrrated reasoning paths into distinct thinking patterns, systemat- ically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized think- ing paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintain- ing accuracy for originally correct responses. Moreover, non-trivial portion of originally incorrect responses are transformed into correct ones, achieving 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks re- veal that method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.
Introduction
Recent advancements in Large Reasoning Models (LRMs) [13, 44, 9] have substantially enhanced their capabilities across various complex reasoning-intensivee tasks. These advancements have largely been driven by outcome-only-based reinforcement learning (RL) [23, 25, 12, 16), which train models to maximize the final answer accuracy. Models trained under this framework prioritize producing the correct answer
generating an optimal reasoning trajectory, and thus sometimes produce long reasoning paths, i.e,, test-time scaling, achieving strong performance even in complex scenarios [28, 36, 15]. While these methods effectively increase the correctness of final predictions, they also reveal inherent limitations [19]. One notable issue frequently observed in current LRMs is the tendency toward overthinking [4, 29, 31], characterized by excessively prolonged reasoning paths or unnecessarily intricate inference steps. This behavior typically results in significant computational inefficiencies, increasing resource usage without improvement performance, and can even degrade overall performance due to excessive exploration [30, 2, 27, 22].
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

We hypothesize that this inefficiency largely stems from current LRMs' limited capability to dynami- cally identify and select optimal reasoning strategies- referred to hereafter as thinking patterns-a at critical junetures within the reasoning process. A thinking pattern is defined as a modular reasoning segment that performs a distinct cognitive function, such as hypothesis generation, self-verification, intermediate summarization, exploring alternative scenarios [7]. An ideal LRM should dynamically utilize beneficial thinking patterns while minimizing or discarding unnecessary or detrimental ones, thus improving computational efficiency without compromising accuracy.
To investigate this hypothesis. we formulate the enhancement of reasoning efficiency as a constrained optimization problem aimed at minimizing the expected computational cost of reasoning trajectories while preserving or improving task performance. Subsequently, we propose framework for Dynamic Thinking pattern Optimization (DTO). specifically designed to refine the selection of modular reasoning strategies. Our proposed method operates by first segmenting model-generated reasoning trajectories into identifiable thinking patterns. We then systematically evaluate each segment's s contribution, classifying it as positive or negative based on its impact on reasoning efficiency. By identifying appropriate finalization points and selectively pruning negative segments while reinforcing positive ones, our approach not only compresses the original reasoning paths into concise, effective trajectories, but also enables the transformation of flawed reasoning traces associated with incorrect outcomes into more coherent and accurate alternatives. In contrast to prior methods, which rely heavily heuristic truncation [4] aggregate metries like token length [27, 17]. our framework explicitly models and optimizes the individual contributions of reasoning segments, enabling a more precise enhancement of reasoning efficiency.
To explicitly guide LRMs toward more optimal reasoning behaviors, we integrate a preference optimization approach [20], leveraging specialized pairwise dataset that contrasts suboptimal and optimal reasoning trajectories based on our framework. This encourages models to preferentially adopt thinking patterns demonstrated to yield superior efficiency and effectiveness. We validate our framework through extensive experiments conducted across multiple established mathematical reasoning benchmarks. The results consistently demonstrate that our approach reduces computational requirements while simultaneously enhancing reasoning performance. Our contributions and findings summarized as follows:
We formulate the enhancement of LRM reasoning efficiency as a constrained optimization problem, and introduce dynamic optimization framework called IJTO, for this purpose.
We empirically validate that dynamically selecting optimal thinking patterns significantly improves reasoning efficiency.
Leveraging a preference optimization strategy based on pairwise trajectory comparisons, we achieve high reasoning efficiency across various mathematical reasoning benchmarks, attaining up to 12% higher accuracy over the original LRM, while reducing token usage from around 5,000 to 3,000.
2 Related Work
Large Reasoning Models. LLMs have traditionally exhibited rapid, intuitive decision-making aligned with System / thinking. Recent efforts aim to equip them with more deliberate, System reasoning abilities. Early studies primarily adopted coompinng-bssed methods, such chain-of- thought, to elicit explicit step-by-step reasoning [34, 32, 39, 14]. While effective for structured reasoning, these methods often struggled with complex, multi-step problems [36]. To address this, later work introduced test-time scaling techniques [28, 3, 35, 24], incorporating search and verification during inference to boost accuracy. More recently, Large Reasoning Models (LRMs) have been developed to internalize sophisticated reasoning capabilities within the model itself [9, 44, 13). They are typically trained via autcome-based RL that focuses on maximizing final answer accuracy [23, 25, 12]. While effective for improving correctness, it may inadvertently lead to overthinking- unnecessarily long or complex reasoning paths that reduce computational efficiency [4, 29, 31].
Reasoning Efficiency of LRMs. Several recent studies have addressed the issue of reasoning efficiency in LRMs. For example, some studies [22, 41, 2, 30, 1, 38, 26, 11] have introduced various length-based objectives integrated with RL. approaches, while other efforts [40, 42) have employed SFT supplemented by the collection of effective datasets. Complementary to these strategies, another line of research [17, 4, 27] has investigated post-hoc refinement and scoring mechanisms for reasoning

---

Q: a and b are integers such that ab 17 mod 20, then what the remainder when (a+10)/b-10) divided by 20? (Answer: 17)
Wait, 10b be factored 10 bi. 10(a mod
P: 0.0
Hmm, so that term is 10 times something, and modulo 20. remember that you have a multiple of 10 modulo 20, it's either or 10. Because 10 even number is 0 mod 20, and 10 odd number is 10 mod 20. mod depending that would
Ptn
So, 10(a either
whether e b) is
odd.
So,
even, 10[s if b odd, then 10(a + b) 10 mod 20, so the total is 17 10 27 mad 20, which is
10ja
mod the total 17 Keep Pattern
Ptn 3
Walt, ss depending on whether
even odd, result elther o.
Pa 0.0
it's passible that a+ b.can can be alther even or odd, we might have two possible remainders.
Remove Pattern 3
Ptn 11
+100, already So, 10[a b) mod 20 is either o or 10, depending on a
Wait, maybe express (+ 10jlb 10)
P11 0.0
Remove Pattern 11
-a!
Walt, but maybe we can find the parity of a b. Let's think about that. congruent mod modulo Since is modulus, a
P12
Given that ab mod
Ptn 12
Let's about the possible values
be 19.
both a and b are odd, so their sum + is even. Because odd add - even. So, is even. 10*even multiple 20. Therefore, 10/a b) mad 20.
Therefore,
20
So, going back, (a 10|(b 10)
Keep Pattem 12
Ptn 13
But hold on, earlier thought it could be 17 but now since both a and b are odd, their sum even, 10% is mod 17 17. So, remainder is 17.
P11
Keep
ê finatise (Hmm,, I think this is enough to derive the final answer.) @
Ptn 37
key point that must be odd because add and 20 is even, 5o their product has to be odd, so both a and are odd....
Walt, this getting tedious, but
1.0
Illustration of DTO. We construct truncated reasoning trajectory At by identifying the point where the probability score p; in Equation (6) exceeds threshold T = 1.0, and then applying the binary selection function f() from Equation (7), We then append the finalization pattern draatize and sampled answer s* (Equation (9) form ÂL. Finally, the pruning function g(-) (Equation (I1)) refines the trajectory into the optimized version Ag, as illustrated in the orange box.
Figure 1:
trajectories generated by models, demonstrating promising results with relatively low computational overhead. Our method builds this line of work, leveraging its demonstrated efficiency and broad applicability. Although primarily evaluated on base LRMs, these approaches can be generally applied to models trained fine-tuned through other efficiency-enhancing strategies. More specifically, Luo et al. [17] introduced the Hongth-Harmonizing score, combining reasoning accuracy and token length within PPO-style fine-tuning objective to encourage more concise reasoning paths. Preference- based optimization approaches, as explored by Chen et al. [4] and Shen et al. [27], have also proven effective. These methods construct pairwise datasets guide models toward more efficient reasoning. Specifically, Chen et al. [4] generates positive samples by instructing an LLM to truncate correct reasoning at the point where an initial solution followed by a reflective step, while Shen et al. [27] employs a scoring mechanism favoring shorter correct and longer incorrect responses when forming pairwise comparisons. Nevertheless, these methods primarily rely on aggregate-level metrics such as token length or heuristic truncation points. As result, they are limited in their ability to precisely assess and optimize the contribution of individual reasoning segments, potentially hindering more optimal efficiency. To address this limitation, we propose dynamic optimization framework that operates at the segment level.
Dynamic Optimization of Thinking Patterns
Reasoning trajectories generated by LRMs exhibit a discernible structure, where distinct segments serve specific cognitive roles such as selffverification, intermediate summarization, or exploring alternatives [7]. We refer to these segments as thinking patterns, which can often be identified through linguistic cues such as "Wait", "Alternatively" that signal shifts in reasoning strategy. As illustrated in Figure 1, certain thinking patterns promote reasoning progress by facilitating equation formulation and step-by-step computation. Conversely, other patterns hinder efficiency by repeating prior reasoning or continuing unnecessary verification without contributing to the reasoning process. We hypothesize that such inefficiencies in LRMs stem from their limited ability to dynamically select appropriate thinking patterns at critical moments. For example, models may fail to terminate reasoning even after sufficient evidence has been gathered. To investigate this hypothesis, we formulate the enhancement of reasoning efficiency as constrained optimization problem, aiming
3

---

to reduce computational cost while enforcing lower bound on task performance. Building on this formulation, we introduce a dynamic optimization framework termed DTO that identifies and prunes unproductive segments and reinforces those that contribute positively.
3.1 Problem Formulation
Let A, be finite list of thinking patterns for problem i.e., A. 15 ........ : &nd where D denotes the underlying distribution over input problems. Each thinking pattern 8 incurs a non-negative computational cost c(6) 2 typically quantified by metries such as token length FLOPs. The total cost of the reasoning trajectory Ag is therefore given by:
C(A,)= = Σ c(0).
SEA,
Here, our objective is to construct reasoning trajectories that integrate effective thinking patterns to achieve high reasoning efficiency. Formally, we define the constrained optimization problem as follows, aiming to minimize the expected computational cost while maintaining task performance at or above its prior level:
minimize Ongg
ER- D(((,))
subject to
E ER~D (P(A))
where P-)) denotes a task-specitt performance metric such as final answer accuracy, and a represents lower bound the expected task performance, e.g., the expected performance of the original trajectories generated by a base LRM we aim to maintain the original performance.
3.2 DTO: Constructing Optimal Reasoning Trajectories
To solve the problem defined in Equation (2), we must first characterize what constitutes an optimal trajectory under this formulation. We define such a trajectory as one that incrementally generates thinking patterns conducive to achieving the reasoning objective, such as narrowing down possibilities or providing key insights, and terminates the reasoning process once sufficient information has been accumulated to produce correct answer. To extract such optimal reasoning trajectory from an LRM-generated response, we follow a two-step procedure: (1) identify the appropriate point at which the reasoning should be finalized, and (2) prune intermediate thinking patterns that do not meaningfully contribute to the reasoning objective.
Given a reasoning trajectory y generated by LRM тe for problem æ with a known ground-truth answer a", we segment y into a sequence of distinct thinking patterns:
"i.....,n,,), ~ TT(x).
To systematically determine optimal termination points, inspired by [6], we define exit thinking pattern, dexit, expressed as "... Wait, I suddenly got the final answer to the whole problem. Final Answer: \boxed(". For each candidate termination point construct partial trajectory Tú by appending the exit pattern:
T 81 ① 82 θ ..... @ 8; @ dexit, for i = 1, Byy
(4)
We then employ Monte Carlo estimation, sampling multiple completions:
R2 {r1, 72... TMb. rj ~ To(T))
(5)
Benefiting from highly efficient and parallelizable inference frameworks [45], and by restricting generation to small number of tokens with a slight margin over the token length of the ground -ruth answer a", this process can be executed in lightweight manner. We then determine the probability p: of deriving the correct answer index by:
P = (r E R4 a" Er)//RR))
We define the earliest index i = i' such that exceeds a predefined threshold T, and apply a binary selection function over the thinking patterns:
{1 if E otherwise.
f(6))=

---

max pi Distribution
DeepSeek-RL-Dlstill--e
DeepScaleR-1.55 -5.errewwww
100.0%,
2550
1852
Accuracy (%)
100.0%,
1358
Original (Correc)
Optimized (Correct)
Accuracy (%)
100
100.0%
1114
Original (Correct) Optimized (Correst) Original (Incommec) Optimized (ncorrect)
Density
3t
Original (Incornect)
20-
Optimiced (inoreect)
0.0%.
0.0%.
15.6%,
12520
7.8% 8582
9078
10940
1k
2.5k... 11k
12.5k
1k
2k
8.5k 9k
8.0
0.2
0.4
0.5
0.8
1.0
FLOPs (x10")
FLOPs (x10")
max
(a) DeepSeek-RI
(b) DeepScaleR
(c) DeepSeck-RI
Figure 2: Comparison of dynamically optimized vs. original responses, and max; Pi distributions in incorrect cases. (a), (b) Dynamic optimization preserves accuracy for correct responses while reducing attention FLOPs (47%, 40%), and improves accuracy for incorrect ones (15.6%, 7.8%) with lower FLOPs. (c) shows max, pc, maximum estimated correctness probability across thinking patterns (Equation (6)). High values suggest that even incorrect trajectories often contain a promising intermediate segment.
yielding the truncated reasoning trajectory:
06 E ((6,) =1,
(8)
where y is the whole trajectory in Equation (3).
Next, we introduce special finalize thinking pattern, Óiialices which signals that sufficient reasoning has been conducted- similar to how a human might intuitively recognize when to stop deliberating and provide an answer. This is expressed as "Hmm, think this enough to derive the final answer Unlike Sexits ofnalize coherently concludes the reasoning process. We sample completions conditioned on the finalized trajectory:
SA {81, 82,,8,,kkk) 8j To(A/ ( Dfmalize).
(9)
Among the correct completions in SAf, select the shortest one, st, and construct refined reasoning trajectory:
A A/ + òfinalize + s"
(10)
To further optimize Â/. we evaluate the utility of each intermediate thinking pattern using auxiliary LLM μug. Given dedicated prompt (see Appendix A.4), the model determines whether each & e A/ meaningfully contributes to deriving a". Note that we instructed the model to remove segments only if they add meaningful content, are factually incorrect in harmful way, or unhelpfully redundant, so as to avoid compromising the model's reasoning capability. To further ensure that the pruned sequence, which excludes o,, still leads the correct answer, consider the following trajectory:
entirely off-topic
AMA
b, E /
6, 8, and before "(ooxed""
and perform quick decoding step for validation. Patterns that are deemed redundant and pass validation are removed via the following pruning function:
{
if &; can be removed from Á/ otherwise.
g (6.)
(11)
This results in the final optimized reasoning trajectory as follows:
A j6 A 9(6,) + 1]. Please refer Appendix A.3 for the full algorithm of our framework.
(12)
3.3 Analysis
In this section, we compare the original trajectory sampled from the base LRM with the optimized trajectory Ag defined in Equation (12).
5

---

Setup. We use a dataset consisting of 5,000 samples drawn from the MATH [10] training set' and employ the DeepSeek-RI 1iii------Di------- Distill-Qwen-I.. Qwen-1.5B [9] and DeepScaleR- Prevview [18] as TT and aama-3.3-70B-Ime
[8] as an auxiliary LLM μs- For each problem, we sample 4 responses. If at least one response correct, we construct a reasoning trajectory Ag by applying our proposed framework to a randomly selected correct response. If no correct responses are available, we instead apply the same procedure to a randomly selected incorrect response. We set the temperature to 0.6, top_p to 0.95, and moa_ttkees to 8192. The value of M in Equation (5) was set to 10, K in Equation (9) was set to 4, and the threshold is set to 1.0, signaling that the model has accumulated sufficient information produce the correct answer.
Results. As illustrated in Figure 2a and Figure 2b, the responses optimized using our method require substantially fewer attention FLOPs compared to the original responses from the base LRM. Specifically, for responses that originally produced a correct answer, our method reduces attention FL.PPs consumption by 47% % and 40% for -eepSeek----iistill-O-eee
and DeepScaleR- 1.5B-Preview, respectively, while preserving correctness. Interestingly, for responses that initially yielded incorrect outcomes, applying our framework induce more effective thinking patterns such as finalizing reasoning at appropriate termination points transforms a non-trivial portion of them into correct ones, improving accuracy by 15.6% and 7.8% for DeepSeek- CaISeck-RI--istilll HL1-Ditill-Qwen= respectively, while also reducing FLOPs consumption. To better understand why this is possible, we analyze max; pa for responses that were originally incorrect in Figure 2c and Figure 4. As described in Equation (6), denotes a Monte Carlo estimate of the probability that the model produces the correct answer when terminated at the i-th thinking pattern. We find that, even in incorrect responses, many intermediate segments exhibit high p; values, suggesting that the model temporarily arrives at high-quality partial reasoning steps. This observation indicates that our method can effectively restructure these responses with more appropriate thinking patterns, thereby improving accuracy while consistently lowering the computational cost.
and DeepScaleR-115B-Prree
Preference Optimization Towards Optimal Reasoning Behaviors
Thus far, we have demonstrated that our dynamic optimization framework enables the construction of significantly more efficient reasoning trajectories by selecting appropriate thinking patterns at the right points in the reasoning process. In this section, we leverage the framework to construct contrasting pair dataset of optimized and suboptimal reasoning trajectories, and examine the impact of applying a preference optimization technique using this dataset.
4.1 Preference Optimization with Dynamically Optimized Trajectories
To apply the preference optimization technique, we first construct a pairwise dataset (Yur y1) for each problem x ~ 'D. For each æ, aim to generate N response pairs. Specifically, begin by sampling 4 responses from the LRM тy. Let Ne denote the number of correct responses among them. If N. 2 N. we select the N shortest correct responses and apply our dynamic optimization framework to generate optimized trajectories, which are used as you If No < N, we select all No correct responses and additionally sample N NN incorrect responses random. We then apply our framework to these N responses to obtain optimized trajectories as yw. For each Vw. we select the longest unoptimized trajectory among the sampled responses serve as the corresponding yI+ thereby constructing the final pairwise dataset D'. We then apply SimPO [20], which demonstrates strong performance while incurring relatively low computational cost, in order to guide the LRM toward more optimal reasoning behaviors:
B [an
| xx) -
(TE) =-E -E(z.pe.))
log a
log mo (Bu
|x)
log To T
(13)
where / and y are hyperparameters, (-) denotes the sigmoid function, and yywl and |y/| represent the token lengths of you and yı, respectively. Please refer to Appendix A for more details.
We followed the split used in Luo al. [17]

---

Table 1: Comparison with other methods the DeepSeek-RI -iie--RR---isit-wwweeea Seessill--wenn1.555 1.5B model. We evaluate the effectiveness of our method using a dynamic optimization framework and preference optimization technique applied to DeepSeek- RI--RR--Diiiii L1--istilll-ee D--Disilll-wen-- Qwen-1.5BB by comparing it against existing methods.
MATH
GSM8K
Gaokao
Method
(1)
#Tokens
EIT. (1)
(1)
#Tokens
E... (1)
(1)
#Tokens ())
Eff. (1)
Instruct ver. [37]
76.36
555.16
N/A
85.37
315.44
N/A
65.13
575 86
N/A
Baseline
79.80
3543.44
1,000
82.13
1382.99
1,000
66.62
3725.16
1.000
Fast Prompt
81.17
3354.99
1.074
85.14
1894.73
0.757
69.68
3634.30
1.072
SFT
81.28
3180.10
1.135
80.12
933.89
1.445
67.34
3245.37
1.160
Ol-Pruner [17]
82.31
2593.06
1.409
80.67
669,4
2.029
66.69
2827.81
1.319
DAST (27)
83.35
2817.94
1.313
84.02
1174.89
1.204
69.42
3058.96
1.269
FCS Ref. [4]
84.72
2548.55
1.476
84.29
1080.19
1.314
71.30
2750.35
1.450
(Ours)
1936.19
844.18
72.66
2137.59
AMC2023
AIME2024
AIME2025
Method
Acc. (1)
#Tokens ())
Eff. (1)
Acc. (1)
#Tokens (U)
ER. (1)
Aec. (1)
#Tokens (U)
EIT. (1)
Instruct ver. [37]
54.75
786.43
NIA
11.22
956.11
N/A
8.11
887.40
N/A
Baseline
58.25
5338.54
1,000
21.44
7359.24
1.000
18.89
7236.66
1.000
Fast Prompt
61.00
5073.15
1.102
21.56
7261.19
1.019
20.33
7137.90
1.091
SFT
61.08
5030.76
1.113
23.78
7151.84
1.141
18.44
7122.97
0.992
O1-Pruner [17]
65.50
4370.83
1.373
21.78
7015.30
1.066
17.67
6742.34
1.004
DAST
66.58
4590.91
1.329
24.00
7077.45
1.164
19.78
6846.85
1.107
FCS Ref. [4]
68.92
4166.60
1.516
24.44
6698.77 77
1.252
20.67
6545.62
12100
(Ours)
70.25
3376.98
28.00
5877.44
21.11
5689.38
1,421
4.2 Experiments
Dataset. We evaluate our method against various existing approaches across several established mathematical reasoning benchmarks, including the test sets of MATH [10], GSM8K [5], Gaokao (Mathematics) [43], AMC2023, AIME2024, and AIME2025.
Baselines. In line with prior works [4, 27, 17], we compare our method against the following baselines: Instruct ver. refers to the instruction-tuned version of the base model on which the LRM trained. Baseline denotes the base LRM TT without any additional prompting or fine-tuning. Fast Prompt [17] appends the instruction "Solve the problem as quickly possible" to the original prompt (see Appendix A.4) and uses the resulting prompt to generate responses. SFT represents supervised fine-tuning of нa using N correct and shortest responses from the model. O1-Pruner [17] scores reasoning trajectories generated by the LRM using the Length- Har--nizimnngggg score, which jointly considers accuracy and token length. N trajectories per problem are then used to fine-tune the model via a PPO-style objective. DAST [27] introduces a self-defined token length budget, formulated linear combination of the average token length of correct responses and predefined maximum generation length. Leveraging this, it assigns preference scores to responses sampled from LRM, favoring shorter correct responses and longer incorrect ones during pairwise data construction. A response pair is formed when the score margin exceeds 0.3, and the resulting dataset is used to apply preference optimization method with most N trajectories per problem x. FCS Ref. [4] constructs a pairwise dataset by leveraging heuristic truncation points in LRM-ggeerated trajectories. Specifically, when correct response present, the LLM Po prompted to identify the locations of the First Correct Solution and the subsequent Reflection. The segment up to the reflection point is extracted as the positive example (at most N per problem .r), while the longest trajectory among the sampled responses is selected as the negative example. Preference optimization technique is then applied problems for which such pairwise data can be constructed that is, when least one correct response is available.
Metrics. For each dataset, report both the average accuracy and the average number of generated tokens. Additionally, inspired by Qu et al. [21], we compute the following efficiency metric
E En y- (ax) P(y)] Do
[C(b))] (=)
(14)
E ErwD No (x) (2o)] E,wD, goe (z) [c()
Here, P(.)) measures final answer accuracy, C(.) denotes the number of generated tokens, represents the original base model, while тh- corresponds to the model after applying specific method. higher value of indicates more favorable trade-off between inference efficiency and performance.

---

Table 2: Comparison with other methods the DeepScalcR-11SB-Preeee We evaluate the effectiveness
our method using a dynamic optimization framework and preference optimization technique applied to DeepScaleR- 1.5B-Preview by comparing it against existing methods.
MATH
GSM8K
Gaokao
Method
(1)
#Tokens
EfT. (1)
(1)
#Tokens
ERT. (1)
(1)
#Tokens ())
Emf. (1)
Instruct ver. [37]
76.36
555.16
N/A
85.37
315.44
N/A
65.13
575.
N/A
Baseline
88.48
2700.37
1,000
87.38
1601.98
1,000
75.97
3053.67
1.000
Fast Prompt
89.41
2601.49
1.049
88.38
1652.94
0,980
77.01
2941.73
1.052
SFT
89.19
2634.80
1.033
86.43
1469.03
1.079
76.23
2950.22
1.039
O1-Pruner [17]
89.74
2259.56
1,212
86.41
1235.48
1.282
77.47
2539.68
1,226
DAST (27)
89.74
2551.49
1.073
86.71
1502.93
1.058
77.21
2880.06
1.078
FCS Ref. [4]
88.81
2247.38
1.206
88.10
1254.06
1.288
77.21
2531 105
1.226
(Ours)
89.14
1994.27
77.01
1.364
AMC2023
AIME2024
AIME2025
Method
Acc. (1)
#Tokens ())
Eff. (1)
Acc. (1)
#Tokens (U)
ERT. (1)
Acc. (1)
#Tokens (U)
EIT. (1)
Instruct ver. [37]
54.75
786.43
NIA
11.22
956.11
N/A
8.11
887.40
N/A
Baseline
76.88
4268.77
1,000
36.67
6455.16
1.000
29.17
6420.07
1.000
Fast Prompt
76.25
4119.06
1.028
30.83
6505.43
0.834
27.50
6338.55
0,955
SFT
71.88
4405.87
0.906
35.83
6755.42
01934
27.50
6192.65
0.977
O1-Pruner [17]
79.38
3831.73
1.150
35.83
6242.41
1010
28.33
6086.82
1.024
DAST (27)
78.75
4158.48
1.051
32.50
6551.17
11873
27.50
6462.76
0.937
FCS Ref. (4]
77.50
3755.56
1.146
35.00
6219.26
0.991
26.67
6016.55
0.976
(Ours)
77.50
3403.56
38.33
5742.61
27.50
$820.90
1.040
Results. Here, we set N = 2, with the remaining experimental setup following Section 3.3. Table I and Table summarize the performance comparisons between our method and existing approaches on two models: BeepSeek-R1-DDe He1-Disill--wenn -arill--wen-1.5BB 1.5B and DeepScaleR-1.555 -.5B-Preview, evaluated across six benchmark datasets. Overall, our approach achieves superior efficiency metrics on almost all datasets and models. Specifically, on DeepSeek R --iittill -wen---eennnp (Table 1), DTO significantly outperforms existing methods in efficiency while maintaining comparable or better accuracy on out of 6 datasets. For challenging benchmarks such as AMC and AIME, DTO improves average accuracy by almost 7% over the base model, while also reducing token usage by approximately 1,700 tokens. This improvement likely stems from DTO's ability transform some initially incorrect trajectories into correct reasoning paths, even in cases where no correct sampled trajectory is available, which often indicates that the problem is particularly difficult. On the other hand, in such cases, FCS+Ref. fails to construct a pairwise dataset, while DAST relies solely on token length, i.e., assigns higher scores longer incorrect responses, which may limit its ability generalize. On DeepScaleR-14 1.5.--Preiiiee (Table 2), DTO continues to achieve the highest efficiency, though with narrower margins due to this model's inherently higher accuracy and lower baseline token counts. Nonetheless, DTO consistently delivers a favorable balance between accuracy and computational efficiency.
4.3 Analysis
In this section, we present several analyses to validate the effectiveness of our framework using the DeepSeek-Re Bitteekk-R--iisee RI--istill Qwen- 1.5B model.
Comparison with Token-Limitte Baselines. In addition to Section 4, further compared against a strong baseline assessing the impact of varying token limits on the base model's performance. This baseline involves forcing the base model (DeepSeek-F) -istee----isiill-eeeeee answer once it reaches a maximum token limit (1024, 2048, 4096, and 6144). To facilitate this forced finalization, we appended the instruction: "Wait, I suddenly got the final answer to the whole problem. \nAnFinal Answer:". As shown in Table 3, the results exhibit a consistent trend: the token limit increases, both accuracy and the number of generated tokens increase, indicating that longer sequences enable more complete reasoning. However, our method, DTO, achieves higher accuracy while using fewer comparable tokens, highlighting its strength in both reasoning quality and efficiency.
to produce final
Frequency of Thinking Pattern Transitions. We further examine the frequency of thinking pattern transitions by analyzing the occurrence of the linguistic cue "Wait". As shown in Figure 3,

---

Table 3: Comparison against the base model with varying token limits. DTO (Ours) consistently achieves higher accuracy while using fewer or comparable tokens.
Base + 1024
Base
2048
Base
4096
Base + 6144
DYTO (Ours)
Dataset
Acc.(1)
#Toks([)
Aoc.(t)
#Toks(L)
Acc.(")
#Toks(
Acc:(1)
#Toks(L)
Acc.(t)
#Toks(U)
MATH
63.59
1009.65
74.78
1783.91
78.55
26-12.43
79.97
3124.27
86.
1936.19
GSM8K
79.40
576.62
80.48
722-42
79.78
850.67
80.12
928.66
83.91
844.18
Gaokno
50.06
957.04
57.86
1661.44
65.26
2551.03
67.86
3092.08
72.66
2137.59
AMC2023
32.50
1022.44
50.00
1965.05
67.50
3416.82
68.12
4385.90
70.25
3376.98
AIME2024
3.33
1024.00
14.17
2048.00
20.83
4009.87
24.17
5686.45
28.00
5877.44
AIME2025
1.67
1024.00
12.50
2048.00
17.50
3986.50
18.33
5715.72
21.11
5689.35
Baseline
Fast Prompt
SFT
O1-Pruner
DAST
FCS Ref
DTO (Ours)
60
20
Average Count
Average Count
15-
40
10
20
5
0
0
MATH
GSMBK
Gaokao
AMC2023
AIME2024
AIME2025
Figure 3: The average count of "Wait", which one the words signaling a thinking pattern transition. Compared to all baselines, our framework generally results in the lowest average count of "Wait" suggesting more concise and less interrupted reasoning trajectories. The results are averaged over 4 runs.
all methods exhibit increased frequencies as task difficulty rises. Notably, DTO consistently achieves the lowest average frequency of "Wait" across multiple benchmarks, while maintaining comparable or superior accuracy relative to all baseline methods, with the exception of GSM8K (see Table 1). This result suggests that DTO effectively reduces unnecessary cognitive shifts during reasoning, leading to more concise and coherent reasoning trajectories.
Qualitative Analysis of Generated Reasoning Trajectories. As shown in Table optimized reasoning trajectory achieves the same correct answer with significantly fewer tokens (814 vs. 1790) compared to the baseline. The baseline response exhibits signs of overthinking, including repeti- tive verification, redundant restatements, and unnecessary self-correction. In contrast, our method concise trajectory by directly applying the relevant formula and confidently pro- gressing through the necessary steps. This example illustrates how dynamic reasoning optimization effectively reduces token overhead without compromising correctness, producing more efficient reasoning paths.
generates
Generalization to different domains. We evaluate the generalization capability of our framework by examining whether model trained on the MATH dataset, as detailed in the previous section, can improve reasoning efficiency beyond the mathematical domain. To this end, use the MMLU- Pro dataset [33], which comprises challenging, reasoning-centtrc questions across a wide range of domains. Among these, we conduct evaluations on three domains using 100 randomly sampled questions per domain and the same five CoT few-shot examples across all methods. As shown in Table 5, method consistently achieves the highest reasoning efficiency across all three domains, significantly reducing token usage while maintaining comparable accuracy to baselines. This suggests that framework generalizes well beyond the mathematical domain, effectively condensing reasoning in tasks that differ from the training domain.
Conclusion
In this paper, we introduced a dynamic optimization framework termed DTO to mitigate the ineffi- ciencies arising from overthinking in LRMss. By dynamically identifying and optimizing modular reasoning strategies, our approach substantially reduces computational overhead while improving reasoning accuracy. Empirical evaluations across diverse benchmarks demonstrate the effective-

---

Table 4: Comparison of Reasoning Trajectories between Baseline and DTO. Due to space constraints, the middle part has been replaced with The segment highlighted in yellow redundantly restates the same fact as the one in green. For more dctails, please refer to Appendix B.
Question: "What is the degree measure of the acute angle formed by lines with slopes and 3 (Answer: 45)
Baseline (1790 tokens): "Okay, so I need to find the acute angle between lines with slopes und 1/3. ... So, the slopes /[L + ma)) Is that right? Let me check. Yeah. think that's correct because the tangent of the angle between two lines is equal the absolute value of (mg my)/ (1 minal. have: 8 arctan (5/3))
and 12g, the angle / between them is given by: / = arctan( [mg
arctann 1I) aretan( (1. Because the absolute value of -1 is I. So, arctan(1) is... 45" right? Since tan(45") ) = 1. Wair, but hold on, the question asks for the acute angle. So, 45' is already acute, since it's less than 90" So, that the answer? It seems struightforward. But let me make sure ... Slope my m2 1/3. ... So, arctan(1) is 45". That seems correct. Wait second. but remember that the angle between two lines
So, putting it together,
found using the formula: (an(9) [m mi)/(1 mymaal ... Final Answer: The acute angle formed
by the lines is 45
lines with slopes and 1/3, Let write that down: (0) = [[mn [//1 + myjmal. M So substituting the values: tan(0) = 11/3 - 2)/(1 (2) (1/3))] Oh, tan(0) is I. Then is aretan of remember that tum(45") is 1, so 0 is 45", Since we' re asked for the acute angle, 45" is already acute because it's less than 90% So, I think that's it. The acute angle is 45 Final Answer: The acute angle is 45
DTO (814 tokens); "Alright, I need to find the acute ungle formed
Table 5: Evaluation on MMLU- to validate generalization beyond mathematics. All methods use the
same five CoT shw-shot examples.
Law
Chemistry
Engineering #Tokens (L)
Method
(1)
#Tokens
Eff. (1)
(1)
#Tokens ())
Eff. (1)
Acc. (1)
Emf. (1)
Instruct ver. [37]
11.00
183.98
N/A
21.00
226. 18
N/A
20.25
377.11
N/A
Baseline
17.50
1716.77
1,000
40.75
4427.44
1,000
22.00
6173.27
1.000
Fast Prompt
17.00
1685.09
0.990
37.25
4508.80
0.898
20.75
5972.20
0.975
SFT
17.75
1590.35
1.095
39.25
4270.96
0,998
19.25
6038.40
0.895
O1-Pruner (17)
16.25
995.03
1.602
39.25
3688.90
1.156
23.00
$225.53
1,235
DAST (27)
16.25
1180.12
1,351
38.00
4433.26
0,931
23.75
6137.51
1.086
FCS Ref. [4]
15.75
1034.84
1.493
39.25
4096.80
1.041
22.75
5875.08
1.087
DTO (Ours)
16.75
734.20
39.75
3142.64
1.374
23.00
4186.74
1.542
ness of our method when combined with preference optimization, underscoring the importance of strategically managing reasoning processes in LRMss
Acknowledgements
This work partially supported by NSF 2048280, 2325121, 2244760, 2331966 and ONR N00014- 23-1-2300:P00001.
References
[1] Pranjal Aggarwal and Sean Welleck, Ll: Controlling how long a reasoning model thinks with reinforcement learning, 2025. URL https::///attiiia httprxii.orggbb//550022 04697.
[2] Daman Arora and Andrea Zanette. Training language models to reason efficiently. arXiv preprint arXiv:2502.04466: 2025.
[3] Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V Le, Christopher Ré, and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling. arXiv preprint arXiv: 24Xiv:2407.21788 2024.
[4] Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu. Mengfei Zhou, Zhuosheng Zhang, et al. Do not think that much for 2+ 3=? the overthinking of ol-ke 1lms. arXiv preprint arXiv:2412.21187, 2024.
[5] Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reichhrr Nakano, et al. Training verifiers to solve math word problems. arXiv preprint arXiv:2110. 14168, 2021.
[6] Yichao Fu, Junda Chen, Siqi Zhu, Zheyu Fu, Zhongdongming Dai, Aurick Qiao, and Hao Zhang. Efficiently serving Il reasoning programs with certaindex. arXiv preprint arXiv:2412. 22..22122.2000 20993, 2024.
10

---

[7] Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D Goodman. Cognitive behaviors that enable self- improving reasoners, or, four habits of highly effective stars. arXiv preprint arXiv:2503.01307, 2025.
[8] Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.2178. 2024.
[9] Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseek-rl: Incentivizing reasoning capability in Ilms via reinforcement learning. arXiv preprint 2tti::2500.129445. 2025.
[10] Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. arXiv preprini arXiv: 103.032., 2021.
[11] Bairu Hou, Yang Zhang. Jiabao Ji, Yujian Liu, Kaizhi Qian, Jacob Andreas, and Shiyu Chang. Thinkprune: Pruning long chain-of-thoughh of IIms via reinforcement learning, 2025. URL https://arxis: wwrggabs//555 01296.
[12] Jian Hu. Reinforce++: A simple and efficient approach for aligning large language models. arXiv preprini arXiv:2501.03266 2025.
[13] Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, et al. Openai ol system card. arXiv preprint arXiv:2412. 2024.
[14] Bowen Jin, Chulin Xie, Jiawei Zhang, Kashob Kumar Roy, Yu Zhang, Zheng Li. Ruirui Li, Xianfeng Tang, Suhang Wang, Yu Meng, et al. Graph chain-of-thought: Augmenting large language models by reasoning on graphs. arXiv preprint wxXv::2444007103 2024.
[15] Zhong- Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Jic Wang, Xiuyi Chen, et al. From system to system 2: A survey of reasoning large language models. arXiv preprint (rXix:2502.174199 2025.
[16] Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin. Understanding rl rl-zero-like training: A critical perspective. arXiv preprint arXiv:2503.2078. 2025.
[17] Haotian Luo. Li Shen, Haiying He, Yibo Wang. Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. O1-pruner: Length- hangth-harmonizing fine-tuning for ol-like reasoning pruning. arXiv preprint arXiv:2501. 12570, 2025.
[18] Michael Luo, Sijun Tan, Justin Wong, Xiaoxiang Shi, William Y. Tang, Manan Roongta, Colin Cai. Jeffrey Luo, Li Erran Li, Raluca Ada Popa. and Ion Stoica. Deepscaler: Surpassing ol op-prev with a 1.5b model by scaling rl, 2025. Notion Blog.
[19] Sara Vera Marjanović, Arkil Patel, Vaibhav Adlakha, Milad Aghajohari, Parishad BehnamGhader, Mehar Bhatia, Aditi Khandelwal, Austin Kraft, Benno Krojer, Xing Han Lù, et al. Deepseek-rl thoughtology: Let's< think> about Ilm reasoning. arXiv preprins arX4::2504.07/28 2025.
[20] Yu Meng, Mengzhou Xia, and Danqi Chen. Simpo: Simple preference optimization with a reference-free reward. Advances in Neural Information Processing Systems, 37:124198-124235, 2024.
[21] Xiaoye Qu, Yafu Li, Zhaochen Su, Weigao Sun, Jianhao Yan, Dongrui Liu, Ganqu Cui, Daizong Liu, Shuxian Liang. Junxian He, al. A survey of efficient reasoning for large reasoning models: Language, multimodality, and beyond. arXiv preprint arXiv:2503.21614. 2025.
[22] Yuxiao Qu, Matthew YR Yang. Amrith Setlur, Lewis Tunstall, Edward Emanuel Beeching, Ruslan Salakhutdinov, and Aviral Kumar. Optimizing test-time compute via meta reinforcement fine-tuning, arXiv preprint arXiv: 2rX1:22503.0572, 2025.

---

[23]
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:170.00647, 2017.
[24] Amrith Setlur, Chirag Nagpal, Adam Fisch, Xinyang Geng, Jacob Eisenstein, Rishabh Agarwal. Alekh Agarwal, Jonathan Berant, and Aviral Kumar. Rewarding progress: Scaling automated process verifiers for UI reasoning. arXiv preprint wwxiv:2410.081444 2024.
[25] Zhihong Shao, Peiyi Wang. Qihao Zhu, Runxin Xu, Junxiao Song. Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300 2024.
[26] Jianshu She, Zhuohao Li, Zhemin Huang, Qi Li, Peiran Xu, Haonan Li, and Qirong Ho. Hawkeye:effiiiet reasoning with model collaboration, 2025. URL httpp::/arxiv..ooo org/abs/ 2504. 00424.
[27] Yi Shen, Jian Zhang, Jieyun Huang, Shuming Shi, Wenjing Zhang, Jiangze Yan, Ning Wang, Kai Wang, and Shiguo Lian. Dast: bffficult--daptiii slow- wow-thinking for large reasoning models. arXiv preprint arXiv:2503.04477 044472, 2025.
[28] Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling Ilm test-time compute opti- mally can be more effective than scaling model parameters. arXiv preprint 2:X 2024.
[29] Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Hanjie Chen, Xia Hu, et al. Stop overthinking: A survey on efficient reasoning for large language models. arXiv preprint arXiv:2503.16419 2025.
[30] Kimi Team, Angang Du, Bofei Gao, Bowei Xing, Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun Xiao, Chenzhuang Du, Chonghua Liao, et al. Kimi k1. 5: Scaling reinforcement learning with llms. arXiv preprint arXiv:2501. 125999 2025.
[31] Rui Wang, Hongru Wang, Boyang Xue, Jianhui Pang, Shudong Liu, Yi Chen, Jiahao Qiu, Derek Fai Wong, Heng Ji, and Kam-Fai Wong. Hamnsssing the reasoning economy: A survey of efficient reasoning for large language models. arXiv preprint arXiv:2503.2337,, 2025.
[32] Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoe Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models. Xrxiv preprint ar arXiv:223..11177 2022.
[33] Yubo Wang, Xueguang Ma, Ge Zhang, Yuansheng Ni, Abhranil Chandra, Shiguang Guo, Weiming Ren, Aaran Arulraj, Xuan He, Ziyan Jiang, al. Mmlu-pro: more robust and challenging multi-task language understanding benchmark. arXiv preprint 45X15:2406.01574, 2024.
[34] Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoe V Le, Denny Zhou, et al. Chain-of- of-thhuthtt prompting elicits reasoning in large language models. Advances neural information processing systems, 35:24824 24424824-24837, 2022.
[35] Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang. Inference scaling laws: An empirical analysis of compute-optinn optimal inference for problem-solvie with language models. arXiv preprint arXiv:2408.0077 2024.
[36] Violet Xiang, Charlic Snell, Kanishk Gandhi, Alon Albalak, Anikait Singh, Chase Blagden, Duy Phung, Rafael Rafailov, Nathan Lile, Dakota Mahan, et al. Towards system 2 reasoning in lims: Learning how to think with meta chain-of-thouge arXiv preprint arXiv:2501 .04682, 2025.
[37] An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, Keming Lu, Mingfeng Xue, Runji Lin, Tianyu Liu, Xingzhang Ren, and Zhenru Zhang. Qwen2.5-math technical report: Toward mathematical expert model via self-improvement. arXiv preprint urXiv:2409.12122 2024.
[38] Junjie Yang, Ke Lin, and Xing Yu. Think when you need: Self-adaptive chain-of-thought learning, 2025. URL https:://arxiv www.arwwwww...raaaeeaeee a20p////..///.....//// 2534233344........
12

---

[39] Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths. Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Ad- vances in neural information processing systems, 36:1 1099-18822 2023.
[40] Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. Limo: Less is 03387.
more for reasoning, 2025. URL
[41] Edward Yeo, Yuxuan Tong, Morry Niu, Graham Neubig, and Xiang Yue. Demystifying long chain-of-thought reasoning in llms. arXiv preprint arX1iv:5522.0337,, 2025.
[42] Zhaojian Yu, Yinghao Wu, Yilun Zhao, Arman Cohan, and Xiao-Ping Zhang. Z1: Efficient test-time scaling with code, 2025. URL https: //axxiv www.aiwwww....a...eeeeooeeeeeeee arggabs/256/ 00810.
[43] Xiaotian Zhang, Chunyang Li. Yi Zong. Zhengyu Ying, Liang He, and Xipeng Qiu. Eval- uating the performance large language models on gaokao benchmark. arXiv preprint arXiv:2305. /2474, 2023.
[44] Chujie Zheng. Zhenru Zhang, Beichen Zhang, Runji Lin, Keming Lu, Bowen Yu. Dayiheng Liu, Jingren Zhou, and Junyang Lin. Processbench: Identifying process errors in mathematical reasoning. arXiv preprint arXiv:2412.06559 2024.
[45] Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Livia Sun, Jeff Huang. Cody Hao Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E Gonzalez, et al. Sglang: Efficient execution of structured language model programs. Advances in Neural Information Processing Systems, 37:62557-62583, 2024.
A Experimental Details
A.1 The Distribution of Maximum Correctness Probability for Incorrect Responses.
max pj Distribution
Due to space limitations, we report the distribution of max; pj for incorrect responses of the DeepScaleR-1 1.5B--reviiw model in Fig- ure In Section 3.3, we analyze the distribution max; Pt values computed from reasoning trajectories that initially resulted in incor- rect answers. Here, p. denotes Monte Carlo estimate of the prob- ability that the model would generate the correct final answer if the reasoning process were terminated at the i-th thinking pattern. Our analysis reveals that non-trivial amount of intermediate segments exhibit high p; values, indicating that the model frequently pro- duces useful reasoning components even within incorrect responses. These findings underscore the potential of selectively terminating the reasoning process appropriate points recover correct answers.
Density
2
8.0
1.0
Figure 4: Distribution of max; p: in incorrect responses of DeepScaleR- 1.SB-Preview.
A.2 Implementation Details
For all training- based methods, the batch size was fixed at 128, and trained the model using four NVIDIA RTX A6000 GPUs. The value of 3 in Equation (13) is set to 10.0, and the ratio 7/9 / is set to 0.3. For DeepSeek-B
[9] and DeepScaleR- 1.5B-Preview [18], we the sampling parameters temperature of 0.6, top_p of 0.95, top_k k of -1, and a maximum generation length 8192 tokens. For the Qwen2.5-Man Instruct model [37]. we the same configuration. However, due limitation in the SGLang framework [45], which raises an error when the maximum number of tokens exceeds 4096, we adjusted our settings accordingly.
-Distill-Qwen----
13

---

A.3 Algorithm of DTO
We provide summary of the full optimization procedure in Algorithm 1.
Algorithm 1 DTO: Dynamic Thinking pattern Optimization
Require: 2: input problem, reasoning trajectory from LRM we. a": ground -ruth answer, 7' correctness threshold, M: samples for exit prediction, K: completions for finalize, pai auxiliary LLM
I: Segment y into thinking patterns (ō1,-.., Öny)
2: i'
3: for i to Tly do Ti f- 81 @
6, & desit
& Construct partial trajectory by appending exit thinking pattern
Sample R, = fri...., TM r2 ~ To (T)))
Monte Carlo sampling
6:
P. + {r Ra a" E (R,
b Estimate correctness probability
7:
if T then
8:
t-i
break
10: end if
11: end for
12: f(6.) =iii
Define binary selection function f(-)
13: A c66 [(:)==
14: Define Ófimliie "Hmm, I think this is enough to derive the final answer
15: SAL f81.,.... 8, Te(Ad @ ônmaliz)
Sample completions
16: Select shortest E EAA such that a* E
17: À + +f Sanatize +
18: for each ò E A do
19:
Query the utility of 6 based on the Me 's evaluation conditioned on the context of and a"
(see Appendix A.4) f
20:
Construct A
8, A 6, * 6, and before "\,boxed"
21:
g(ó.) < if 8, deemed redundant by μe and decoding from A f/6 yields a
22:
end for
23: Ag + j6, A ( * 1]
24:
return dynamically optimized reasoning trajectory A
14

---

A.4
Prompts
Default Prompt
Please reason step hy step, and put your final answer within Vhoxed [
|| problem })
Fast Prompt
Please reason step by step, and pat your final answer within (boxed(), )
Solve problem quickly possible.
|| problem }]
Prompt for the Auxiliary LLM (Po in Section 3)
You will be given:
problem
A ground-truth answer
A series of reasoning chunks
Your lask hus two purts:
STEP Filtering Decide for each chunk whether KEEP AS REMOVE, KEEP IS the chunk contributes meaningfully:
Narzowing down possiblities
Showing intermediate calculations
Offering partial insight (even incomplete)
Reinforcing understanding through repetition
REMOVE
meaningful
It factually incorrect in harmful way
entirely off topic or unbelpfally redundant
STEP 2: F Final Reasoning Construction Using only the KEPT chunks:
Concutenate them with minimal edits flow.
Use each kept chunk verhatim.
Do paraphrase skip ideas.
Preserve original (informal, exploratory,
End the reasoning with the final this format: \boxed((...
Output Format:
[OUTPUT]
[CHUNK_FILTERRE] FILTERING, RESULTS)
LChunk
[Chunk 23 REMOVE
[Chunk KEEP IS
[FINAL_ WWW.RREOOSTRUCTEDREAAEEEOE R
<Clean explenation using only the Mininal edits for End with the boxed final answer.> ene
your input:
Problem: (problen)
#ds Ground-Truth grround_truth_aatt
WN Reasoning Chunks: (thinking_patteral
15

---

B Qualitative Analysis
We selected a question from the AMC2023 dataset qualitatively compare the reasoning trajectories of the baseline model and ours. The question is "What is the degree measure of the acute angle formed by lines with slopes and 3² and the correct answer is 45.
B.1 A Reasoning Trajectory of the Baseline (1790 tokens)
okay, so neze to find the acute angle between twe lines with slopes 2 and 1/3. li,, remember there's fornula for the angle between two lines based on their slopes. Let ne try recall.
difference slopes divided by slopes. So, if the slopes are at and 12, the angle Nuesbe between then is given by:
think
involves the arctangent
product
su82bs pretan(I(es
m))/(1 m)Am2)
is that right? Let me check. Yeah, think that's correct because the tangent of the angle between two lines is ecual to the absolute value of (x2 n1)/(1 mlAn2). So, this fornula gives the angle between then.
Airight, so assign
Plugging these formula:
Kudlbs arctan(1(1/3 2)/(1 (2)x(1/3))1)
First. compute murerator: 1/3 That's 1/3 (-5)/3.
Then, the denoninator: (2)a(1/3) 1 2/3 5/3.
50, putting togother, have:
Nu030s aretan(1(- (Cct)(((-5/3)/(//3)) - arctan(|-1]) arctan(1)
Because absolute
So, arctan(1) is... degrees, right? (45
Mait, but hold on, the question asks for the acute angle. So. degrees is already acute, since it's less than degress. is the It straightforward.
But let ae make sure didn't 't make any mistakes in my calculations. Let's ge through it again.
Difference in slopes: a2 ml 1/3 = -5/1.
Product mlan2 2x(1/3)
Denoninator: 2/3 5/3.
argunant inside
((-5/3)/(5/3))
50. arcton(1) is 45 degrees. That seers correct.
wait second, renenber
be l'ound the fornula:
cantuaaba [[n2 a1)/(1 al=n2)]
Which exactly
used. that
But just to couble-chock, 1et ne visualize. If one line has slope of 2, that's pretty steep, going up units for every unit to the right. The other line has slape of 1/3, which is gentle stape, going
unit for every units
So, if you imagine these two lines intersect ing, the angle batween then is likely to be acute because both slopes are positive but one is stoeper. So, 45 degrees is reasonable.
Malt, degrees common angle, that seens plausible.
Al ttternatively can think of the angle each line nakes with the xraxis and then find the difference between angles.
The angle \u83b1 that line with slope makes with the xeaxis is given by \u83b1 ar)tan(t). So, for at sualbil aretan(2), and for u2 1/3, 1683612 a113)
Then, the angle between the two lines would Nuesbt1 Yua3b121. Since \u83b11 and Nu83b12 are positive angles less than ga degroes (since stopes are positive), the cifferance will also ba positive, and since 're taking the absolute value, it'll give the acute angle.
conputo that way verify.
approxinate that. I know that arctan(1) is 45ku00ba, arctan()u21a3) delueabe, so arctan(2) sonewhere between selueabe 75Nueabe, naybe 63, 4349%
First, compute \683b11 arctan
Similarly, (1/3) Since 1/3 is less than 1, arctan(1/3) asproxinately 18. u.ebb So, diffarence 63.494 18, 4349%88bb8 45/u8abe. So, that confirns it.
Therefore, the acute angle between the lines 45 degrees.
16

---

Mast, nethods
titernatively can think about the tangent of the angle between then, which wo found was 1, so (retan(1)) is 45tuBebe, so that's consistent.
so, whather I the subtract then, get 45 degrees. Therefare, I think that's the correct ansuer.
slopes or conpute angles nakes with x-axis and
ny
The
1. zecognize the Fornula for the angle between tao lines: lualad ( m1)/(1 al
Plug in the slopes al = and n2 1/3
falculate
denesinator
Simplify expression
aretan
Find that it equals arctan(1) 45%u0abe
Confirs with another rethod, 1ike computing the Individual angles and subtracting then
steps check out, so I'n pretty sure 45 degrees
answer.
Finnnl Answer**
angle by
W4oxed(45) degrees </think>
To rind the acute angle forned by lines with slopes ((25)) and ())))) we use the formula for the angle W(ASthetal)) between lines with slopes W(K211) and W(L_2()):
Wtheta (iretann
- n.100 +.1 n.2]WWright
BJ
assigning W(RL 201) and W[n_2 Wfrac())))))
Compute the (F(a (1rac(1)(3) (3rae(e)(3) -VVrac(()(3)
n_2
11]
Compute the denoninator:
n. a.2 = Wedat (3r = (rrae())(3) (Frac())
11
Simplify the argunent inside arctangent:
Wlefft] Mffrec/) Wright] Wleft] Wright|
4. Therefore, the angle t(Whthetal)) is:
WWrccan 45-Weeire
01
To verify, also the angles each line makes with the x-axis and find the difference. The
angies are:
WW/Waalpho_1 Warctan(2) Wapprox (399
-Wllialphe_2 (arccanlllett(fffrre(((MMeeee Wapprox 16, (eprirr))))))
difference
63. 1349n/iccir Verere 45rMrc
W]
Thus, the acuce angle forned by the lines is W(Nbbxed(45))))
degrees.
B.2 A Reasoning Trajectory of the Ours (814 tokens)
Okay, so nead to find the acute angle between two lines with slapes 2 and 1/3. 8m, renerber that there 's fornula involving the slopes of two Lines to find the angle betaeen thex. Let think. think divided soneching x1)/(1 al+a2). Yeah, that sounds Fantllar from my geonetry
it's sonething tan(theta) equals the absoluta value class.
aretangent of
of
it's
Alright, so ne 1/3. Plugging those in, it should tan(theta) equals absolute value of (173 2)/(1 (1/3). Let no conpute nunerator and canoninator separataly.
down.
tan(theta) 1(n2 at)/(1 mien2))
First, easter. equal 6/3. Se 1/3 5/3 is -5/3. okay, nuserator -573.
subtract
thirds
benoninator: (11(13) let compute that, tines 1/3 is 2/3. Then, adding which is 3/3, 2/3 denoninator
Therafore, tan(theta) equals the absolute value of (55/3)/(5/3). When you divide those fractions, the 5/3 tan(theta)
cancels leaving
Now tan(theta) 1, then thata arctangent 1. remesber that tan degrees) 1. theta
degrees. lit, since it's asking for the acute angle, which is less than 90 degrees, , and 45 degrees is acute. that should be the answer.
17

---

Applied
negative, denoninator positive, got (an(thet))=,, theta degrees. Yeah, sounds good.
MAFinal Answerva
angle
(4oxed(455) degrees.
</think>
To rind the acute angle forned lines with slopes (X(21)) and ((NVracc()))))))) use the Formula for the
WE
(ttan(Wthetaa) Weett) 2 1 n_1 (L2) Wright]
Here, WERL = 201) and W1 (M Plugging these values into the fornula, we get:
(ttan(tttetta) Wleft] Wrrac(( 2)(1 Wfrac(13333 Wright]
W1
First, conpute
(frra(())3) Wifra(())))) Wfrac(()()) -V)Frac(5(1)
Next, comрute the denoninator:
Wedet Wfrae())() (Xra)(?)(3) (Frae(3))) Wfrac(2))) (Frae())(3)
W1
Tuus
(ttahWWh W[eff]] WFFAecCAMSneee))X)))MMXAMCCC Wright] Wleft] -1 Wright]
Since W(1tan()thhet) = 18), ae Find that WCVttheta 45-Veirr)))).
(45x
W
C
Datasets
The information about the dataset used is as follows:
MATH [10]: https: //gi thub. com/hendrycks//mtti The dataset is released under the MIT license, and we adopt the same data split as used in et [17].
GSM8K [S]: /ttps://huggii inn .ae.fac.comm /tt/c//atttes///peaaaa//s/aaa The dataset is released
der the MIT license.
Bench. The dataset is released under the Apache-2.0 license, and adopt the same data split used in Luo al. [17].
Gaokao [43]: httt::///ggtuub..om//eeennnnn
AMC:
AIME:
MMLU-Pro [33]: https:: htapgs///huggngaaaeee.. http:///www..a...oaaaaaaaaaaaaaa The dataset is
released under the Apache-2.0 license.
D Limitations
While our method demonstrates consistent improvements in reasoning efficiency and accuracy, it has several limitations. First, the effectiveness of our approach has been primarily validated on mathematical and reasoning-focet focuused benchmarks. While we validated our method on other domains using the MML.U-Pro dataset in Section 4.3, extending the evaluation broader domains, such as open-ended tasks, remains a promising direction for future work. Second, the approach assumes access to multiple model-generated responses per problem, which may not always be feasible in highly resource-constrained settings. Investigating ways reduce the computational overhead of the optimization phase itself could further improve the practicality of the approach real-world deployments.
18

---

E
Broader Impacts
This work aims enhance the reasoning efficiency of Large Reasoning Models (LRMs) by optimizing their internal decision-making processes. By reducing unnecessary reasoning steps while maintaining or improving accuracy, the proposed method has the potential to substantially lower inference cost and latency. This can benefit downstream applications by enabling more computationally efficient and environmentally sustainable deployment of LRMs, particularly in resource conssteinnd settings. However, if LRMs are misused- for instance, to generate plausible fake information, automate biased decision-make making. or produce large-scall scale deceptive content-ther they may contribute to negative societal impacts. It is therefore important to remain mindful of the potential for such technologies to be applied in harmful ways, even when developed with efficiency and performance mind.
NeurIPS Paper Checklist
The checklist is designed to encourage best practices for responsible machine learning research, addressing issues of reproducibility. transparency, research ethics, and socictal impact. Do not remove the checklist: The papers not including the checklist will be desk rejected. The checklist should follow the references and follow the (optional) supplemental material. The checklist does NOT count towards the page limit.
Please read the checklist guidelines carefully for information on how to answer these questions. For each question in the checklist:
You should answer [Yes], [No], [NA].
[NA] means either that the question is Not Applicable for that particular paper or the relevant information is Not Available.
Please provide short (1-2 sentence) justification right after your answer (even for NA).
The checklist answers are an integral part of your paper submission. They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers. You will be asked to also include it (after eventual revisions) with the final version of your paper, and its final version will be published with the paper.
The reviewers of your paper will be asked While "[Yes] is generally preferable to "[No]" ", it is perfectly acceptable to answer "[No] provided proper justification is given (e.g., "error bars are reported because it would be too computationally expensive" or "we were unable to find the license for the dataset we used"). In general, answering binary way, we
the checklist one of the factors in their evaluation.
"[No] " or "[NA] is not grounds for rejection. While the questions are phrased acknowledge that the true answer is often more nuanced, so please just use your best judgment and write justification elaborate, All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix. If you answer [Yes] to a question, in the justification please point to the section(s) where related material for the question can found.
IMPORTANT, please:
Delete this instruction block, but keep the section heading "NeurIPS Paper Checklist",
Keep the checklist subsection headings, questions/answers and guidelines below.
Do not modify the questions and only use the provided macros for your answers.
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The main claims in the abstract and introduction reflect the paper's contribu- tions and scope. See Section 3 and Section 4.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
19

---

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.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
See Appendix D.
Guidelines:
The answer NA means that the paper has no 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 "Limitations" section 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 on 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 is low 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 be 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 an impor- tant role in developing norms that preserve the integrity of the community. Reviewers penalize honesty concerning limitations.
will be specifically instructed
3. Theory assumptions and proof's
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
Justification:
This paper does not include theoretical results.
Guidelines:
The answer NA means that the paper does include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should complemented by formal proofs provided in appendix supplemental material.
20

---

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 of 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 or not)?
Question:
Answer: [Yes]
Justification: See Appendix A.
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 novel architecture, describing 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, or 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.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurlPS does not require releasing code, the conference does require all 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) If the contribution is 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 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., registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, described in supplemental material?
Answer: [Yes]
Justification: [NA]
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
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
21

---

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:
/ //npsscc//ubb
deggdeeee//oduubmmi wwwiiiimsssiiniii ssionPolinn Piyy) for more details.
The authors should provide instructions 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. 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 much information possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: 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?
Answer: [Yes]
Justification: See Section 3, Section 4 and Appendix A.
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
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer: [Yes]
Justification: See Figure 3.
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, or statistical significance tests, at 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, overall run with given experimental conditions).
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).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
is OK to report I-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 show in tables figures symmetric error bars that would yield results that are out range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
22

---

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: See Appendix A.
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, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs well 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 failed experiments that didn't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips... http://icc/ctctcccctiiiia ines?
Answer: [Yes]
Justification: Ethics.
The research conducted in this paper conforms with the NeurlPS Code of
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances 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 their jurisdiction..
Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes]
Justification:
See Appendix E.
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA No, they should explain why their work has 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., deploymentt of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a 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 unintentional) misuse of the technology.
23

---

If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks. mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of MI.).
11. Safeguards
Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (c.g., pretrained language models, image generators, scraped datasets)?
Answer: [NA]
Justification:
This paper poses no such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have a 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 to 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. Licenses for existing assets
Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and the license and terms of use explicitly mentioned and properly respected?
Question:
Answer: [Yes]
Justification: We cite the original paper and see Appendix for more details.
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package dataset.
The authors should state which version of the asset used and, possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paper swi thcode. com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if has changed) should be provided.
this information not available online, the authors are encouraged to reach out to the asset's 's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes]
Justification:
We provide the code and documentation for running it in the supplementary
material.
Guidelines:
The answer NA means that the paper does not release new assets.

---

Researchers should communicate the details of the dataset/codeemmodel as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL or include anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification: This paper does involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Including this information 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 to the NeurIPS Code of Ethics, workers involved in data collection, curation, other labor should be paid at least the minimum wage in the country of the data collector.
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: This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does involve crowdsourcing nor research with human subjects.
Depending on 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 we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if' applicable), such as the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA]
Justification: The core method development this research does not involve LLMS as any important, original, or non-standard components.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
25

---

Please refer to our LLM policy http::///eeerrssssccooooereeeees for
what should or should not be described.
26


Reviews:
[{"review_id": "pDjnbeIknW", "reviewer": "Reviewer_iNNv", "summary": "The paper present a novel method to improve quality of the reasoning in a dynamic manner. In particular, after model generating examples in the RL procedure, it refine these examples by cutting in the middle to only preserve the first-half part that are believed to be sufficient to derive the final answer. Additionally, it also presents another method to remove unnecessary reasoning steps in the middle, by testing if the correct answer can be obtained by removing the middle steps. Experimental evaluation shows that the proposed method effectively reducing the reasoning length while improving the reasoning accuracy as well.", "questions": "Removing in-the-middle reasoning steps:\n\nConsider this reasoning pattern: A->B->C->D->Result. The D may contain sufficient information to obtain Results (many LLMs explicitly or implicitly generate results in D before finally conclude the results). But the fact is the B is necessary to obtain C and then D. Removing B is not OK and can ruin the model. So I think the method proposed in the paper is faulty.", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The idea of refining the reasoning patterns seems reasonable to me, but the method to achieve this goal is not quite convincing. The model eventually learns from generated reasoning patterns and as a result improving the patterns is useful. In terms of the method proposed, I think the method of removing in-the-middle reasoning steps is dangerous to me.", "was_revised": false, "final_justification": "", "rebuttal": "**[W1 & Q1]**\n> **Reviewer’s Comment**: Stage 2 of DTO might have a risk of over-pruning.\n\nWe appreciate the concern regarding the risk of over-pruning. As described in Section 3, our method, DTO, consists of two stages:\n\n1. Identifying the appropriate point at which the reasoning should be finalized, and\n2. Pruning intermediate thinking patterns that do not meaningfully contribute to the reasoning objective.\n\nStage 2, in particular, is **carefully designed to prevent harmful pruning** through a **conservative, multi-step verification process**. To begin, we assess the utility of each intermediate reasoning chunk using an auxiliary LLM. To avoid inadvertently removing valuable reasoning steps, we guide this LLM using explicitly conservative filtering criteria. As detailed in Appendix A.6, the prompt includes the original problem, the complete reasoning trajectory, the correct final answer, and the following instructions:\n\n- **Retain** any chunk that contributes meaningfully, including narrowing down possibilities, offering partial insight (even if incomplete), performing sub-computations, supporting downstream reasoning, or even reinforcing understanding through redundancy.\n- **Remove** only those chunks that are clearly off-topic, factually incorrect in a harmful way, or provide no meaningful content - with the default bias *toward retaining* unless strong justification for removal is found.\n\nTo further verify the safety of each removal, we perform a lightweight decoding-based validation. For each candidate chunk $\\delta_i$ - previously identified by the auxiliary model as a removable thinking pattern - we define the following sequence:\n$\\tilde{\\Delta}_x^{f\\setminus \\delta_i} = \\left[\\ \\delta_j \\in \\tilde{\\Delta}_x^f \\middle| \\delta_j \\ne \\delta_i,\\ \\text{and before ``}\\backslash\\text{boxed''} \\ \\right]$\n\nWe then quickly decode from this sequence to check whether the model can still produce the correct answer. The pruning of $\\delta_i$ is accepted only if the answer remains correct; otherwise, the chunk is retained.\n\nAs shown in Tables 1 and 2 of the main paper, this careful procedure enables **DTO to consistently outperform baselines in terms of reasoning efficiency**, achieving similar or better accuracy while generating fewer tokens.\n\nAdditionally, motivated by your comment, we conducted an **ablation study** to assess the isolated impact of Stage 2, using DeepSeek-R1-Distill-Qwen-1.5B as the base model. Below, we present the results comparing DTO with only Stage 1 to the full version with both stages applied:\n\n| Dataset |  | Base | DTO (Stage 1) | DTO (Stage 1 + 2) |\n| --- | --- | --- | --- | --- |\n| **MATH** | ACC | 79.8 | 85.21 | 85.48 |\n|  | #Tokens | 3543.44 | 2256.26 | 1936.19 |\n|  | Eff. | 1.000 | 1.677 | **1.960** |\n| **GSM8K** | ACC | 82.13 | 83.95 | 83.91 |\n|  | #Tokens | 1382.99 | 1050.54 | 844.18 |\n|  | Eff. | 1.000 | 1.346 | **1.674** |\n| **Gaokao** | ACC | 66.62 | 72.79 | 72.66 |\n|  | #Tokens | 3725.16 | 2559.51 | 2137.59 |\n|  | Eff. | 1.000 | 1.590 | **1.901** |\n| **AMC2023** | ACC | 58.25 | 70.00 | 70.25 |\n|  | #Tokens | 5338.54 | 3768.81 | 3376.98 |\n|  | Eff. | 1.000 | 1.702 | **1.907** |\n| **AIME2024** | ACC | 21.44 | 30.00 | 28.00 |\n|  | #Tokens | 7359.24 | 6301.40 | 5877.44 |\n|  | Eff. | 1.000 | 1.634 | **1.635** |\n| **AIME2025** | ACC | 18.89 | 21.67 | 21.11 |\n|  | #Tokens | 7236.66 | 6237.63 | 5689.38 |\n|  | Eff. | 1.000 | 1.331 | **1.421** |\n\nThese results show that **adding Stage 2 on top of Stage 1 has minimal impact on accuracy, while improving efficiency**. This confirms that our pruning procedure removes redundant or distracting reasoning without harming the underlying logic.\n\nWe appreciate the reviewer’s thoughtful comment again, which prompted us to conduct this additional analysis. We will include these results and clarifications in the revised version to more clearly communicate the safety and effectiveness of our pruning strategy."}, {"review_id": "9hEUSstUwV", "reviewer": "Reviewer_Nq5r", "summary": "The authors introduce Dynamic Thinking Pattern Optimization (DTO), a mechanism designed to solve the 'overthinking' of large reasoning models (LRMs). DTO first segments a generated reasoning trace into modular thinking patterns and locates the earliest point where the model can produce the correct answer, yielding a truncated path. Then, DTO elicits a minimal answer token string, which produces an optimized trajectory by removing inefficient patterns. These optimized reasoning traces achieve reasoning efficiency by reducing attention FLOPs by up to 47%. The authors also provide preference optimization with DTO, which also enhances the accuracy performance.", "questions": "1) Can DTO handle queries where no golden label is available? I wonder whether DTO is applicable in such settings.\n\n2) Can we use the same LRM as an auxiliary LLM? For instance, in this paper, can we use DeepSeek-R1-Distill-Qwen-1.5B or DeepScaleR-1.5B-Preview? If so, why didn't the authors conduct the experiments? If not, it would be helpful to explain the reason.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n1) While current studies have focused on making longer reasoning traces, the authors' motivation to shorten and optimize the length of reasoning is fascinating. It is also intriguing to formulate this as a constrained optimization problem.\n\n2) By delivering simultaneous gains in both efficiency and accuracy, DTO outperforms baseline methods, except for #Tokens of Instruct ver. DTO's ability to generate minimal yet sufficient reasoning paths not only lowers inference cost but also supplies high-quality supervision for further model improvement.\n\n3) I can see that DTO is not tied to arithmetic reasoning alone, but can compact and preserve the correctness of chains-of-thought in diverse subject areas from Table 4. Although the authors mentioned mathematical-focused validation as one of their limitations, I am pretty confident that DTO would reduce the reasoning token lengths or attention FLOPs in more varied benchmarks.\n\n\n## Weaknesses\n\n1) DTO's pruning stage, after determining the 'finalize' thinking pattern, requires an auxiliary LLM, which is different from the original LRM. The auxiliary LLM judges and removes redundant thinking patterns. The authors use a 70B model for an auxiliary model, whereas the original model's size is 1.5B. I wonder whether it is fair to use the auxiliary model of such a large size, when the baselines seem to only use 1.5B, which is the same size as the original LRM. However, I do not see any justification for using the large auxiliary model for DTO.\n\n2) DTO splits the reasoning trace with words such as 'Wait' or 'Alternatively'. DTO cannot split if such words are not contained in the reasoning trace. I presume the paper needs a more sophisticated method to segment a reasoning trajectory in a sequence of thinking patterns. If the current method is sufficient, please explain the reason.\n\n3) Tables 1--4 contain Instruct ver. as a baseline, which is an instruction-tuned version of LRMs. I noticed the accuracy of this baseline is low, but it has the lowest #Tokens. For instance, if we examine the #Tokens of Instruct ver. for GSM8K in Table 2, it shows approximately 3 times fewer tokens than DTO, even with on-par accuracy scores. I wonder if a simple in-context learning technique, such as providing few-shot demonstrations or Chain-of-Thought (CoT), would be more powerful than DTO in both accuracy and #Tokens. The authors should also analyze the result of #Tokens of Instruct ver. compared to DTO.", "was_revised": true, "final_justification": "I am maintaining my evaluation as \"vorderline accept\" because the paper's core idea is reasonable, and the authors have committed to addressing my main concern in the final version.\n\n- **Strengths:** The paper's core idea, the DTO framework, addresses the \"overthinking\" problems in large reasoning models.\n\n- **Remaining Concern:** My main concern is the use of an oversized auxiliary LLM (70B). This makes it difficult to assess the standalone contribution of the DTO methodology, separate from the power of the large model. **However**, this concern is addressed by the authors' rebuttal and also the firm commitment to include the crucial ablation study I requested in the final version. Thus, I maintain my position to \"borderline accept\", contingent on this revision.", "rebuttal": "**[W1 & Q2]**\n> **Reviewer’s Comment:** Please provide the justification for the choice of auxiliary model used in DTO.\n\nWe thank the reviewer for this thoughtful and important comment. To clarify, our use of the auxiliary LLM (LLaMA 3.3-70B-Instruct) was intentionally aligned with the setup used in one of our primary baselines, **FCS + Ref.**, which also relies on the same model. By adopting the same auxiliary model, we ensure that the performance gains observed in our method are attributable to the proposed framework itself - rather than differences in model capacity - thereby enabling a fair and controlled comparison.\n\nWe agree that the motivation for this design choice should be made more explicit. In the revised version, we will clarify this point to enhance the transparency and fairness of our experimental setup.  \n\n\n\n**[W2]**\n> **Reviewer’s Comment:** Please explain the rationale behind segmenting reasoning trajectories using discourse cues that signal transitions in thinking, and possible strategies for handling cases where such cues are absent.\n\nThank you for highlighting this important point. Firstly, we follow prior work [1, 2] in segmenting the reasoning trajectory into multiple thinking patterns using discourse cues such as *“Wait”* or *“Alternatively”*, which frequently appear in the outputs of large reasoning models [1, 2]. These cues are widely known to reflect shifts in the model’s reasoning process, including transitions into self-verification, intermediate summarization, or revised hypotheses as described in Section 3.\n\nWe acknowledge, however, that this heuristic may not be applicable in all cases, particularly when such cue words are absent. In those situations, a promising extension would be to first analyze the lexical or structural patterns that commonly appear at the beginning of new paragraphs or sentences, and then leverage these patterns to define segment boundaries in a more systematic manner.\n\nWhile our current approach provides a simple and effective segmentation method grounded in observed discourse patterns, we agree that developing a more general and robust segmentation strategy would be a valuable direction for future work. We will clarify both this limitation and potential extensions in the revised version.\n\n**[W3]**\n> **Reviewer’s Comment:** Compare DTO with a simple in-context learning technique, such as providing few-shot demonstrations or CoTs to Instruct version.\n\nThank you for the thoughtful comment. While we appreciate the interest in comparing DTO against instruction-tuned variants, we would like to firstly clarify the intended evaluation scope of our work. As described in Section 3.1, our primary goal is to improve the efficiency of the base Large Reasoning Model, e.g., DeepSeek-R1-Distill-Qwen-1.5B, while maintaining or improving its reasoning performance. Accordingly, the efficiency metric defined in Equation (14) is designed to measure gains relative to this shared base model.\n\nIn contrast, the Instruct version is not directly derived from our target LRM but is instead based on its backbone model with separate instruction tuning. While we include Instruct ver. for completeness and to offer a broader perspective, it is not the main comparison target for efficiency evaluation, and we therefore do not compute the efficiency metric for them.\n\nTo further assess the effectiveness of instruction-tuned models and the feasibility of simple prompting-based enhancements, we conducted additional experiments based on the reviewer’s suggestion. Specifically, using DeepSeek-R1-Distill-Qwen-1.5B as the base model, we evaluated its instruction-tuned version, Qwen2.5-Math-1.5B-Instruct, under two prompting strategies, using 10 examples sampled from the training set: **(1) few-shot demonstrations** and **(2) few-shot CoTs**.\n\nThe results are presented in the table below. As shown, these prompting strategies do not lead to meaningful improvements in accuracy, and in some cases even degrade performance. This suggests that simply appending demonstrations or CoT examples may be insufficient for eliciting effective reasoning behavior in instruction-tuned models..\n\nWe also observe that the Instruct variants tend to perform relatively well on simpler datasets such as GSM8K, where they achieve reasonable accuracy with strong efficiency. However, their performance drops significantly on more challenging benchmarks such as AMC and AIME, suggesting a lack of robustness in handling complex reasoning tasks. These trends imply that while instruction-tuned models can be effective for relatively straightforward tasks, their generalizability may be limited in settings that demand deeper reasoning. Investigating which types of models or prompting strategies best suit different task complexities could be an interesting direction for future work.\n\nWe will include these additional results and analyses in the revised version to strengthen the comparison and highlight the advantages of our method.\n\n| Dataset |  | Instruct ver. + few-shot demos | Instruct ver. + few-shot CoTs | DTO (Ours) |\n| --- | --- | --- | --- | --- |\n| **MATH** | ACC | 73.91 | 76.47 | **85.48** |\n|  | #Tokens | 570.94 | 546.32 | 1936.19 |\n| **GSM8K** | ACC | 82.60 | **83.95** | 83.91 |\n|  | #Tokens | 318.37 | 307.04 | 844.18 |\n| **Gaokao** | ACC | 59.48 | 61.36 | **72.66** |\n|  | #Tokens | 589.41 | 590.32 | 2137.59 |\n| **AMC2023** | ACC | 48.12 | 50.00 | **70.25** |\n|  | #Tokens | 796.97 | 770.47 | 3376.98 |\n| **AIME2024** | ACC | 12.50 | 10.83 | **28.00** |\n|  | #Tokens | 1055.50 | 945.04 | 5877.44 |\n| **AIME2025** | ACC | 5.83 | 6.67 | **21.11** |\n|  | #Tokens | 896.23 | 816.89 | 5689.38 |\n\n**[Q1]**\n> **Reviewer’s Comment**: Can DTO handle queries where no golden label is available? I wonder whether DTO is applicable in such settings.\n    \nThank you for this insightful question. As described in the main paper, our current implementation of **DTO** leverages access to a ground-truth answer to supervise two stages:\n\n1. **Identifying the appropriate point** at which the reasoning should be finalized, and\n2. **Pruning intermediate thinking patterns** that do not meaningfully contribute to the reasoning objective.\n\nWhile our method currently operates in a supervised setting, we agree that it is meaningful to consider how our framework could be applied in weakly supervised or unsupervised settings. Importantly, **DTO can be naturally extended** to scenarios where ground-truth answers are unavailable, by utilizing a **reward model** as a surrogate for correctness. Below, we outline how each stage of DTO can be adapted accordingly.\n\n**1. Identifying the Finalization Point via Reward Comparison**\n\nIn the absence of a golden answer, we can replace the answer-likelihood signal, which is defined in Equation (6) of the main paper, with a scalar reward function $R(\\cdot)$, obtained via a reward model. For each truncated trajectory $\\tau_i$ (as defined in Equation (4)), we compute its reward: $R(\\tau_i)$.\nWe also compute the reward for the full reasoning trajectory $y$, denoted $R(y)$.\nWe then identify the earliest index $i'$ such that: $|R(\\tau_i) - R(y)| \\leq \\epsilon$,\n\nwhere $\\epsilon$ is a small threshold. This condition ensures that the partial trajectory is nearly as valuable (in terms of reward) as the full trajectory.\n\nWe then truncate the reasoning at index $i'$ using the same binary selection function $f(\\cdot)$ from Equation (7): \n$f(\\delta_i) = 1$ if $i \\leq i'$, $0$ otherwise.\nThis enables DTO to finalize reasoning at an appropriate point based on reward saturation, rather than answer correctness.\n\n**2. Pruning Redundant Chunks via Reward Sensitivity**\n\nTo adapt the pruning stage, we redefine the binary pruning function $g(\\delta_i)$ using the reward sensitivity of each chunk:\n$g(\\delta_i) = 1$ if $|R(\\Delta^f_x \\setminus \\{\\delta_i\\}) - R(\\Delta^f_x)| \\leq \\epsilon$, $0$ otherwise.\n\nThat is, we remove a chunk $\\delta_i$ only if its removal does not significantly degrade the reward. This allows us to safely discard segments that do not meaningfully contribute to high-reward outputs, while preserving critical content.\n\nBefore applying this function, we may optionally employ the same auxiliary model used in the supervised setup to narrow down candidate chunks, identifying those likely to be redundant and reducing the risk of over-pruning.\n\nThis reward-based extension maintains DTO’s core motivation while removing its reliance on ground-truth answers. It broadens the method’s applicability to **weakly supervised or unsupervised settings**, where annotated labels are unavailable.\n\nWe appreciate the reviewer’s suggestion and will include a discussion of this extension in the revised version, as we believe it represents a promising direction for future work.\n\n\n### References\n\n[1] Marjanović, Sara Vera, et al. \"DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning.\" *arXiv preprint arXiv:2504.07128* (2025).\n\n[2] Lu, Ximing, et al. \"Retro-search: Exploring untaken paths for deeper and efficient reasoning.\" *arXiv preprint arXiv:2504.04383* (2025)."}, {"review_id": "KgTCq2fARx", "reviewer": "Reviewer_LB6E", "summary": "This paper proposes a response optimization method for LRMs (large reasoning models). Specifically, it first uses Monte Carlo sampling to truncate responses and then employs an auxiliary LLM to remove redundant segments, aiming to reduce length without compromising accuracy. Preference optimization based on the optimized responses achieves competitive efficiency.", "questions": "1. I'm confused about how DTO is applied to incorrect responses, as discussed in Sections 3.3 and Section 4.1.\n    1. In Section 3.3, DTO relies on the gold answer in three ways: to truncate the given response, to get the shortest correct completion, and to remove redundant segments. Then the optimized response should achieve 100% accuracy if a correct trajectory exists in the sampling space. Therefore, Lines 192-196 are *not interesting*, as this is an unfair comparison with the initially yielded responses.\n    2. In Section 4.1 Lines 216-217, it is not guarenteed that applying DTO to a randomly sampled incorrect response will lead to an optimized response. How do you handle this?\n2. How do you segment a response y into a sequence of distinct thinking patterns? How many segments does a response have in average? And calculating all of these, how many completions need to be sampled per response to get an optimized response using DTO?\n3. FCS employs QwQ-32B. Can your proposed method show efficiency in larger LRMs, at least on 7B models?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n1. The idea of optimizing the individual contributions of reasoning segments is insightful, and the authors make a clear effort to achieve this goal through their proposed method.\n2. The experimental results are competitive and the statistical analysis is well-executed and easy to appreciate.\n3. The paper is content-rich, and the method section is clearly described.\n\n**Weaknesses**\n\n1. The proposed method is less efficient in collecting training samples compared to several baselines like FCS.\n2. The experiments are limited to two 1.5B models, making it unclear whether the proposed method remains effective on larger LRMs.", "was_revised": true, "final_justification": "I think using DTO to construct preference data is a reasonable and promising idea. While the improvements (e.g., saving a few hundred tokens in long responses) are relatively modest, the experiments are solid and the method could inspire future work in this direction.", "rebuttal": "**[W1 & Q2]** \n> **Reviewer’s Comment**: The method seems less efficient in collecting training samples. How is the response segmented into thinking patterns, and how many completions are needed per response to optimize it using DTO?\n\nAs described in Section 3 of the main paper, we segment the reasoning trajectory $y$ into distinct thinking patterns by leveraging discourse cues such as *“Wait”* or *“Alternatively”*, following prior work [1, 2]. These expressions commonly emerge in large reasoning models' outputs and are known to mark shifts in the model’s reasoning process, including transitions into self-verification, intermediate summarization, or revised hypotheses.\n\nEmpirical analysis reveals that a typical reasoning trajectory contains approximately 22 thinking patterns on average. However, not all of these require decoding. For the first stage of DTO - which identifies the point at which the reasoning should be finalized - we evaluate the probability of producing the correct answer from each partial trajectory $\\tau_i = \\delta_1 \\oplus \\cdots \\oplus \\delta_i \\oplus \\delta_{\\text{exit}}$, as defined in Equation (6). We then determine the earliest index $i'$ at which the probability surpasses a predefined confidence threshold. On average, this threshold is reached around the 14th segment, which implies that only the remaining 8 chunks typically require decoding.\n\nAltogether, following the setup in Section 3.3, DTO requires approximately 92 completions per response. Importantly, these completions are lightweight, since the decoding is limited to a small number of tokens - just 16 more than the length of the ground-truth answer- and can be efficiently parallelized using fast inference frameworks [3, 4]. Additionally, while DTO may involve a higher sample collection cost than some baselines, such as FCS + Ref., it is important to note that this procedure is performed offline during training. Once trained, the model yields substantial improvements in inference-time reasoning efficiency, as demonstrated in Tables 1 and 2 of the main paper. Therefore, we believe that the one-time cost of training is justifiable given the long-term benefits in runtime efficiency and scalability.\n\nWe will update the manuscript to clarify these aspects more explicitly. Thank you again for your valuable feedback.\n\n**[W2 & Q3]**\n> **Reviewer’s Comment**: Can your proposed method show efficiency in larger LRMs, at least on 7B models?\n\nThank you for your thoughtful question regarding the scalability of our method to larger language reasoning models. To address this point, we conducted additional experiments within our available resources to empirically evaluate DTO’s performance in larger-scale settings.\n\nSpecifically, we tested our method on a **larger model, i.e., DeepSeek-R1-Distill-Qwen-7B,** and considered three different settings on this model:\n\n- the base model,\n- the strongest baseline (**FCS + Ref.**), and\n- our proposed method (**DTO**).\n\nThese experiments followed the same training and evaluation protocols as outlined in the main paper, except for one change: due to computational constraints, we used **2,500 training instances** instead of 5,000. All other experimental settings remained consistent to ensure comparability. Additionally, please note that, due to the same computational constraints, we did not perform hyperparameter tuning and instead used the default configuration from the main paper.\n\nAs shown in the extended results table below, **DTO continues to achieve superior efficiency metrics** even at the 7B scale. It **outperforms both the base model and the FCS + Ref. baseline, which is the strongest baseline,** across all benchmarks, delivering improvements in both accuracy and token efficiency. These findings suggest that the **benefits of DTO generalize beyond 1.5B-sized models** and that the method is robust to increased model capacity.\n\nWe sincerely appreciate your suggestion, and we believe that these additional results strengthen the case for the applicability of DTO to larger reasoning models. We will incorporate these findings into the revised version of our main paper.\n\n| Dataset |  | Baseline | FCS + Ref. | DTO (Ours) |\n| --- | --- | --- | --- | --- |\n| **MATH** | ACC | 90.01 | 90.83 | 92.63 |\n|  | #Tokens | 3288.73 | 2756.03 | 2339.03 |\n|  | Eff. | 1.000 | 1.204 | **1.447** |\n| **GSM8K** | ACC | 92.32 | 92.59 | 93.03 |\n|  | #Tokens | 1731.13 | 1356.28 | 1148.84 |\n|  | Eff. | 1.000 | 1.280 | **1.518** |\n| **Gaokao** | ACC | 78.57 | 79.87 | 81.30 |\n|  | #Tokens | 3402.44 | 2924.27 | 2519.02 |\n|  | Eff. | 1.000 | 1.183 | **1.398** |\n| **AMC2023** | ACC | 78.75 | 82.50 | 86.25 |\n|  | #Tokens | 4885.61 | 4356.48 | 3731.45 |\n|  | Eff. | 1.000 | 1.175 | **1.434** |\n| **AIME2024** | ACC | 37.50 | 43.33 | 45.00 |\n|  | #Tokens | 6803.64 | 6724.27 | 6047.72 |\n|  | Eff. | 1.000 | 1.169 | **1.350** |\n| **AIME2025** | ACC | 30.00 | 32.50 | 33.33 |\n|  | #Tokens | 7013.32 | 6580.07 | 6548.10 |\n|  | Eff. | 1.000 | 1.155 | **1.190** |\n\n**[Q1]**\n> **Reviewer’s Comment:** It is unclear how DTO is applied when the initial response is incorrect.\n\nThank you for raising this question. Let us clarify the intended interpretation and provide further explanation.\n\nFirstly, the analysis in lines 192-196 is not about optimizing responses that are already correct. Rather, it highlights an important capability of our framework: even when the originally sampled response is incorrect, applying DTO can sometimes recover a correct reasoning trajectory.\n\nThis behavior is particularly valuable in challenging settings where most or all sampled responses from the base reasoning model are incorrect. In such cases, prior methods such as FCS + Ref. or DAST are unable to generate preference pairs and must discard the instance entirely, as they rely on having at least one correct response in the sampled pool.\n\nIn contrast, DTO enables us to rescue such difficult instances by producing a correct, optimized trajectory from an initially incorrect response. While this recovery is not guaranteed in all cases, when it does succeed, it allows us to include these cases in the pairwise training dataset, potentially offering strong learning signals in hard problem regimes. We believe this capability is one of the strengths of our approach, as reflected in the strong accuracy results reported in Tables 1 and 2 of the main paper, and we will revise the corresponding section to make this point more explicit.\n\n### References\n\n[1] Marjanović, Sara Vera, et al. \"DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning.\" *arXiv preprint arXiv:2504.07128* (2025).\n\n[2] Lu, Ximing, et al. \"Retro-search: Exploring untaken paths for deeper and efficient reasoning.\" *arXiv preprint arXiv:2504.04383* (2025).\n\n[3] Zheng, Lianmin, et al. \"Sglang: Efficient execution of structured language model programs.\" Advances in neural information processing systems 37 (2024): 62557-62583.\n\n[4] Fu, Yichao, et al. \"Efficiently Scaling LLM Reasoning with Certaindex.\" arXiv preprint arXiv:2412.20993 (2024)."}, {"review_id": "7tLV8QSBhI", "reviewer": "Reviewer_z6Kh", "summary": "This paper tackles the \"overthinking\" issue in Large Reasoning Models (LRMs), where they produce overly long and complex reasoning, harming efficiency. The authors propose a Dynamic Thinking pattern Optimization (DTO) framework. This framework aims to segment reasoning paths into \"thinking patterns,\" then identify and promote useful ones while removing those that are detrimental. The DTO process involves finding good stopping points for reasoning using Monte Carlo estimation and then pruning unhelpful segments with an auxiliary Large Language Model (LLM). The authors further refine LRMs by using preference optimization, creating a dataset of DTO-improved trajectories versus unoptimized ones to guide the model. Experiments across mathematical reasoning tasks show their method can reduce computational load (like FLOPs and token count) while keeping or even boosting accuracy. For instance, it reduced attention FLOPs by up to 47% while maintaining accuracy for initially correct responses, and improved accuracy by 15.6% for some initially incorrect ones. With preference optimization, they report up to a 12% accuracy gain and a token reduction from about 5,000 to 3,000.", "questions": "See weakness", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "I think the paper is reasonably spund. The approach of optimizing thinking dynamics in LRMs by segmenting reasoning into \"thinking patterns\" and then refining them is quite interesting. The empirical results, showing reductions in computational overhead like FLOPs and token usage while often maintaining or even improving accuracy, appear promising. I particularly noted the ability of the DTO framework to sometimes correct initially flawed reasoning paths, which is a valuable outcome. The reported efficiency gains, such as reducing attention FLOPs by up to 47% and token usage from around 5,000 to 3,000 while also achieving accuracy improvements, are significant.\n\nHowever, I have a few points:\n\n1.  It seems the DTO framework has two main stages: identifying an optimal termination point using Monte Carlo estimation, and then pruning redundant segments with an auxiliary LLM. I'm wondering if there was an ablation study performed to understand the individual contribution of each of these stages. It would be insightful to know which component contributes more to the overall improvement, or if both are equally critical.\n\n2.  The maximum response length was set to 8192 tokens for the experiments. I'm a bit concerned whether many of the baseline models might not have fully generated their responses within this limit, potentially truncating their reasoning, leading to incorrect answer (which is a super critical problem). This could affect the comparison, especially if the DTO-optimized models inherently produce shorter responses.\n\n3.  Based on my experience, smaller models like 1.5B or even 7B parameters can sometimes (even often) get stuck in loops or fail to finalize their answers. I think a simple but potentially strong baseline could involve forcing the model to generate an answer once it reaches a certain token limit, perhaps using a similar \"finalization\" mechanism as described in the paper. This might offer a more direct comparison for the conciseness and termination aspects of DTO. \n\n4. While I understand compute limitations might restrict extensive experiments on much larger models, I do have some slight reservations about the generalizability of these findings to significantly larger models without further evidence (considering small models' may have limited \"self-correction\" ability).", "was_revised": true, "final_justification": "In my original review, I raised concerns about the significance of DTO’s improvements and whether some experimental settings—particularly the fixed 8192-token truncation—might unfairly disadvantage models that naturally produce longer reasoning chains. I also questioned whether simpler baselines, like forced-finalization, were considered, and whether the method generalized beyond small-scale models.\n\nThe rebuttal addressed these points with thoughtful experiments, including ablations, extended token limits, and stronger baselines. I found these responses helpful and well-executed.\n\nHowever, my overall assessment remains cautious due to the lack of rigor in the original submission. Some of the evaluation setups could have been more balanced and better justified in the main paper. As a result, I have increased my score to reflect the strength of the rebuttal, but slightly lowered my confidence due to concerns about the paper's initial rigor.", "rebuttal": "**[W1]**\n\n> **Reviewer’s Comment**: An ablation study to understand the individual contribution of each of these stages would be insightful.\n\nThank you for raising this valuable point. To better understand the contribution of each stage, we conducted an ablation study that incrementally introduces each component of our framework:\n\n1. **DTO (Stage 1)**: We first add the mechanism that identifies the appropriate point at which reasoning should be finalized.\n2. **DTO (Stage 1 + 2)**: Building on top of Stage 1, we incorporate a module that prune intermediate thinking patterns that do not meaningfully contribute to the reasoning objective.\n\nWe used DeepSeek-R1-Distill-Qwen-1.5B as the base model for this study, and the results are presented in the table below. As shown, both stages independently yield meaningful improvements. Notably, Stage 1 alone provides substantial gains in reasoning efficiency by enabling early termination once sufficient evidence has been gathered. While the additional gains from Stage 2 are more moderate, we can observe that it still brings meaningful improvements. The full DTO (Stage 1 + 2) consistently delivers the strongest results, outperforming all baselines in terms of efficiency while maintaining or even improving accuracy, as reported in Tables 1 and 2 of the main paper.\n\nWe will include the full ablation results and analysis in the revised version.\n\n| Dataset |  | Base | DTO (Stage 1) | DTO (Stage 1 + 2) |\n| --- | --- | --- | --- | --- |\n| **MATH** | ACC | 79.80 | 85.21 | 85.48 |\n|  | #Tokens | 3543.44 | 2256.26 | 1936.19 |\n|  | Eff. | 1.000 | 1.677 | **1.960** |\n| **GSM8K** | ACC | 82.13 | 83.95 | 83.91 |\n|  | #Tokens | 1382.99 | 1050.54 | 844.18 |\n|  | Eff. | 1.000 | 1.346 | **1.674** |\n| **Gaokao** | ACC | 66.62 | 72.79 | 72.66 |\n|  | #Tokens | 3725.16 | 2559.51 | 2137.59 |\n|  | Eff. | 1.000 | 1.590 | **1.901** |\n| **AMC2023** | ACC | 58.25 | 70.00 | 70.25 |\n|  | #Tokens | 5338.54 | 3768.81 | 3376.98 |\n|  | Eff. | 1.000 | 1.702 | **1.907** |\n| **AIME2024** | ACC | 21.44 | 30.00 | 28.00 |\n|  | #Tokens | 7359.24 | 6301.40 | 5877.44 |\n|  | Eff. | 1.000 | 1.634 | **1.635** |\n| **AIME2025** | ACC | 18.89 | 21.67 | 21.11 |\n|  | #Tokens | 7236.66 | 6237.63 | 5689.38 |\n|  | Eff. | 1.000 | 1.331 | **1.421** |\n\n**[W2]**\n\n> **Reviewer’s Comment**: Because the evaluation was conducted under an 8192-token limit, there is a possibility that some responses were truncated due to this length constraint.\n\nThank you for raising this concern regarding the potential truncation of responses. We would like to firstly clarify that **all models were evaluated under the same maximum response length of 8192 tokens**, ensuring a fair and consistent comparison across methods.\n\nTo further examine whether this constraint may have disadvantaged baseline methods, we conducted additional experiments under a **higher token limit of 16,384**, using DeepSeek-R1-Distill-Qwen-1.5B as the base model. As shown in the tables below, we observe that all methods exhibit a general increase in both accuracy and token usage when granted more space to complete their reasoning. This is expected, as longer context allows models to better develop and finalize their solutions.\n\nHowever, **DTO continues to outperform** both the base model and the strongest baseline (FCS + Ref.), even under this more generous constraint. In particular, DTO achieves the **highest accuracy while using the fewest tokens**, leading to the best efficiency scores overall. For example, on AMC2023, DTO improves accuracy by **8.2 points over the baseline**, while reducing token usage by over 50%, resulting in an efficiency gain of **2.43x**. Similar patterns are observed on Gaokao and AIME2024.\n\nThese findings confirm that DTO’s effectiveness is **not merely a byproduct of producing shorter responses** under certain token limits, but rather reflects **genuine improvements in reasoning quality efficiency**, even when models are allowed more room to reason.\n\n| Dataset |  | Baseline | FCS + Ref. | DTO (Ours) |\n| --- | --- | --- | --- | --- |\n| **Gaokao** | ACC | 69.35 | 72.92 | 73.12 |\n|  | #Tokens | 4845.63 | 3214.31 | 2277.71 |\n|  | Eff. | 1.000 | 1.585 | **2.243** |\n| **AMC2023** | ACC | 66.88 | 73.75 | 75.00 |\n|  | #Tokens | 8051.86 | 5648.81 | 3712.44 |\n|  | Eff. | 1.000 | 1.572 | **2.432** |\n| **AIME2024** | ACC | 26.67 | 27.50 | 30.00 |\n|  | #Tokens | 12345.34 | 9756.87 | 7871.91 |\n|  | Eff. | 1.000 | 1.305 | **1.764** |\n\n**[W3]**\n\n> **Reviewer’s Comment**: A simple yet potentially strong baseline could involve forcing the model to generate an answer once it reaches a certain token limit.\n\nThank you for the thoughtful suggestion. We agree that smaller models such as 1.5B or 7B parameters may occasionally struggle to finalize their reasoning and that encouraging termination at a specific token threshold can serve as a useful baseline for evaluating our method.\n\nTo assess this idea, we implemented the proposed baseline: for a range of maximum token limits (1024, 2048, 4096, and 6144), we prompted the base model, DeepSeek-R1-Distill-Qwen-1.5B, to produce a final boxed answer when nearing the token limit. To facilitate finalization, we appended the following instruction: *\"Wait, I suddenly got the final answer to the whole problem.\\n\\nFinal Answer:\"*.\n\nThis prompt-based mechanism was applied to the base model under each token constraint, simulating a forced finalization strategy similar in spirit to the one described in our paper.\n\nAs shown in the results, we observe a consistent trend: **as the token limit increases, both accuracy and the number of generated tokens increase**, indicating that longer sequences enable more complete reasoning. However, we can observe that **our method, DTO, achieves higher accuracy while using fewer or comparable tokens**, highlighting its strength in both **reasoning quality and efficiency**.\n\nWe will include the full result table in the revised version.\n\n| Dataset |  | Baseline + 1024 | Baseline + 2048 | Baseline + 4096 | Baseline + 6144 | DTO (Ours) |\n| --- | --- | --- | --- | --- | --- | --- |\n| **MATH** | ACC | 63.59 | 74.78 | 78.55 | 79.97 | 85.48 |\n|  | #Tokens | 1009.65 | 1783.91 | 2642.43 | 3124.27 | 1936.19 |\n| **GSM8K** | ACC | 79.40 | 80.48 | 79.78 | 80.12 | 83.91 |\n|  | #Tokens | 576.62 | 722.42 | 850.67 | 928.66 | 844.18 |\n| **Gaokao** | ACC | 50.06 | 57.86 | 65.26 | 67.86 | 72.66 |\n|  | #Tokens | 957.04 | 1661.44 | 2551.03 | 3092.08 | 2137.59 |\n| **AMC2023** | ACC | 32.50 | 50.00 | 67.50 | 68.12 | 70.25 |\n|  | #Tokens | 1022.44 | 1965.05 | 3416.82 | 4385.90 | 3376.98 |\n| **AIME2024** | ACC | 3.33 | 14.17 | 20.83 | 24.17 | 28.00 |\n|  | #Tokens | 1024.00 | 2048.00 | 4009.87 | 5686.45 | 5877.44 |\n| **AIME2025** | ACC | 1.67 | 12.50 | 17.50 | 18.33 | 21.11 |\n|  | #Tokens | 1024.00 | 2048.00 | 3986.50 | 5715.72 | 5689.38 |\n\n**[W4]**\n\n> **Reviewer’s Comment**: There is some concern regarding the generalizability of the findings to larger models.\n\nThank you for raising this important question regarding the generalizability of our method to larger language reasoning models. To address this point, we conducted additional experiments within our available resources to empirically evaluate DTO’s performance in larger-scale settings.\n\nSpecifically, we tested our method on a **larger model, i.e., DeepSeek-R1-Distill-Qwen-7B,** and considered three different settings on this model:\n\n- the base model,\n- the strongest baseline (**FCS + Ref.**), and\n- our proposed method (**DTO**).\n\nThese experiments followed the same training and evaluation protocols as outlined in the main paper, except for one change: due to computational constraints, we used **2,500 training instances** instead of 5,000. All other experimental settings remained consistent to ensure comparability. Additionally, please note that, due to the same computational constraints, we did not perform hyperparameter tuning and instead used the default configuration from the main paper.\n\nAs shown in the extended results table below, **DTO continues to achieve superior efficiency metrics** even at the 7B scale. It **outperforms both the base model and the FCS + Ref. baseline, which is the strongest baseline,** across all benchmarks, delivering improvements in both accuracy and token efficiency. These findings suggest that the **benefits of DTO generalize beyond 1.5B-sized models** and that the method is robust to increased model capacity.\n\nWe sincerely appreciate your suggestion, and we believe that these additional results strengthen the case for the applicability of DTO to larger reasoning models. We will incorporate these findings into the revised version of our main paper.\n\n| Dataset |  | Baseline | FCS + Ref. | DTO (Ours) |\n| --- | --- | --- | --- | --- |\n| **MATH** | ACC | 90.01 | 90.83 | 92.63 |\n|  | #Tokens | 3288.73 | 2756.03 | 2339.03 |\n|  | Eff. | 1.000 | 1.204 | **1.447** |\n| **GSM8K** | ACC | 92.32 | 92.59 | 93.03 |\n|  | #Tokens | 1731.13 | 1356.28 | 1148.84 |\n|  | Eff. | 1.000 | 1.280 | **1.518** |\n| **Gaokao** | ACC | 78.57 | 79.87 | 81.30 |\n|  | #Tokens | 3402.44 | 2924.27 | 2519.02 |\n|  | Eff. | 1.000 | 1.183 | **1.398** |\n| **AMC2023** | ACC | 78.75 | 82.50 | 86.25 |\n|  | #Tokens | 4885.61 | 4356.48 | 3731.45 |\n|  | Eff. | 1.000 | 1.175 | **1.434** |\n| **AIME2024** | ACC | 37.50 | 43.33 | 45.00 |\n|  | #Tokens | 6803.64 | 6724.27 | 6047.72 |\n|  | Eff. | 1.000 | 1.169 | **1.350** |\n| **AIME2025** | ACC | 30.00 | 32.50 | 33.33 |\n|  | #Tokens | 7013.32 | 6580.07 | 6548.10 |\n|  | Eff. | 1.000 | 1.155 | **1.190** |"}]

Author rebuttal:

Meta-review: Summary of the paper: This paper introduces Dynamic Thinking Pattern Optimization (DTO), a framework that treats long reasoning traces as sequences of modular “thinking patterns.”  Using Monte-Carlo sampling, DTO first identifies the earliest prefix of a trace that still yields the correct answer, truncating the remainder.  It then feeds the remaining trace into an auxiliary LLM that prunes any intermediate steps whose removal does not harm correctness.  The resulting minimal traces are used to build a preference dataset that is optimized via RL.  Across mathematical benchmarks and two 1.5 B-parameter LRMs, DTO reduces attention FLOPs by up to 47 % and token counts from ~5,000 to ~3,000 while maintaining accuracy on originally-correct problems and improving accuracy by 15.6 % on originally-incorrect ones; preference optimization further yields up to 12 % absolute accuracy gains. 

Strengths of the paper:
1. Timely problem framing: directly tackles the emerging over-thinking issue in LRMs by formulating reasoning-path compression as a constrained optimization problem. The proposed two complementary mechanisms—early-stopping via Monte-Carlo estimation and LLM-based segment pruning—are simple, model-agnostic, and empirically effective. The preference-optimization pipeline converts the distilled traces into high-quality supervision, opening a path for continual self-improvement.
2. Strong empirical results: simultaneous gains in efficiency (FLOPs/tokens) and accuracy, including the valuable ability to repair previously incorrect chains. Rich ablations and statistical analyses lend credibility to the findings.
3. Presentation: The paper is clearly written and content-rich, making the method easy to reproduce.

Weaknesses of the paper: After reading the rebuttal, I think the authors have addressed the major concerns raised by all the reviewers. Except for Reviewer iNNv, he did not reply or even acknowledge the rebuttal. Please incorporate the content during rebuttal into the camera-ready version of the paper.

Reasons for the decision: This work presents a clear, principled method for shortening and refining lengthy reasoning traces while simultaneously improving accuracy—a key advance toward more efficient and reliable LRMs. Strong experimental results, a reproducible design, and broad potential offset the noted limitations, and all three responsible reviewers expressed clear support after the rebuttal and area-chair discussion. I therefore lean towards accepting this paper.
Decision: Accept (poster)