Dynamic Early Exit in Reasoning Models
Authors: Chenxu Yang
Qingyi Si
Yongjie Duan
Zheliang Zhu
Chenyu Zhu
Qiaowei Li
Minghui Chen
Zheng Lin
Weiping Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Large Language Models
Efficient Reasoning
Early Exit
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Recent advances in large reasoning language models (LRMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or redundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at potential reasoning transition points and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires no additional training and can be seamlessly integrated into existing o1-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g., GSM8K, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 11 cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average of 19.1% to 80.1% while improving accuracy by 0.3% to 5.0%.

Published as a conference paper at ICLR 2026
DYNAMIC EARLY EXIT IN REASONING MODELS
Chenxu Yang Qingyi Si Yongjie Duan Zheliang Zhu Qiaowei Li Minghui Chen Zhenng Lin o Weiping Wang
Chenyu Zhu
Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China Huawei Technologies Co., Ltd.
[yangehenxu, Linzheng] i ie ac. en, siqingyi com
100%
100%
100% 100%
100%
100%
100%
90%
90%
80%
Pearl Reasoning
Exit Position
70%
70%
70%
60%
60%
50%
50%
40%
30% 30% 30%
30%
30%
O
20%
20%
20%
20%
20%
1
2
5
6
9 10 11 12 13 14 15 16 17 18 19
20 21
22 23 24 25 26 27 28 29 30
AIME24 Question ID
Incornect
earliest correct
pasition where LRLM exitt
correctly
Figure Correctness statistics for early exits at various reasoning steps.
ABSTRACT
Recent advances in large reasoming language models (LRMs) rely on test-time scaling, which extends long chain-of-thougle (CoT) generation to solve complex tasks. However, overthinking long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or re- dundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at po- tential reasoning transition points and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires additional training and can be seamlessly integrated into isting ol-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g.. GSMSK, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 1l cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average 19.1 % to 80.1 % while improving accuracy by 0.3% to 5.0%.
INTRODUCTION
The emergence large reasoning models (Xu et al. 2025a), such as DeepSeek-RI (DeepSeek-Al et al. 2025) and GPT-O1 (OpenAl 2025), has marked significant breakthrough in natural language processing, particularly in soiving complex and intricate tasks (WANG et al., 2025). These models leverage the test-time scaling (Snell et al. (2244 law by generating longer CoT (Wei et al. 2023 with rich and diverse reasoning paths, unleashing the potential of their reasoning ability.
1 Equal Contribution.
Zheng Lin is the corresponding author.
The code is available altttps: http:://///ttttbcccoioceeeeeee

---

Published as a conference paper at ICLR 2026
However, the generation of overlong CoT significantly increases computational overload and rea- soning latency, which hinders their deployment in computationally sensitive applications. Moreover, recent research (Chen et al. 2025b; Team et al. 2025a) reveals an intrinsic overthinking problem in LRMs: These models persistently generate verbose reasoning sequences (Wu et al. 2025: Cuadron et al. 2025]. introducing irrelevant information and unnecessary thought steps. Such redundant processing not only wastes computational resources but also leads to accuracy degradation by de- railing from correct reasoning paths to erroneous ones (see Questions 11, 19 and 26 in Fig. [ This redundancy can be attributed to the design of the Supervised Fine-Tuning (Achiam et a 2023
Wei et al., 202T Ouyang et al.) 2022) or Reinforcement Learning (Bai et al. 2022] Ouyang et al, 2022 Schulman et al., 2017 Ramesh et al. 2024) stage, where the ability to dynamically adjust its reasoning length during generation is overlooked, leaving gap the inference efficiency of LRMs.
Intuitively, as the number of reasoning paths increases, more information is referenced when gen- erating conclusions. If we can identify the critical point where the reasoning information becomes just sufficient (termed Pearl Reasoning) and force the model to stop further thinking and directly output conclusions at this point, we can achieve both accuracy and efficiency, This paper aims to find such pearls in long CoT sequences. To validate our motivation, we forced the model to switches from thinking to directly generating answers, at different transition points in the thought process. If the answers obtained are correct, the existence of such pearl reasoning is verified. As shown in Fig. I about 75% samples contain such pearls (early exit yields correct answers), even 36.7% samples required only less than half of the original reasoning paths to reach correct conclusions. Therefore, how to find the pearl reasoning is a valuable topic to achieve efficient reasoning.
To this end, we propose a novel, training-free approach DEER that allows large reasoning lan- guage models to achieve Dynamic Early Exit in Reasoning. It regards the key moments when the model switches thought chains in reasoning as chances of early exit, and prompting LRMs to stop thinking and generate trial answers at these moments. The confidence of each trial answer is the decision-making reference of early exit reasoning. Specifically, the proposed method con- tains three actions: 1) Reasoning Transition Monitoring. During the generation of long CoT's, DEER monitors the positions of reasoning transitions through either linguistic marker-based (such as "Wait") or entropy-based methods. When the reasoning transition points are found, the action of 2) Trial Answer Inducing is triggered: we replace it with "final answer" " tokens to induce the model immediately generate a trial answer, which will be used for 3) Confidence Evaluating. If the confidence is sufficiently high, set the model to stop further thinking and generate a conclusion based the generated thoughts. Otherwise, the action of Trial Answer Inducing is revoked, and the model continues reasoning along the original path. Moreover, Considering the potential sensi- tivity of models to answer inducing prompts, we propose DEER-Pro (a Parallel and Robust variant of DEER), which performs multiple parallel answer inductions at potential carly-exit points and calibrates confidence based on the aggregated results, thereby further ensuring DEER's robustness.
Our method is simple yet effective, and can be seamlessly extended to eleven reasoning models of varying architectures and sizes, achieving excellent results in the ten reasoning benchmarks, includ- ing mathematical tasks (e.g., AIME 2024, AMC 2023 and MATH-500), scientific tasks (e.g.. GPQA Diamond) and programming tasks (e-g.. BigCodeBench). Specifically, our method, when integrated into cutting-edge reasoning models, can reduce the length of CoT sequences by an average of 19. % to 80.1% % while improving accuracy by 0.3% to 5.0% across different reasoning benchmarks. Our DEER offers plug-and-pla solution for improving both the efficiency and accuracy of LRMs.
2 MOTIVATIONS AND OBSERVATIONS
In this section, we analyze the overthinking phenomenon in LRMs and investigate the impact of static early exits on model performance. We define "pearl reasoning" as the critical juneture where reasoning information becomes precisely sufficient for accurate problem-solving. Our analysis in Figure reveals that approximately 75% of samples contain such pearls (where early exit yields correct answers). Furthermore, we identified subset of samples for which correct answers are exclusively obtainable through early exits (exemplified by Questions 11, 19, and 26 in Figure I]. Quantitative analysis presented in Figure 2 () further demonstrates that 60.8% and 35.1% % of cor- rectly answered samples in MATH-500 and GPQA, respectively, maintain their accuracy when em- ploying early exits after completing merely 20% of the reasoning steps. These empirical findings
2

---

Published as a conference paper at ICLR 2026
MATH-500
GPQA Diamond
MATH-500
GPQA Diamond
Namber of Chnmaz Answer
700
25
375
175
20-
201
150
15
16
15
15
123
125
11
100
90
Exit Position
50
0.4
Exit Posttion
0.6
0.3
1.0
Exit Position
Exit Pasttion
(a) The number of originally correct samples that remain correct with early exiting on different positions.
(b) The number of originally incorrect samples that become correct with early exiting on different positions.
Figure Quantitative pilot experiment results.
Please refer to Appendix A for setups.
substantiate our hypothesis that LRMs possess the potential to achieve simultaneous improvements in both computational efficiency and prediction accuracy through strategic early termination.
Fig. 2)b) illustrates that exiting at different positions corrects varying proportions of wrong answers. For the MATH dataset, the highest correction rate is achieved when exiting at 40% of the reasoning steps, whereas for the GPQA dataset, the optimal correction occurs when exiting at 50%. The optimal early exit point varies for each problem and is closely related to the inherent difficulty of the problem itself. Therefore, it is intuitive that relying on static early exit strategy based on fixed heuristics suboptimal, underscoring the necessity of designing a dynamic early exit mechanism.
3
METHOD
3.1 THE GENERATION PATTERN OF LARGE REASONING MODELS
Li In contrast to traditional large language models (System 1), large reasoning models (System 2) ct al. 2025b) exhibit distinct generation patterns during the inference stage. (1) LRMs use delimiters to divide the output into two processes: slow thinking and conclusion. LRMs conduct systematic and thorough reasoning in the slow thinking, ultimately summarizing the thought process and pro- viding the final answer in the conclusion. (2) During the slow thinking process, LRMs engage in complex thinking actions (thoughts), such as problem comprehension, approach exploration, and result verification (Luo et al.) 2025b). Within each reasoning action (thought), the model performs specific procedural action execution, while transitions between different reasoning actions are typi- cally marked by action transition points (ATP), such as "Wait", "Alternatively"
System 1: [Prompt] + [Completion],
System 2: [Prompt] + (think) + [Slow Thinking] + (/think) + [Conclusion].
(2)
[Slow Thinking]: [Action Execution] + (ATP) + |Actio Execution] + (ATP) +...,
(3)
where (think) and (/think) are begin-of- and end-of-thinking delimiters respectively.
3.2 DYNAMIC EARLY EXIT IN REASONING
In this section, we introduce the Dynamic Early Exit in Reasoning (DEER) method to determine optimal positions for early exits (pearl reasoning path), thereby alleviating the overthinking issue.
The core idea behind DEER that model's confidence in its trial answer dynamically indicates whether the thinking information required for LRMs to generate the final answer is sufficient. We observe that when the model's reasoning process is incomplete or flawed, the trial answer tends to exhibit significantly lower confidence. Conversely, when the reasoning is comprehensive and logically sound, the model generates answers with higher confidence, as illustrated in Fig. [77 This suggests that the model implicitly recognizes when pearl reasoning occurs, but lacks explicit mechanism during inference to leverage this awareness for early termination. DEER aims to bridge this gap by converting implicit awareness into explicit early-exit decisions.
As shown in Fig. 3 DEER involves three designs to determine whether to exit early: reasoning transition monitor, answer inducer, and confidence evaluator.
3

---

Published as a conference paper at ICLR 2026
Original CoT
Question
Define Sp laam (E 1jMially Viact1 215 and Sq laam (k- 11 Vractticknass Find write Stumm 1:-ynity Ieam, 1)4innty theet1ig 42-318 4pd
Large Reasoning Language Model
Original CoT
0O
-kkyyy, so have thes problem where need to somitteds
Wait, Ty that seems too strigghtorword Let me check comitted
DEER
Thought
Wait, T; woothe appmach note that can somitteds
Wait, another
the sum perhass.. somitted:
Ruzdoning Transition Monitor
Answer Leducer
Confidence Evoluster
Wait. Tg: that's different from the
result
</h
Thought Sigrel
contradiction Which one cornect? Let check somittedS
/bhink CCnndusion Vbosedip s]
Prompt
More than 5000 tokens
Large Reasoning Language Model
Canclusion
DEER
this problem where need somitteds.
Walt
Thoughts
Confidence Evalustor
"Final Answer" 'itlbooed
Trepebsch
Confidence
/thinii
C :Conndusion
(boxedip
Only 1037 tolenss
Figure 3: An overview of the Dynamic Early Exit in Reasoning (DEER) method.
Reasoning transition monitor. Within the DEER framework, we propose two alternative monitor design strategies: (i) linguistic marker-based, and (ii) entropy-based monitoring. For the first strategy, as mentioned in Section 3.1 LRMs explicitly utilize ATPs to mark boundaries between dif- ferent thoughts. This feature enables DEER to recognize ATPs potential early-exit opportunities. In the second strategy, DEER employs "\n'nn" as delimiters to demarcate reasoning steps. Follow- ing each reasoning step, DEER computes the entropy of the initial token, denoted as H (p(((x=<<)) Low entropy values indicate that the model is engaged in procedural action execution, characterized by stable reasoning patterns. Conversely, high entropy values suggest that the model is deliberating on its subsequent reasoning action, with multiple potential pathways being activated concurrently. These positions exhibiting high entropy are identified candidate points for early-exit.
demonstrate that DEER with external linguistic markers satisfies similar properties as the second internal state-based approach while achieving comparable performance. When applied to English LRMs, existing models consistently exhibit a pattern of gen- erating such linguistic markers. Following the Occam's Razor principle (Rasmussen & Ghahramani] 2000), we recommend adopting the first strategy. For non-English reasoning scenarios, the alterna- tive second strategy can also accurately capture early-exit points, demonstrating the generality and robustness of DEER.
Our subsequent experiments in Section 4.3
Answer inducer. When the LRM pauses at a potential early exit point, the trial answer inducer module prompts the model to generate an intermediate answer based on the reasoning content pro- duced so far. We incorporated the answer delimiters ((boxed()) into the prompt to facilitate a more precise identification of the trial answers, as follows: A LRM(P, I) where P denotes the input prompt, T denotes the generated thoughts, I denotes the answer inducer prompt, and A (ag, .1,..... an.] is the trial answer.
Confidence evaluator. The confidence evaluator computes the confidence of the induced trial an- swer. takes the maximum predicted probability of each token its confidence. For multi-token trial answers, the overall confidence is computed as their mean score across all tokens as follows:
1/n
p(a;) softmax
C=
max p(a.) D.EV
where M the language model head at the final layer the LRM. The calculation C employs the geometric mean, which better aligns with the multiplicative nature of joint probabilities and exhibits greater sensitivity to low probability values, thereby providing enhanced robustness.
Finally, the comparison between the obtained confidence and the empirical threshold À determines whether to exit early. C > X, we consider the reasoning information currently generated by the LRM to be sufficient, indicating that the model has reached the pearl reasoning. At this point, DEER stops further reasoning actions and proceeds to deliver the conclusion. Otherwise, the model reverts to the previous transition point generate the next thoughts.
4

---

Published as a conference paper at ICLR 2026
DEER-PRo. To further improve the reliability and accuracy of pearl reasoning identification, introduce DEER-PRo, a Parallel and Robust variant DEER. Through answer elicitation using varied prompts at early-exit points, DEER-PRo calculates both the mean and Mean Absolute Devi- ation (MAD) of multiple confidence values, deriving a calibrated confidence score Ceali as follows:
N
1
Ceali = Cavg a CMAD, Coug
C..
Σ -Ceal CMAD = N
(5)
where C. (II eV softmax (MP, T. I, a'zx) a'z)))) 4/1 denotes the confidence score ob- tained using specific answer inducing prompt I,, N denotes the number of inducing attempts, and a the fluctuation penalty strength coefficient. The introduced conservative bias CADD effectively prevents erroneous early exits caused by overestimated confidence scores resulting from positive noise in prompts, where the estimated confidence exceeds the true confidence. We demonstrate in the Appendix [ that Ceati effectively eliminates the influence of the model's is sensitivity to answer inducer prompts on early-exit accuracy, thus substantially improving DEER's s robustness.
3.3 BRANCH-PARALLEI DECODING ACCELERATION
Intuitively, the computation of the answer inducer and confidence evaluator in DEER introduces additional latency during inference, particularly in code generation tasks where trial answers remain lengthy. This overhead diminishes the efficiency gains achieved through substantial reduction of generated CoT sequences. To address this challenge, we integrate DEER with a branchhparallae acceleration strategy (Fig. D that mitigates these efficiency limitations through two key mecha- nisms: (1) lincarization of multiple branches into single sequence for parallel generation using a specialized causal attention mask, and (2) dynamic KV cache management via confidence-ber pruning. This strategy facilitates temporal overlap between trial answer evaluation and concurrent reasoning-chain generation, thereby optimizing overall inference efficiency.
4 EXPERIMENTS
4.1 EXPERIMENTAL SETUP
Benchmarks, Metrics and Implementations. We evaluate model performance across 10 bench- marks, including 6 mathematical reasoning benchmarks: GSMSK (Cobbe et al. (001). MATH-500 (Hendrycks al. 2021), AMC 2023 (AI-MO, 2024), AIME 2024, AIME 2025 (MAA Committees),
OlynpiadBench (He et al. 2024), one scientific reasoning benchmark: GPQA Diamond (Rein et al.) 2023 and code reasoming benchmarks: HvmanEval (Chen et al. 2021). BigCodeBench (Zhuo et al. 2024). and LiveCodeBench (Jain et al. 2024p. Among the six mathematical reasoning bench- marks, GSMSK, MATH-500 and AMC 2023 are generally considered to be relatively simple rea- soning tasks, whereas AIME 2024, AIME 2025, and OlympiadBench are regarded as more chal- lenging. Given the extensive set of evaluation benchmarks, we selectively present the most popular ones (GSM8K, MATH-500, AMC 2023, AIME 2024 and GPQA Diamond) in the main experiment. More experimental results are provided in the Appendix K We selected Accuracy (Acc), Token Number (Tok), and Compression Rate (CR) the evaluation metries. Ace denotes the final answer accuracy. Tok denotes the average generation length per sample to evaluate the cost. CR is defined the ratio of the average response length to that of the original model, with lower values indicating higher compression. Given the limited number of samples in datasets AMC 2023, AIME 2024, and AIME 2025, we conduct sampling rounds per instance and average the results across all metrics to ensure stability and reliability. We have implemented DEER using both HuggingFace Transform- ers (Wolf et al. (020) and the vLLM inference acceleration framework (Kwon et al.] (023). The experimental results presented in this paper are based on the vLLM implementation. We set the 0.95). For entropy-based DEER, following the 80/20 principle pro- posed in (Wang et al., 2025b), we designate reasoning step termination positions with entropy values exceeding 0.672 as carly-exit points. For DEER-Pre -Pro, we set N = 4 and a = More experimental setup details are placed in Appendix C
hyperparameter
0.95
Backbone LRMs and Baselines. We conducted experiments on the open- spurcsource DeepSeek- Distill-Qwen series of models (1.5B, 7B, 14B, and (2B)(DeepSeek-Alee et 2025), Qwen3 series of
5

---

Published as a conference paper at ICLR 2026
Table 1: Experimental results across various types of reasoning models. "Acc" denotes accuracy, "Tok" denotes token count, and "CR" denotes compression rate. 1 indicates that higher values are better, while 1 indicates that lower values are better. The best results are highlighted in bold.
MATH
SCIENCE GPQA-D
Method
GSM8K
MATH-500
AMC23
AIME24
Overall
Aoct
Toki
CRL
Acet
Tok.
CR.
Acct
Tok.
CR.
Acct
Tok.
CR.
Acct
Tok
CR.
Acc?
CR.
Vanilla
89.6
1,484
100%
87.4
3,858
100%
78.8
6,792
100%
41.7
13,765
100%
23.7
10.247
100%
100%
TCC
88.0
892
60.1%
89.2
3,864
100.2%
82.5
6,491
95.6%
48.4
10,603
77.0%
27.3
8,442
82.4%
67.1
83.0%
CoD
84.7
298
20.1%
83.2
1.987
51.3%
77.5
4,440
65.4%
40.0
10,519
76.4%
37.9
6,431
62.8%
64.7
55.3%
NoThinking
87.1
284
19.1%
80.6
834
21.6%
65.0
1,911
28.1%
26.7
4,427
32.2%
29.8
724
7.1%
57.8
21.6%
Dynavor CoT
89.6
1,285
86.6%
89.0
2.971
77.0%
85.0
5,980
88.0%
46.7
12,695
92.2%
30.5
7,639
74.5%
68.2
83.7%
SEAL
88.4
811
54.6%
89.4
2,661
69.0%
DEER
90.6
917
61.8%
89,8
2,143
55,5%
85.0
4,451
65.5%
49.2
9,839
71.5%
31.3
5,469
53.4%
69.2
61.5%
DEFR.PRo
989
66.7%
90.2
2,391
62.0%
87.5
4,877
71.8%
49.2
10,046
73.0%
30.6
5,682
55.5%
65.8%
Qwen3-74B
Vinilla
95.1
2.047
100%
93.8
4,508
100%
95.0
7,139
100%
20.0
10,859
100%
60.1
7.339
100%
100%
TCC
95.7
1,241
60.6%
94.6
4,484
99.5%
95.0
7,261
101.7%
70.8
11,573
106.6%
60.1
7,138
97.3%
83.3
93.19%
CoD
648
31.7%
75.2
2.359
52.3%
72.5
4.122
57.7%
60.0
99.2%
51.0
1.177
16.0%
51.4%
NoThinking
94.8
286
14.0%
85.0
1,228
27.2%
77.5
2.135
29.9%
26.7
7,337
67.6%
50.5
2,320
31.6%
66.9
34.1%
Dynosor-CoT
95.6
1,483
72.4%
93.8
4,063
90. 1%
95.6
6,582
92.2%
73.3
10,369
95.5%
59.6
5.968
81.3%
83.6
86.3%
DEER
95.3
840
41.0%
94.0
3.074
68.2%
95.0
4,763
66.7%
76.7
7,619
70.2%
57.6
2,898
39. 19.
83.7
57.1%%
DEER-PRO
95.3
926
45,2%
94.4
3,260
72.3%
95.6
4,905
68.7%
75.0
8.135
74.9%
61.2
4,062
55.4%
84.3
63.3%
OwQ-32H
Vanilla
96.7
1.427
100%
93.8
4,508
100%
92.5
6.792
100%:
66.7
10.821
100%
63.1
7,320
100%
82.6
100%
TCC
95.8
1,348
94.5%
94.4
4,315
95.7%
90.0
6,818
100.4%
60.0
11,263
104.1%
61.6
7,593
103.7%
80.4
99.798
CaD
96.0
627
43.9%
94.0
3,630
80.5%
92.5
5,943
87.5%
60.0
10,731
99.2%
62.6
6.039
82.5%
81.0
78.7%
NoThinking
96.2
1,113
78.0%
94.8
3,930
87.2%
87.5
6,908
101.7%
66.7
10,859
100.4%
63.6
7.668
104.8%
94.4%
Dynasor CoT
95.2
1,095
76.7%
94,2
4,176
92.6%
93.8
6,544
96.3%
63.3
11,156
103.1
64.1
7,024
96.0%
82.1
93.0%
DEER
94.6
3,316
73.6%
95.0
5.782
85.1%
70.0
93.3%
64.1
6.163
84.2%
80.9%
DEER-PRo
96.2
1032
72.3%
94.8
3,650
80.9%
95.0
5,811
85
636
70.0
10,264
94.9%
64.7
6.201
84.7%
84.1
83.7%
2025), QwQ-32B [Team] 2025). and DeepSeek-RI eLiu al. 2025c). Due to the large number of models evaluated, we selectively present DeepSeek- RI-Distill -wlln- 7B, Qwen3-14P 14B, and QwQ-32B as representative examples in the main experi- ment. More experimental results are provided in the Appendix C
models (1.7B, 4B, 8B, 14B, 32B) (Qwen et al.
We compare DEER against exist- ing prompt-based and output- based efficient reasoning approaches, including Vanilla, TCC (Muen- nighoff et al. 2025), Col (Xu et al., 2025c). NoTThnkkig (Ma et al., 2025a), Dynasor- CoT (Fu al. (025), ,, and SEAL (Chen et al.) 2025a). Vanilla performs direct evaluation of the LRM with- out any intervention. Token-Conditional Control (TCC) specifies a fixed token count in the system prompt to enforce token budget; in our experiments, we set this limit based on the actual token length generated by DEER. Chain-of-Drail (CoD) reduce verbosity by limiting the number of words used in each reasoning step, focusing only on the essential calculations or transformations needed to progress. NoThinking prompts the model to skip the reasoning phase and directly generate the final answer. Dynasor-CoT periodically prompts the model to produce intermediate answers at fixed token intervals and triggers early exit when three consecutive answers are consistent. SEAL trains a steering vector calibrate the CoT process, guiding the model toward more reliable reasoning.
4.2
MAIN RESULTS
Overall Performance. Due to space constraints, Tab presents five widely adopted reasoning benchmarks, evaluated across three state-of-the-art reasoning models specifically covering three model scales, which comprehensively demonstrates DEER's superior performance. We also pro- vide more results across 10 datasets covering 11 models ranging from 1.5B to 671B parameters in the Appendix. It can be found that DEER demonstrates strong adaptability across various rea- soning models and tasks, achieving accuracy improvements of 0.9 to 4.8 points while reducing se- quence length by 19.1% 42.9% compared to vanilla models. DEER- -rro achieves higher accuracy with only marginal increase in generation length ranging from 2.8% to 6.2% compared to DEER. We conducted comparative experiments between DEER and DEER- Pro on additional smaller-scale models. The experimental results in Table demonstrate that DEER-Pro achieves more significant accuracy improvements. It indicates that DEER-Pro effectively addresses the prompt sensitivity issues in smaller models, demonstrating its superior robustness.
Comparison with Efficient Reasoning SoTs Tab. prresents comparisons between DEER and recent efficient reasoning methods. It can be observed that DEER consistently outperforms all base- lines, whereas baselines either struggle to generalize across tasks and base models, or must trade off accuracy for efficiency. Specifically, while TCC Muennighoff et al. (2025) achieve reasonable
6

---

Published as a conference paper at ICLR 2026
Accurocy Vanilla COT
Accurocy DEER (Ouns)
Generation Length of Vanilla COT
Generatten Length DEER (Ours)
M421-500
NATH-500
ARC 2004
AMC 2014
Averoge: $3.5
Average: Vasill:: DEER: 52
Acorog (M
$1.
20.5
3615.0
GL.3
33:00
8227.0
11211.C
15233.
3126-
8000
2021.
02.
27.674
2000
2000
Figure 4: Experimental results of DEER compared to Vanilla CoT across DeepSeek- R1 RI-Distill- Qwen-Series models of varying sizes MATH-500 and AIME 2024.
afficiency-accurrccy tradeoff's on simpler tasks like GSM8K by incorporating token budgets into prompts, fails on complex problems (such as AIME24) where models ignore prompts' length con- straints and generate even longer responses than vanilla COT. As for NoThinking and CoD, while achieving dramatic length reduction, they severely compromises models' inherent reasoning capa- bilities. In contrast, Dynasor-CoT preserves reasoning quality but suffers from late termination due to its conservative early-exit condition, resulting in minimal length reduction. Notably, nearly all baselines fail completely on QwQ-32B due the sporadic invalidation of its end-of-thinking delim- iter </think> where the model continues generating reasoning steps after it and often produces duplicate </think> tokens (as shown in Appendix Fig. 18). Remarkably, DEER still achieves a 19.1% length reduction on QwQ-32B despite these challenges, further demonstrating its robustness.
Performance on Programming Tasks. Tab. reports DEER's evaluation results across three programming tasks, completing our comprehensive coverage of reasoning models' three primary domains: mathematics, science, and programming. demonstrates DEER's s consistent effectiveness across varying programming tasks and model sizes, achieving smaller compression ratios compared to math and science tasks (average 19.9% vs. 61.5%). This enhanced compression likely originates from the inherent characteristies of code generation, where each reasoning step typically produces verbose code segments containing substantial redundant tokens.
Performance Trends across Model Sizes and Reasoning Difficulty. Fig 4 10 presents evaluation results on MATH-500 and AIME 2024 datasets to examine DEER's ' performance gains across dif- ferent model sizes. It can be seen that DEER consistently enhances accuracy while reducing token consumption across all model sizes. A key observation is that smaller models (e.g., 1,5B) tend to generate significantly longer reasoning sequences with more severe overthinking phenomena. This stems from their limited reasoning capacity in discovering the correct reasoming steps during CoT generation. Consequently, our method achieves greater length reduction for these smaller models. Fig. utilizes the MATH-500 (simple reasoning) and AIME 2024 (challenging reasoning) datasets as representative benchmarks. The results demonstrate DEER's 's dual capability: it achieves more superior compression ratios on simpler problems while delivering more substantial accuracy gains on complex tasks. This precisely addresses two critical needs in reasoning systems: the efficiency demands in simple scenarios and the growing accuracy requirements in challenging scenarios.
4.3 ABLATION STUDY
Performance Trends across Token Budges. Fig. eJealluttss DEER's ' performance across varying token budgets (controlled by different max length settings). In plots (a) and (f), the x-axis represents the actual length of model-generated CoT sequences, while the y-axis indicates model accuracy. The optimal balance between accuracy and efficiency is demonstrated by curves positioned closer to the top-left corner. The blue shaded regions quantitatively represent DEER's performance gains: vertical height corresponds to accuracy improvement and horizontal width to token compression benefit. It can be seen that DEER consistently outperforms vanilla methods, as all points located upper-left to vanilla ones. As shown in the four-column plots on the right, we observe that vanilla models generate longer sequences with higher accuracy token budgets increase, confirming test- time scaling. Notably, DEER demonstrates an adaptive tradeoff: under constrained token budgets, it achieves greater gains in accuracy but reduced benefits in length compression. Conversely, the opposite trend is observed with larger token budgets. This indicates that our method can dynamically adjust token budgets to meet varying requirements for accuracy-efficieng in different scenarios.
7

---

Published as a conference paper at ICLR 2026
(4)
(b)
(c)
(d)
MATII
MATTI
A/M124
Tirmnnival
Vaaille
66.5
ACCUPIC
20
2008
5000
4000
3290
10
30
20
30
30 Di
(
AIME24
(2)
MATH
(b)
A/ME24
HumanEval
DEER
Lan Becoaase
15000
3000
Imprevcmant
20:0
1000
10000
12003
30
30
25
rith 3elmm1
Langt? (KSsban))
Plx Langts
Langth colannl
Figure 5: Performance comparison between DEER and basclines based on the DeepSeck-RI-DD Qwen- 14B model across four datasets under different token budget settings.
Impact of Reasoning Transition Monitor Choices. In the main experiments, we employ "Wait" " as the early-exit monitoring signal, denoted as DEER(W), This simple linguistic marker-based ap- proach yields promising results. To compare the impact of different early-exit signals on DEER performance, we conduct additional experiments using "Alternatively" entropy-based monitoring for early-exit detection. The corresponding results are presented in Tab. 6 Tab. coolllets statisties the number and average length of reasoning chunks obtained by dividing the original CoT with potential exit points. The chunk numbers indicate that DEER(Ent) presents the most early-exit opportunities while DEER(A) offers the fewest, exhibiting a negative correlation with average generation length. The results in Tab. olacross additional datasets and mod- els demonstrate that both entropy-basee based and linguistic marker-based monitoring exhibit comparable superior performance, significantly outperforming the baseline. In large-scale real-world deploy- ments, we advocate for the linguistic marker-based approach given its implementation simplicity and efficiency. Appendix provides further exploration between these two monitoring strategies.
the signal, well as
Robustness of threshold Fig. shsows the performance of DEER on MATH-500 dataset with different threshold X. The results indicate that when the threshold is set too low, a minor additional reduction in reasoning length lcads to a significant drop in accuracy, reflecting an overcorrection of overthinking. Conversely, when the threshold is too high, the model exits reasoning too late, resulting in pro-
500
Accurssy
LCE
102
Threshold A
Length (tokone)
4000
longed reasoning lengths with decline in accuracy. Moreover, it can be seen that our method is robust to whthin the range of 0.9-0.97,
1000
walla cot
eliminating the need for hyperparameter tuning. Tab. 4 presents our robustness investigation of the threshold across additional datasets using Qwen3. The experimental results demonstrate that Qwen3 ex- hibits superior robustness X, maintaining consistently strong performance within the range of 0.8-0.97. Additionally, the experimental results in the appendix, conducted across 11 models and 10 datasets, uniformly employ 0.95 as the threshold value. The consistently strong results further demonstrate DEER's ' generalization capability and robustness. Appendix Section underlying source of DEER's s robustmess originates from confidence polarization phenomenon.
2000
3.00
3.56
102
Threshold A
Figure 6: Impact of A.
[ reveals that the
4.4 DISCUSSION
Efficiency Improvement. To accurately verify the gains brought by DEER and its Branch-Parallel ac-
Donp 1
Durition Sceede Lengls Steedup
celerated variant in end-to-end inference efficiency, we measured the average latency on MATH-500 and AMC 2023 datasets based on huggingface transformers (Wolf et al., 2020). As shown in Fig. (a), original DEER reduces the latency by 27.9% to 40.1% while the proposed cranch-parallle decod- ing variant reduces the latency by 36.3% to 58.6%. DEER achieves
aeraaattonn 1ith 200
280
4200
145
MATH
JMC
MATHH
XMC
Ginneration Latency
(b) Speedup Ratio
This suggests that Branch-Paraie further speed improvements by efficiently reducing the latency of trial answer inducing and confidence evaluation. Additionally, we mapped the latency speedup against the length savings for every sample on MATH-500. Fig. (b) illustrates that the
Figure 7: Efficiency Improvement.
8

---

Published as a conference paper at ICLR 2026
305
1.70
-.00
48
Exit Accuracy
200
100
Esrly Exit Accurasty
65
Eary Exit
320
90
Early Exit
60
42
42-
50
20-
(6)
CON MATH ANC Zhym AME Benchmarks
(b)
0354 MAth ADC Chyn AMR
3.76
48
80
142
320
(d)
1.78
45
145
525
Benchmarks
Model Size
Model Size
Figure 8: Early-exit rates and accuracy of carly-exited samples of DEER. Figures (a) and (b) share a common legend, as do figures (c) and (d). The height of each bar reflects the average value.
ratio between latency speedup and length savings exhibits a superlinear trend, reinforcing the sig- nificance of DEER in enhancing inference speed. In Section H of the Appendix, we theoretically prove the efficiency of DEER and explain the underlying cause of the superlinear speedup.
Exploring the Effectiveness of DEER's Early-Exit Mechanism. Fig. 8 presents the early-exit rate and the accuracy of early-exited samples across Qwen3- series models of varying sizes. As shown in Fig. a8,, DEER's 's early-exit rate decreases with increasing task difficulty, which accounts for its relatively lower compression performance on complex tasks compared to simpler ones. Fig- (() reveals that, although early-exit accuracy declines somewhat as task difficulty increases, it remains consistently high-ranging from 88% to 98%. In a concurrent study, Zhang et al. (2025a) trained probe to decide whether to early exit. However, their probe achieves accuracy of only around 80% on MATH-500, which is significantly lower than DEER's 95%. This indicates that the model inherently possesses the ability to assess answer correctness, and that DEER effectively hamnesses this capability. As illustrated in Figures (() and (d), although minor differences exist across tasks of varying difficulty, there is a general trend toward higher early-exit rates and improved accuracy as model size increases. This observation implies a positive relationship between DEER's performance and the capacity of the model: larger models yield more accurate confidence estimates. which in turn lead to better carly-exit decisions. We further investigate the reasons behind DEER's 's accuracy gains. Fig. indicates that DEER corrects more answers (green bars) than alters incorrectly (red bars) through early exits. This suggests that DEER not only saves computational cost by exiting early on questions it could correctly answer, but also corrects problematic thinking.
Case Study. Fig. 13 shows that both DEER and vanilla CoT arrive at the correct answer during the first reasoning step, as shown in the green box. The difference lies in the fact that DEER exits early after evaluating the confidence of the trial answer as sufficiently high, thus producing the correct result. In contrast, the vanilla CoT proceeds to the next reasoning action. After double-checking and switching reasoning approaches, the model becomes trapped in an endless cycle of verification due to inconsistent answers from the two approaches, ultimately failing to provide a final answer. Besides, Fig. [7 shows that LRMs implicitly know when to leave early, and our method is simple and effective to realize such potential of the model itself. Please refer to Appendix for details.
RELATED WORK
Following the taxonomy of efficient reasoning established in (Sui et al. 2025 Wang et al. 2025a)
categorize related work into three classes: post-traning based methods use SFT (Yu al. 2024
Kang et al. 2025) Xia et al. 2025: Ma et al.
2025b Munkhbat et al. 2025 Liu et al.
20024
Han
al.
2024 with variable-length CoT data or incorporate length rewards (Team al.
2025b
Luo
et al. 2025a a Aggarwal & Welleck 2025 Arora & Zanette 2025 Yeo et al.) 2025
Shen et al.)
20256 Qu et al. 2025 Cui al. (025) reinforcement learning to enable the model to adaptively
generate chains of thought of different lengths, which is beyond our training-free scope. Prompt-
based methods (Han et al., 2024, Xu et al.] 20256 Lee et al., 2025 Renze & Guven 2024 Chen et al. 2024) use varying prompts to enforce reasoning models to generate concise CoT with less unnecessary reasoning steps. Output- Output-based methods aim to accelerate reasoning generation during the model's decoding phase, and DEER falls into this category. However, most prior works (Xie
et al. 2023: Liao et al., 2025: Li et al. 2024, Manvi et al. 2024; Aggarwal et al. 2023) focus on optimizing best-of-N sampling, which is irrelevant to our study. Instead, we select three recent concurrent works Nothinking (Ma et al. 2025a), Dynasor-Coo CoT (Fu et al. (025). and SEAL (Chen
et al. 2025a) baselines for comparison. More related works can be seen in Appendix M

---

Published as a conference paper at ICLR 2026
6 CONCLUSION
This paper verifies the rationale behind the early exit motivation in CoT generation, and accordingly proposes training- frre dynamic early exit algorithm, which makes the reasoning model withdraw from subsequent thinking when the thinking amount is just enough. Our method comprehensively evaluated across reasoning models of varying model sizes and demonstrates superior performance with fewer tokens ten classical reasoning benchmarks, which offers win-win solution to the trade-off between accuracy and efficiency commonly encountered in test- eest-time scaling.
7 ETHICS STATEMENT
This work adheres to the ICLR Code of Ethics. We affirm that research has been conducted with integrity, honesty, and respect for ethical principles throughout all stages of the work.
All findings presented in this paper are reported accurately and honestly. We have not fabricated, falsified, or misrepresented any data results. Our methods and experimental procedures are described transparently to ensure reproducibility.
All datasets used in this research were obtained and utilized in accordance with their li- censes and terms of use. For any data involving personal information, we ensured compli- ance with privacy regulations and obtained appropriate ethical approvals where necessary.
All contributions to this work have been properly acknowledged. We have appropriately cited all sources and prior work that influenced our research. All co-authors have made substantial contributions to the work and have agreed to the submission.
We have carefully considered the broader implications of our work. While research aims to advance the field positively, we acknowledge potential dual-use concerns and en- courage responsible deployment of our methods in real-world applications.
REPRODUCIBILITY STATEMENT
To ensure the reproducibility of our results, we have provided detailed descriptions of our experi- mental setup, hyperparameters, and implementation details. Code and supplementary materials made available where possible to facilitate verification and future research.
ACKNOWLEDGMENTS
This work supported by the National Natural Science Foundation of China (Nos. 62472419, 62472420) and the Enterprise Project (No. (4V0681113).
REFERENCES
Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Ale- man, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303. 087744, 2023.
Pranjal Aggarwal and Sean Welleck. LI: Controlling how long reasoning model thinks with reinforcement learning. arXiv preprint arXiv:2503.04697 2025.
Pranjal Aggarwal, Aman Madaan, Yiming Yang, et al. Let's sample step by step: Adaptive- consistency for efficient reasoning and coding with 1ms. arXiv preprint att. 2023.
AI-MO. Ame 2023, 2024.
URL httper///uugginffeeeec.o/ttsssts
iimo va 1 diatiiiooooommm amc
Daman Arora and Andrea Zanette. Training language models to reason efficiently. arXiv preprint vrXiv:2502.04455 2025.
10

---

Published as a conference paper at ICLR 2026
Simon A Aytes, Jinheon Back, and Sung Ju Hwang. Sketch-of-thought. Efficient Ilm reasoning with adaptive cognitive-inss -inppiiiee sketching. arXiv preprint arXiv:2503.05179 2025.
Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, Deep Ganguli, Tom Henighan, et al. Training a helpful and harmless assistant with reinforcement learning from human feedback. arXiv preprint (tf::2204008866 2022.
Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela Mishkin, Brooke Chan, Scott Gray, Nick Ryder, Mikhail Pavlov, Alethea Power, Lukasz Kaiser, Mohammad Bavarian, Clemens Winter, Philippe Tillet, Felipe Petroski Such, Dave Cummings, Matthias Plappert, Fo- tios Chantzis, Elizabeth Barnes, Ariel Herbert- Voss, William Hebgen Guss, Alex Nichol, Alex Paino, Nikolas Tezak, Jie Tang, Igor Babuschkin, Suchir Balaji, Shantanu Jain, William Saunders, Christopher Hesse, Andrew N. Carr, Jan Leike, Josh Achiam, Vedant Misra, Evan Morikawa, Alec Radford, Matthew Knight, Miles Brundage, Mira Murati, Katie Mayer, Peter Welinder, Bob Mc- Grew, Dario Amodei, Sam McCandlish, Ilya Sutskever, and Wojeiech Zaremba. Evaluating large language models trained on code, 2021. URL /tt.ttts///aaateae org/ htapr/ggab////01/ 03374
Qiguang Chen, Libo Qin, Jiaqi Wang, Jingxuan Zhou, and Wanxiang Che. Unlocking the capa- bilities of thought: A reasoning boundary framework to quantify and optimize chain-of-thought. Advances in Neural Information Processing Systems, 37:54872-54904, 2024.
Runjin Chen, Zhenyu Zhang, Junyuan Hong, Souvik Kundu, and Zhangyang Wang. Seal: Steerable reasoning calibration of large language models for free, 2025a. URL /tttps://arxi...
07986
Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, Rui Wang, Zhaopeng Tu, Haitao Mi, and Dong Yu. Do not think that much for 2+3=? on the overthinking of ol-like lims, 2025b. URL https:::::/ //arxiv. org/abs/ 21187
Jeffrey Cheng and Benjamin Van Durme. Compressed chain of thought: Efficient reasoning through dense representations. arXiv preprint drXiv:2412.13171, 2024.
Yu-Neng Chuang, Helen Zhou, Prathusha Sarma, Parikshit Gopalan, John Boccio, Sara Bolouki, and Xia Hu. Learning to route Ilms with confidence tokens. arXiv preprint arXiv, 2410, 2024.
Yu-Neng Chuang, Leisheng Yu, Guanchu Wang, Lizhe Zhang, Zirui Liu, Xuanting Cai, Yang Sui, Vladimir Braverman, and Xia Hu. Confident or seek stronger: Exploring uncertainty- bassd on- device I1m routing from benchmarking to generalization. arXiv preprint arXiv:2502. 2444042800,, 2025.
Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. Training verifiers to solve math word problems, 2021. URL
oxg/abbs2110.1410
Alejandro Cuadron, Dacheng Li, Wenjie Ma, Xingyao Wang, Yichuan Wang, Siyuan Zhuang, Shu Liu, Luis Gaspar Schroeder, Tian Xia, Huanzhi Mao, et al. The danger of overthinking: Examin- ing the reasoning-action dilemma in agentic tasks. arXiv preprint 00X2:22502.08235. 2025.
Yingqian Cui, Pengfei He, Jingying Zeng, Hui Liu, Xianfeng Tang, Zhenwei Dai, Yan Han, Chen Luo, Jing Huang, Zhen Li, al. Stepwise perplexity-guice guided refinement for efficient chain-of- thought reasoning in large language models. arXiv preprint arXiv:2502. 13260, 2025.
Muzhi Dai, Chenxu Yang, and Qingyi Si. S-grpo: Early exit via reinforcement learning in reasoning models, 2025. htth:::s::/
Renfei Dang, Shujian Huang, and Jiajun Chen. Internal bias in reasoning models leads to overthink- ing,

---

Published as a conference paper at ICLR 2026
DeepSeek-AL, Daya Guo, Dejian Yang, Haowei Zhang. Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang. Xiao Bi, Xiaokang Zhang. Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng. Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, Damai Dai, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangho Hao, Guanting Chen, Guowei Li, H. Zhang, Han Bao, Hanwei Xu, Haocheng Wang. Honghui Ding, Huajian Xin, Huazuo Gao. Hui Qu, Hui Li, Jianzhong Guo, Jiashi Li, Jiawei Wang, Jingchang Chen, Jingyang Yuan, Junjie Qiu, Junlong Li, J. L. Cai, Jiaqi Ni, Jian Liang, Jin Chen, Kai Dong, Kai Hu, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Liang Zhao, Litong Wang. Liyue Zhang, Lei Xu, Leyi Xia, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Meng Li, Miaojun Wang, Mingming Li, Ning Tian, Panpan Huang. Peng Zhang, Qiancheng Wang, Qinyu Chen, Qiushi Du, Ruiqi Ge, Ruisong Zhang, Ruizhe Pan, Runji Wang, R. J. Chen, R. L. Jin, Ruyi Chen. Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shengfeng Ye, Shiyu Wang. Shuiping Yu, Shunfeng Zhou, Shuting Pan, S. S. Li, Shuang Zhou, Shaoqing Wu, Shengfeng Ye, Tao Yun, Tian Pei, Tianyu Sun, T. Wang, Wangding Zeng. Wanjia Zhao, Wen Liu, Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang. W. L. Xiao, Wei An, Xiaodong Liu, Xiaohan Wang, Xiaokang Chen, Xiaotao Nie, Xin Cheng, Xin Liu, Xin Xie, Xingchao Liu, Xinyu Yang, Xinyuan Li, Xuecheng Su, Xuheng Lin, X. Q. Li, Xiangyue Jin, Xiaojin Shen, Xi- aosha Chen, Xiaowen Sun, Xiaoxiang Wang, Xinnan Song, Xinyi Zhou, Xianzu Wang, Xinxia Shan, Y. K. Li, Y. Q. Wang. Y. X. Wei, Yang Zhang, Yanhong Xu, Yao Li, Yao Zhao, Yaofeng Sun, Yaohui Wang, Yi Yu, Yichao Zhang, Yifan Shi, Yiliang Xiong, Ying He, Yishi Piao, Yisong Wang, Yixuan Tan, Yiyang Ma Yiyuan Liu, Yongqiang Guo, Yuan Ou Yuduan Wang. Yue Gong, Yuheng Zou, Yujia He, Yunfan Xiong, Yuxiang Luo, Yuxiang You, Yuxuan Liu, Yuyang Zhou, Y. X. Zhu, Yanhong Xu, Yanping Huang. Yaohui Li, Yi Zheng, Yuchen Zhu, Yunxian Ma, Ying Tang, Yukun Zha, Yuting Yan, Z. Z. Ren, Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, Zhenda Xie, Zhengyan Zhang. Zhewen Hao, Zhicheng Ma, Zhigang Yan, Zhiyu Wu, Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li. Ziwei Xie, Ziyang Song, Zizheng Pan, Zhen Huang, Zhipeng Xu, Zhongyu Zhang, and Zhen Zhang. Deepscek-rl: Incentivizing reasoning capability in llms via reinforce- ment learning, 2025. CRL.https:///
org/ abs 2501. 12948
Razvan-Gabriel Dumitru, Darius Peteleaza, Vikas Yadav, and Liangming Pan. Conciserl: Conciseness-guided reinforcemen learning for efficient reasoning models, 2025. https:
//arxáv.orr//aa//5555...
Yichao Fu, Junda Chen, Yonghao Zhuang. Zheyu Fu, Ion Stoica, and Hao Zhang. Reasoning without self-doubt: More efficient chain-of-the of-thought through certainty probing. In ICLR 2025 Workshop on Foundation Models in the Wild, 2025. URL httpt::// pttttss://pperevtt /oppnrpeeiiieeeeeee ew. net. forum?io
wpK4TMJfa TMJ
Tingxu Han, Zhenting Wang, Chunrong Fang, Shiyu Zhao, Shiqing Ma, and Zhenyu Chen. Token- budget-aware I1m reasoning. arXiv preprint arX1v:2412.18547,, 2024.
Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason Weston, and Yuandong Tian. Training large language models to reason in continuous latent space. arXiv preprint arXiv:2412.06766 2024.
Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Leng Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, Jie Liu, Lei Qi, Zhiyuan Liu, and Maosong Sun. Olympiadbench: A challenging benchmark for promoting agi with olympiad-level bilingual mul- timodal scientific problems, 2024. URL http:///axxvv...oo org/ abs/ /aobs/24022 2402.14008
Dan Hendrycks. Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardr. Measuring mathematical problem solving with the math dataset, 2021.
htt.httss:///axiin. wwwpxxv..orrrrreee abs/alasa0100 03874
Yao Huang, Huanran Chen, Shouwei Ruan, Yichi Zhang, Xingxing Wei, and Yinpeng Dong. Mit- igating overthinking in large reasoming models via manifold steering, 2025. URL https:
/
22411
Naman Jain, King Han, Alex Gu, Wen-Ding Li, Fanjia Yan, Tianjun Zhang, Sida Wang, Armando Solar-Lezama, Koushik Sen, and Ion Stoica. Livecodebench: Holistic and contamination free
12

---

Published as a conference paper at ICLR 2026
evaluation of large language models for code, 2024. URL https://axxv..ro// 24C3.07979
Lingjie Jiang, Xun Wu, Shaohan Huang, Qingxiu Dong, Zewen Chi, Li Dong, Xingxing Zhang, Tengchao Lv, Lei Cui, and Furu Wei. Think only when you need with large hybrid-reasoning models, 2025a. URLhttts::/
/wtp/aaavvvv.vvv////v/eea..aaavv org/ abs/ 250..
Yuxuan Jiang, Dawei Li, and Frank Ferraro. Drp: Distilled reasoning pruning with skill-aware step decomposition for efficient large reasoning models, 2025b. Utttt:::://aaat org/ abs/2505.1397.
Yu Kang, Xianghui Sun, Liangyu Chen, and Wei Zou. Cot:: Generating shorter chain-of-thouue ofothttght without compromising effectiveness. Proceedings of the AAAI Conference on Artificial Intelli- gence, volume 39, pp.
2025.
kvcache ai. KTransformers: A flexible framework for experiencing cutting-edge Ilm inference optimizations.
htt.:///.....o/ccccaaeeeaaaaaaea witteaaaa/aaaatttoeeeaaaaeas formers 2025. URL http://tww...ooeeeeeeeeeeaaaaaaa alb2c3d, accessed 2025-05-16.
GitHub repository, commit
Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph E. Gonzalez, Hao Zhang, and lon Stoica. Efficient memory management for large language model serving with pagedattention, 2023. URLhttps:: //ap:i/aaaiivaaa wwwp:iivvorrroeooooooooo abs///bb//// 2309. 06180
Aycong Lee, Ethan Che, and Tianyi Peng. How well do Ilms compress their own ohain-of-thhughht a token complexity approach. arXiv preprint arXiv:2503.01 141, 2025.
Yiwei Li, Peiwen Yuan, Shaoxiong Feng, Boyuan Pan, Xinglin Wang, Bin Sun, Heda Wang, and Kan Li. Escape sky-high cost: Early-stopping self-consistency for multi-step reasoning. arXiv preprint arXiv:2401 2000:2400.14800 2024.
Zheng Li, Qingxiu Dong. Jingyuan Ma, Di Zhang, Kai Jia, and Zhifang Sui. Selfbudgeter: Adaptive token allocation for efficient Ilm reasoning, 2025a. URL
11274
Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao. Haotian Xu, Junhao Zheng, Pei-Jie Wang, Xiuyi Chen, Yingying Zhang, Fei Yin, Jiahua Dong. Zhijiang Guo, Le Song, and Cheng-Lin Liu. From system to system 2: A survey of reasoning large 255..
language models, 2025b. URL
Baohao Liao, Yuhui Xu, Hanze Dong, Junnan Li, Christof Monz, Silvio Savarese, Doyen Sahoo, and Caiming Xiong. Reward-guidee speculative decoding for efficient Ilm reasoning. arXiv preprint arXiv:2501. 193244 2025.
Hanbing Liu, Lang Cao, Yuanyi Ren. Mengyu Zhou, Haoyu Dong, Xiaojun Ma, Shi Han, and Dongmei Zhang. Bingo: Boosting efficient reasoning of iims via dynamic and serfffcance-bbsse reinforcement learning, 2025a. URL
08125
Tengxiao Liu, Qipeng Guo, Xiangkun Hu, Cheng Jiayang, Yue Zhang, Xipeng Qiu, and Zheng Zhang. Can language models learn to skip steps? arXiv preprint arXiv:241 0.f::2/11.0188 1.01855, 2024.
Wei Liu, Ruochen Zhou, Yiyun Deng, Yuzhen Huang, Junteng Liu, Yuntian Deng, Yizhe Zhang, and Junxiam He. Learn to reason efficiently with adaptive Length-based reward shaping, 2025b. URL https:tt///. pettps://arxiv.oom
abs/ 15612
Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du Wee Sun Lee, and Min Lin. Understanding rl-zero-like training: A critical perspective, 2025c. URL https:
www.iii.rg/aab//22..... 20783
Haotian Luo. Li Shen, Haiying He, Yibo Wang, Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. O1-pruner: hangh--hamonzzing fine-tuning for ol-like reasoning pruning. arXiv preprint 2011: 2025a.
13

---

Published as a conference paper at ICLR 2026
Yijia Luo, Yulin Song, Xingyao Zhang, Jiaheng Liu, Weixun Wang. GengRu Chen, Wenbo Su, and Bo Zheng. Deconstructing long shain-of-thouuhtt. A structured reasoning optimization framework for long cot distillation, 2025b. URL httpt:ttaatai...otttt wwtpa/wwwww...aaaaaaaaaaaaaaaaaa wwwp://pppp....ooooooooooo 16385
Wenjie Ma, Jingxuan He, Charlie Snell, Tyler Griggs, Sewon Min, and Matei Zaharia. Reasoning models can be effecttiee without thinking. arXiv preprint arXiv:2504. 09858, 2025a.
Xinyin Ma, Guangnian Wan, Runpeng Yu, Gongfan Fang. and Xinchao Wang. Cot-valve: Length- compressible chain-of-thought tuning. arXiv preprint arXiv:2502.066)) 2025b.
Rohin Manvi, Anikait Singh, and Stefano Ermon. Adaptive inference-time compute: Lims can predict they can do better, even mid-generation. arXiv preprint 00X122400222 2024.
MAA Committees. Aime problems and solutions. https:/ /ttpss//arttfpproolemmoolvggggg com/ wiki/index. php AAMEE Problems and Solution
Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zetlemoyer, Percy Liang, Emmanuel Candès, and Tatsunori Hashimoto. sl: Simple test-time scaling, 2025. URL
19339
Tergel Munkhbat, Namgyu Ho, Seo Hyun Kim, Yongjin Yang. Yujin Kim, and Se- Youn Yun. Self- training elicits concise reasoning in large language models. arXiv preprint arXiv:2502.21122, 2025.
Isaac Ong, Amjad Almahairi, Vincent Wu, Wei-Lin Chiang, Tianhao Wu, Joseph E Gonzalez, M Waleed Kadous, and Ton Stoica. Routellm: Learning to route Ilms with preference data, 2024. URL https://arxiv. org/abs/2406. 0ttp//2466.86660 18665.
OpenAl. Learning to reason with 1lms.
tearning-to-reaseen wetnn-wwtth-aae 11ms, 2025. Accessed: 15 March 2025.
Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, al. Training language models fol- low instructions with human feedback. Advances in neural information processing systems, 35: 27730-27744, 2022.
Ziqing Qiao, Yongheng Deng, Jiali Zeng, Dong Wang, Lai Wei, Guanbo Wang, Fandong Meng, Jie Zhou, Ju Ren, and Yaoxue Zhang. Concise: Confidence-guided compression step-by-step efficient reasoning, 2025. lttts::/://aax wttp:/wwwww....//////////a////// hbcp//0bb///555555 04881
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 arXi::2503.07572, 2025.
Qwen, An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li. Mingfeng Xue, Pei Zhang, Qin Zhu. Rui Men, Runji Lin, Tianhao Li, Tianyi Tang, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yuqiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu. Qwen2.5 technical report, 2025. org/ abs/ 2412. 15115
URL
Shyam Sundhar Ramesh, Yifan Hu, lason Chaimalas, Viraj Mehta, Pier Giuseppe Sessa, Haitham Bou Ammar, and Ilija Bogunovic. Group robust preference optimization in reward- free RLHF. In The Thirty-eight Annual Conference on Neural Information Processing Systems, 2024. URL/tttps:/ http::::////peeeeeeeee net for.morrmmooo. d- htttt/ffooummmdd-P..... rmXXK
Carl Rasmussen and Zoubin Ghahramani. Occam's razor. In T. Leen, T. Dietterich, and V. Tresp (eds.), Advances in Neural Information Processing Systems, volume 13. MIT Press, 2000. URL
fi
14

---

Published as a conference paper at ICLR 2026
David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R. Bowman. Gpqa: A graduate-level google- proof q&a benchmark, 2023. URL https: /tttpps///riiiiii/ arxiv. org/ abs 12022
Matthew Renze and Erhan Guven. The benefits of concise chain of thought on problem-son sollnnn in large language models. In 2024 2nd International Conference on Foundation and Large Language Models (FLLM), pp. 476-483. IEEE, 2024.
Nikunj Saunshi, Nishanth Dikkala, Zhiyuan Li, Sanjiv Kumar, and Sashank J Reddi. Reasoning with latent thoughts: On the power of looped transformers. arXiv preprint 1tti:2502.174116 2025.
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017.
Xuan Shen, Yizhou Wang. Xiangxi Shi, Yanzhi Wang. Pu Zhao, and Jiuxiang Gu. Efficient reasoning with hidden thinking. arXiv preprint (tt::2500.1920.1 2025a.
Yi Shen, Jian Zhang. Jieyun Huang. Shuming Shi, Wenjing Zhang, Jiangze Yan, Ning Wang, Kai Wang, and Shiguo Lian. Dast: Difficulty-adaptive slow-thinking for large reasoning models.
arXiv preprint ar arXiv:2533.04477 2025b.
Zhenyi Shen, Hanqi Yan, Linhai Zhang, Zhanghao Hu, Yali Du, and Yulan He. Codi: Compressing thhhuht into continuous space via self-distillation. arXiv preprint arXiv:2502.21074 2025c.
Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling IIm test-time compute optimally can be more effective than scaling model parameters, 2024. URL https::/arxiv.orr
abs/ 2aas/2408.0 03314
Jiwon Song, Dongwon Jo, Yulhwa Kim, and Jae-Joon Kim. Reasoning path compression: Com- pressing generation trajectories for efficient I1m reasoning, 2025. URL/httss//arrxi..oo
abs/ 2bs5/505.20 13866
DiJia Su, Hanlin Zhu, Yingchen Xu, Jiantao Jiao, Yuandong Tian, and Qinqing Zheng. Token assorted: Mixing latent and text tokens for improved language model reasoning. arXiv preprint DrXiv:2502.03275.. 2025.
Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Shaochen Zhong, Hanjie Chen, and Xia Hu. Stop overthinking: A survey on effi cient reasoning for large language models, 2025. URL httttttss///axiiii wwwpw/wwwwww..w////aaaaaa//////.
16419
Wenhui Tan, Jiaze Li, Jianzhong Ju. Zhenbo Luo, Jian Luan, and Ruihua Song. Think silently, think fast: Dynamic latent compression of 11m reasoning chains, 2025. /RR/httss//axxiv.coo
abs/2505.16552
Kimi Team, Angang Du, Bofei Gao, Bowei Xing, Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun Xiao, Chenzhuang Du, Chonghua Liao, Chuning Tang, Congcong Wang, Dehao Zhang, Enming Yuan, Enzhe Lu, Fengxiang Tang, Flood Sung, Guangda Wei, Guokun Lai, Haiqing Guo, Han Zhu, Hao Ding. Hao Hu, Hao Yang, Hao Zhang, Haotian Yao. Haotian Zhao, Haoyu Lu, Haoze Li, Haozhen Yu, Hongcheng Gao, Huabin Zheng, Huan Yuan, Jia Chen, Jianhang Guo, Jianlin Su, Jianzhou Wang, Jie Zhao, Jin Zhang, Jingyuan Liu. Junjie Yan, Junyan Wu, Lidong Shi. Ling Ye, Longhui Yu, Mengnan Dong, Neo Zhang, Ningchen Ma, Qiwei Pan, Qucheng Gong, Shaowei Liu, Shengling Ma, Shupeng Wei, Sihan Cao, Siying Huang, Tao Jiang, Weihao Gao, Weimin Xiong. Weiran He, Weixiao Huang, Wenhao Wu, Wenyang He, Xianghui Wei, Xianqing Jia, Xingzhe Wu, Xinran Xu, Xinxing Zu, Xinyu Zhou, Xuehai Pan, Charles, Yang Li, Yangyang Hu, Yangyang Liu, Yanru Chen, Yejie Wang, Yibo Liu, Yidao Qin, Yifeng Liu, Ying Yang, Yiping Bao, Yulun Du, Yuxin Wu, Yuzhi Wang, Zaida Zhou, Zhaoji Wang, Zhaowei Li, Zhen Zhu, Zheng Zhang, Zhexu Wang, Zhilin Yang, Zhiqi Huang, Zihao Huang, Ziyao Xu, and Zonghan Yang. Kimi k1.5: Scaling reinforcement learning with 1lms, 2025a. URL https: wwwxwv..vvv....
abs/ /250/201..mm 12599
15

---

Published as a conference paper at ICLR 2026
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:2501.1259) 2025b.
Qwen Team. Qwq-32b: Embracing the power of reinforcement learning, March 2025. URL
https: http:://wweemm.mmmmmm htt.w//....g.uu.....eeeeeeeeeeae
qwap 32b/
Songjun Tu, Jiahao Lin, Qichao Zhang, Xiangyu Tian, Linjing Li, Xiangyuan Lan, and Dongbin Zhao. Learning when to think: Shaping adaptive reasoning in rl-style models via multi-stage rl,
2025.
10832
Hongru WANG, Deng Cai, Wanjun Zhong, Shijue Huang, Jeff Z. Pan, Zeming Liu, and Kam-Fai Wong. Self-reasoning language models: Unfold hidden reasoning chains with few reasoning catalyst. In Workshop on Reasoning and Planning for Large Language Models, 2025. URI.
Rui Wang. Hongru Wang, Boyang Xue. Jianhui Pang, Shudong Liu, Yi Chen, Jiahao Qiu, Derek Fai Wong, Heng Ji, and Kam-Fai Wong. Harnessing the reasoning economy: A survey of efficient rea- soning for large language models, 2025a. URL. http:::tttsstttttt org/ abs .2367.223377
Shenzhi Wang, Le Yu. Chang Gao, Chujie Zheng. Shixuan Liu, Rui Lu, Kai Dang. Xionghui Chen, Jianxin Yang, Zhenru Zhang, Yuqiong Liu, An Yang, Andrew Zhao, Yang Yue, Shiji Song, Bowen Yu, Gao Huang, and Junyang Lin. Beyond the 80/20 rule: High-entropy minority tokens drive effective reinforcement learning for IIm reasoning, 2025b. httphtss:///::ti..o http//xxxiv.orgab/////
12566.05 01939
Yibo Wang, Li Shen, Huanjin Yao, Tiansheng Huang, Rui Liu, Naiqiang Tan, Jiaxing Huang, Kai Zhang, and Dacheng Tao. R1-compress: Long thoun-o compeessonn via chunk compres- sion and search, 2025c. URL hwllttpps//aarai..rrr//a/////// 16838
Jason Wei, Maarten Bosma, Vincent Y Zhao, Kelvin Guu, Adams Wei Yu, Brian Lester, Nan Du, Andrew M Dai, and Quoc V Le. Finetuned language models are zero-shot learners. arXiv preprint arXiv:2109.0166 0/52,, 2021.
Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Brian Ichter, Fei Xia, Ed Chi, Quoc Le, and Denny Zhou Chain-of- thought prompting elicits reasoning large language models, 2023. URL CtLhttps:: /ttp:iv.//axxv..ooo abs 2201.11903
Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. Huggingface 's transformers: State-of- the-art natural language processing, 2020. URL /tR///tttpe//rrrc..oor////ssb
Yuyang Wu, Yifei Wang, Tianqi Du, Stefanie Jegelka, and Yisen Wang. When more is less: Under- standing chain-of of-tthuuhtt length in llms. arXiv preprint arXiv:2502.07266 2025.
Heming Xia, Yongqi Li, Chak Tou Leong, Wenjie Wang, and Wenjie Li. Tokenskip: Controllable chain-of-thought compression in llms. arXiv preprint arXiv:2502. 12067, 2025.
Yuxi Xie, Kenji Kawaguchi, Yiran Zhao, James Xu Zhao, Min- Yen Kan, Junxian He, and Michael Xie. Self-evaluation guided beam search for reasoning. Advances Neural Information Process- ing Systems, 36:41618-41633 416500, 2023.
Fengli Xu, Qianyue Hao, Zefang Zong, Jingwei Wang, Yunke Zhang, Jingyi Wang, Xiaochong Lan, Jiahui Gong. Tianjian Ouyang, Fanjin Meng, Chenyang Shao, Yuwei Yan, Qinglong Yang, Yiwen Song. Sijian Ren, Xinyuan Hu, Yu Li, Jie Feng, Chen Gao, and Yong Li. Towards large reasoning models: A survey of reinforced reasoning with large language models, 2025a. URL. https::/arxivy org/ abs 2501 09686
Silei Xu, Wenhao Xie, Lingxiao Zhao, and Pengcheng He. Chain of draft: Thinking faster by writing less. arXiv preprint arXiv:2502. 18600, 2025b.
16

---

Published as a conference paper at ICLR 2026
Silei Xu, Wenhao Xie, Lingxiao Zhao, and Pengcheng He. Chain of draft: Thinking faster by writing less, 2025c. URL
abs /tt.v/...rrr/al/2222..00000 2502.18600
Yige Xu, Xu Guo, Zhiwei Zeng, and Chunyan Miao. Softcot: Soft chain-of-thought for efficient reasoning with Ilms. arXiv preprint 25Xi::2502.12134,, 2025d.
Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. Limo: Less is more for reasoning, 2025. URL hwtpt:ttss/sxiiiiee org/ abs 00os/2500 2502. 03387
Edward Yeo, Yuxuan Tong, Morry Niu, Graham Neubig, and Xiang Yue. Demystifying long chain- of-thought reasoning in Ilms. arXiv preprint arXiv:2502.03373, 2025.
Bin Yu, Hang Yuan, Haotian Li, Xueyin Xu, Yuliang Wei, Bailing Wang, Weizhen Qi, and Kai Chen. Long-short chain-of-thougs mixture supervised fine-tuning eliciting efficient reasoning in large language models, 2025. URL /ttp::///axvvvvoeeeeeee. wwg. wtwgabb/////oooo. 2505.55000 03469
Ping Yu, Jing Xu, Jason Weston, and Ilia Kulikov. Distilling system 2 into system 1. arXiv preprint arXiv:2407.060233, 2024.
Anqi Zhang, Yulin Chen, Jane Pan, Chen Zhao, Aurojit Panda, Jinyang Li, and He He. Reason- ing models know when they'r re right: Probing hidden states for verffvecrinnation. arXiv preprint arXiv:2504.0541. 2025a.
Jijjie Zhang, Nianyi Lin, Lei Hou, Ling Feng, and Juanzi Li. Adaptthink: Reasoning models can learn when to think, 2025b. URRtps:::///axxi
httpaaaxxiv.org/bbee org. wttp://a../......1.2/
Wenyuan Zhang, Shuaiyi Nie, Xinghua Zhang, Zefeng Zhang, and Tingwen Liu. S1-bench: A simple benchmark for evaluating system thinking capability of large reasoning mod- cls. ArXiv, 100s/2544.10668, 2025c. URL httpss///ppp.smmmntccchoooooooo
CorpusID:277781100
Zhen Zhang, Xuehai He, Weixiang Yan, Ao Shen, Chenyang Zhao, Shuohang Wang, Yelong Shen, and Xin Eric Wang. Soft thinking: Unlocking the reasoning potential of Ilms in continuous concept space, 2025d. UtL/https://aat ottp:///..r//////5555/5555 15778
Rongzhi Zhu, Yi Liu, Zequn Sun, Yiwei Wang, and Wei Hu. When can large reasoning models save thinking? mechanistic analysis of behavioral divergence in reasoning, 2025. URL https:
flaxiivorg/abll halgg//bb/255505 15276
Terry Yue Zhuo, Minh Chien Vu, Jenny Chim, Han Hu, Wenhao Yu, Ratnadira Widyasari, Imam Nur Bani Yusuf, Haolan Zhan, Junda He, Indrancil Paul, et al. Bigcodebench: Bench- marking code generation with diverse function calls and complex instructions. arXiv preprint arXiv:2406. 15877, 2024.
17

---

Published as a conference paper at ICLR 2026
A PILOT EXPERIMENT SETUP
We selected AIME2024 (MAA Committees) as the test set for exploratory experiments to perform qualitative analysis and further conducted a quantitative analysis through experiments MATH- 500 (Hendrycks et al. 202T), GPQA- (Rein et al. (023). All experiments were conducted on DeepSeek-RI-Distee -wwlll---weeere 14B (DeepSeek-AL et al., 2025). In experiments, we first en- abled the LRM to perform a complete inference on the test set (including both the slow thinking and conclusion contents). Then, We preserved the thinking content and divided it into thinking chunks based on the action transition points. Samples with more than five thinking chunks were retained. For these samples, we retained varying proportions (20%-90%) of their thinking chunks and appended an end-of-thinking token delimiter to each truncated reasoning sequence to forcibly terminate the slow-thinking process. The model then generated its final conclusion based on the par- tial reasoning contents. For the conclusions obtained with varying thinking contents, we evaluated their correctness and presented the results of each sample in Figure Furthermore, we investigated the number of samples that remained correct after early exiting when they were originally correct, as well as the number of samples that became correct after early exiting when they were originally incorrect, across three datasets in Figure 2
B PROOF OF DEER-PRO'S ' EFFECTIVENESS AGAINST NOISE.
B.1 NOISE INDEPENDENCE OF THE DAD-BALID STRATEGY
Let us define the confidence μ as the model's actual probability of deriving the correct answer given the current reasoning content, corresponding to the real probability of pearl reasoning existing this location. The early-exit decision threshold denoted as X, and the model executes early exit when μ > X. Since answer inducing prompts may introduce E, the model's output confidence fluctuates around the true confidence, yielding an observed confidence of C; = ff + & In practical testing environments, we compare C, with À to determine whether to perform early exit. Without loss of generality, we assume the noise terms E; to be independently and identically distributed (i.i.d),, a Gaussian distribution with mean 0 and standard deviation i.e., ~ N(0, o²). Here, represents the model's 's sensitivity to prompt phrasing. larger a indicates higher model sensitivity, resulting in greater confidence fluctuations.
Next, we demonstrate DEER- EREE- effectiveness against noise interference by comparing the de- cision error rates of DEER-PRO (Ceats), DEER (C,), an averaging approach (Caog) in critical risk scenarios. Suppose Ceuti and Cavg each conduct N times answer inducing in parallel, with N identi- cal to that in Equation (5). Given that preserving accuracy takes precedence over early-exit speedup gains in reasoning scenarios, we designate risk scenarios as those where true confidence < X. We then compute the false positive probability of observing C > X due noise interference.
B.1.1 PROBABILITY OF ERROR FOR A SINGLE PROMPT:
Pro P(C, > A) P(u + > A) P(s, X X-
(6)
Since e, NO, o2), we standardize it as:
Pre(Single) = P E1 A-
Let Z = then Z ~ NO0 1), then:
A - p 1 ①b \ #
(Sngge) = Z
(8)
where $ is the cumulative distribution function (CDF) of the standard normal distribution.
1.1.2 PROBARILITY OF ERROR FOR AVERAGED CONFIDENCE:
For the averaged confidence Cang. the noise term is still Gaussian, Eaog ~ N(0, o²/N). The proba- bility of error for averaged confidence is:
PAp(Avg) = P(Cavg > A) = 1- - (V/VN 4)
(9)
18

---

Published as a conference paper at ICLR 2026
Since (A-pl/N Aー for .N' > 1, it follows that (pr(Avg) < Prr(Single). indicates that sim- ply averaging multiple observed confidence values mitigate noise interference. Nevertheless, confidence averaging fails to address the fundamental problem, as the error rate Pyp remains de- pendent the noise standard deviation a, increasing monotonically substantial intrinsic noise (large o), the parameter inside the Φ function converges to zero, driving Pt toward 0.5, This indicates that high-noise models reduce random guessing, regardless of the decision threshold X. Therefore, the reliability of traditional approaches is severely constrained by the model's inherent noise level Ø, factor beyond our control.
grows. For models with
B.1.3 PROBABILITY OF ERROR FOR MAD-CALIBRATED CONFIDENCE (DEER-PRO):
Prp(calibration) P(Ccali > A) P(Cavg CMAD A)
(10)
Substituting Cavg = μ + Eaug. we obtain:
Prr (calibration) P( + Gaog a GMAD > A)
(11)
Rearranging the terms in the equation yields:
Prp(calibration) = = > a CMAD + X A-p) p
(12)
Next, will discuss the robustness of DEER-PRo under distinct scenarios.
Scenario 1: Approximate estimation of CMAD
Under assumption where NNO, o²). have Eavg (N0,02/N) and E[CMAD] =s 0.8c
(we will provide the proof in Section B.3). For large N, the law of large numbers allows us to approximate GMAD 0.8o. Given this assumption, have:
Prp(calibration) = P(Caeg > À + 0.8or)
(13)
The above equation reveals that DEER-PRo fundamentally differs by employing an adaptive thresh- old that scales with noise:
Aeflective + 0.8az
(14)
We proceed to reformulate the equation by transforming (caliibbbattion) into the cumulative dis- tribution function (CDF) of the standard normal distribution ②. For Equation (12). we substitute CMAD 0.8g and obtain:
Per (calbbbrratioon = P(Eaeg > 0.80a + A p)
(15)
Since Sang ~ N N(0,02/NY,
(A 0.80x) Mo
Prp(calibration) =
(16)
Simplifying:
Pvp(calibration) =1 - ① VN A-ド 1² + 0.80
(17)
When noise minimal:
Aeffective A
(18)
The calibrated method behaves like standard thresholding, maintaining high efficiency.
When noise dominates, A- + O. The false positive rate becomes:
Prp +00.8ovNN)
(19)
which is independent of It indicates that DEER-PRo effectively prevent early exit from reducing to random guessing (PFp - 0.5).
Scenario 2: Exact computation of CMAD without approximation.
From CMAD & EN IC; Caugl- we know that CMAD is positive, therefore dividing both sides of the equation by this term, we obtain:
P(Eavg/ /CMAD (A (1)/CMAD)
(20)
19

---

Published as a conference paper at ICLR 2026
Since X, then (A 11)D/CCAAD > a, P(Earg/CMnn > a + (A /))CMAD) < P(Eavg/CMADD > ax)
obtain:
(21)
/CMA a) is an upper bound for /"p(ccaibration) For the ratio Eveg/ /C MCMAD AD. Eang represents the signal of the noise, while CMAD represents the internal disorder of the noise. Therefore, we can define Eavg/CasAD as the Signal-to-Noise Ratio (SNR).
Therefore, P(Eang/ (Eaag//MADD
Next, let us analyze the properties of SNR. Under our assumption where E; (N,00 o2), have Eang ~ [(0, o² /N) and (MMA)] R 0.80. Since both Eavy and CMAD are proportional to a, we can write SNR
SNR = (a (a * ZMAD) =
(22)
where Zang (0, 1/N) is standardized noise mean, and Zenad is random variable related to M AD/o whose distribution does not depend on Hence, the probability distribution of the SNR independent of the model noise standard deviation 0.
Per (cclibbbbraion)) P(Zaug/ZMaa > a)
(23)
Therefore, Prp (rp(caiibration) is influenced only by the number of prompts and the signal-to-noise ratio threshold a, where larger values of N and a lead lower error rates.
Through the transformation from an absolute threshold test to self-normalized SNR test, our MAD strategy effectively decouples decision-making from the model's intrinsic and uncontrollable noise level Ø. In contrast to traditional approaches that break down under high-noise conditions, our method delivers consistent, robust performance independent of model noise levels.
B.2 ANALYSIS MAD-CALIBRATED STRATEGY'S SUPERIOR PERFORMANCE
In this section, we formally prove based on the event space that the false positive probability of the MAD strategy, Prp(MAD) (PPr(calibration), is significantly superior to that the simple averag- ing strategy, (Avg)))), and consequently also outperforms (singl))
The false positive probability of the MAD-calibrated strategy satisfies (MAD) S p. Pre(Avg), where p (ccxp( (NN)) is an exponentially decaying factor in the number of prompts N.
Theorem.
Proof. The false positive events are defined as:
FANng = {s Eavg > c}
(24)
EMAD {E: 5 a MAD c}
(25)
where A- u >> is the threshold gap, MAD N Ei e Engl is the mean absolute deviation,
N i N i=1 E is the average noise, and there are independent noise terms E; ~ N(0, a²) for
Eavp
Since a and MAD 2 0 by definition, we have:
Eavg
MAD Eavg
(26)
Therefore, if Eavg a MAD > c, then necessarily Eavg > c. This establishes:
FMAD C FAvE
(27)
Consequently:
Prr(MAD) P(EMAD) S P(EAv)) = (Av(Avg)
(28)
To quantify the improvement beyond this basic inequality, we decompose the probability using conditional probability:
(MAD) P(EMAD n EAvg) P(EMAD)EAve) P P(EAvE)
(29)
Since EMAD S EAug. we have:
P(FMAD| P(emg a MAD clewn >
(30)
20

---

Published as a conference paper at ICLR 2026
This can be rewritten as:
P(EMAD Eavg) = P
MAD
Savg -
Eavg > )
(31)
Define the improvement factor:
Eavg
p =
MAD
Eavg 2 cc
(32)
a
Then:
Prr(MAD) p. Prr(Avg)
(33)
To evaluate P, we analyze the structure of noise vectors that satisfy Eavg > There are two primary patterns:
Pattern A (Coherent Pattern): All noise terms are close to c. Formally, for some small 5 > 0:
Pattern
(e: lex cl 5 for all 1 1,..., N}
(34)
Under Pattern
Eavg R c + O(6vVN) (by the central limit theorem)
MAD < 25 (since all values are within 26 of each other)
Pattern (Outlier Pattern): A few large outliers with remaining values near zero. For example:
k values with = Nc/k lo (large outliers)
-
- l values with E; s
Under Pattern B:
Savg R C
MAD c(1 ((111/N) 1/N) (large due to outliers)
Probability of Pattern A:
For single noise term to fall in (c - c
c 0
c
< -|
(35)
Using Taylor expansion for small 8:
P(Ee cl < ~
(
28
28
exp
c²
(36)
0/2n
20
For all N noise terms to satisfy this condition independently:
N
P(Pattern A) = Lov2%
exp
(37)
20
Probability of Eavg >
Since Eang NO0,o2/N).
cv
P(ewgg > c) =
(38)
Using Mill's ratio approximation for large arguments:
c²N
P(Eavg > c) ~ cV2TNN
exp
(39)
20
21

---

Published as a conference paper at ICLR 2026
The key insight is that Pattern A is the only pattern where MAD remains small enough to satisfy MAD < (Eavg c)/a.
For Pattern B and other outlier-drieen patterns, MAD = O(c), while Swg c - O(1/vN) when conditioned on Eavg Thus:
Eavg
MAD
(40)
Therefore, the improvement factor is dominated by Pattern A:
P(Patter A)
P X
(41)
P( c)
Substituting the expressions:
N
exp
20²
(42)
2
exp
ctN
2n
Simplifying:
CV N
26
N
2N
P S
exp
+
(43)
TV 2m
2
20
28
N
P PS cVN
(44)
For 5 0(o), let 8 ko where k is constant. Then:
2k
N
P CVN
N
(45)
2m
When V x/2, the term (2k/V2T)) N decays exponentially. The polynomial factor vN is
dominated by the exponential decay, yielding:
0=vNN exp(-3N) = -(()p(-0((N)
(46)
for some positive constant B. We have established that:
Prp(MAD) = p Prp(Avg)
(47)
where p = O(exp(-((N)) decays exponentially with the number of prompts N.
This demonstrates that the MAD-calibrated strategy provides an exponential improvement over the simple averaging approach. D
Conclusion: The MAD penalty term effectively filters out the more probable outlier patterns while only allowing the exponentially rare coherent patterns to trigger false positives, thus achieving superior robustness against prompt-induced noise.
B.3
PROOF OF THE EXPECTED VALUE OF MAD
B.3.1 THEOREM I
For random variable X N(H,,²), the expected value of the CMAD is:
2
E[CMAD] = =ov - 0.8g
(48)
22

---

Published as a conference paper at ICLR 2026
B.3.2 PROOF
Definition. The Mean Absolute Deviation of a random variable with mean p is defined as:
MMAD E al]]
(49)
Let X N(p, Consider the standardized random variable:
Z - N),
(50)
Therefore:
X 11| - =|
(51)
Taking expectations on both sides:
E X la|| E||
(52)
For 2 ~ (N,, with probability density function (<z) = 2/ e.
-22
E [ |2| 6(2) dz
(53)
Due to the symmetry of the standard normal distribution about zero and the even nature of |z|:
B| = / (()))) dz
2
oc
e.e - dz
(54)
2tT Jo
Let 22/2, then du dz. When 0, 0; when 2 -> 0., 11 - 00. -
I 2. x.e 1/ dz e du
- u=]
00 =
(55)
Substituting back:
2
2
E||Z||
1 V π
(56)
2TT
Therefore:
GMAD = E||X - 14] a -E|2
=O = 0.80
(57)
C MORE EXPERIMENT SETUP
Metrics. The goal of DEER is to maintain the correctness performance of LRMs while avoiding
the redundant token overhead caused by overthinking. To this end, we selected Accuracy (ACC) and Generation Length (LEN) as the evaluation metrics. Accuracy (ACC) is calculated as follows:
Accuracy = N' EN T(M(CR.M(zz)) = ys). where x; is the question and y; is the ground-truth answer from the dataset. M(.) extracts the answer from the LRM'ss response. T{-} is an indicator function that determines whether the inside given condition is valid. The accuracy evaluation is based on the evaluation framework publicly released by Ye et al. (2025) (LIMO). Intuitively, the longer the generated text, the greater the inference cost for LRMs. Therefore, we calculate the average generation tokens per sample to evaluate the cost as follows: Generation Length(LEN) = 1 > [R)((s))), where || measures the number of generated tokens. For the two programming benchmarks, we use the Pass@1 metric to measure generated code correctness.
N
Implementation details. All evaluations are conducted in a Zero-shot Chain-of-Thought (CoT) setting with the following prompt: "Please reason step by step, and put your final answer within \boxed[]." For the decoding strategy. we employ greedy decoding with single sample for the correctness evaluation. The ground-truth answers to the evaluation problems in our experiments are all well-structured numerical values or options. Therefore, we apply rule-based evaluations directly to verify mathematical equivalence. We set the maximum generation length at 16,384 to ensure that the evaluation captures complete problem-solving attempts. For DEER, the answer-inducing prompt employed is: "n'nn Final Answer n' bbxoed For DEER-Pro, we additionally incorporated the following three prompts: "nn'n Final Answer n'yn Based the analysis above, the answer is The correct final answer is bboxed', "nn'n Based on the previous thinking, I believe I already know the answer's n Final Answer booxed".
boxed', "in" n Final Answer
yn yn'
23

---

Published as a conference paper at ICLR 2026
Algorithm Dynamic Early Exit in Reasoning (DEER)
1: Initialization: Large Reasoning Language Model LRM(-), zero-shot-CoT 28 2s_cot, question, answer inducer prompt I, set of action transition points P. end-of-thinking delimiter (/think), maximum length max and confidence threshold X.
2: x f 2s_cot + question, r <-
3: while (en(x)) (x) max len do
4:
< (RM
5: if E P then
Generate thoughts until meets action transition points Prompt LRM to generate trial answer tokens D. Calculate the confidence of the trial answer
6:
A +- LRM(x I)
7:
Get C according Equation
8:
ifC > then - + (/think), r t- (/think)
9:
Exit when thinking sufficient
10:
end if
else
12:
- x: + -
13: end
14:
end while
15:
return
Ongeing reasoning-chain generation
Wais, dai ensighiforwon Let <omited-
step 1
Okey as this problem whene
Trial enewer evclastion
pirdl Acswert The faxl auswer thessal i.. Somitall
stop 2
step 3
f
f
1
122
1-3
15
112
1/
11
100
step 4
stop1
step 2
step
stop
Figure 9: Branch maanc-larallll decoding and dynamic KV cache management.
D MORE METHOD DETAILS
Fig. illustrates the workflow of the proposed Branch-Parallel Decoding Acceleration. Algorithm presents the pseudocode of DEER.
E MORE BENCHMARK DESCRIPTIONS.
Benchmarks. thoroughly evaluate the models' performance across various reasoning capabili- ties, we have chosen 6 math reasoning benchmarks, science benchmarks, and 3 coding benchmarks as follows:
MATH BENCHMARKS:
GSM8K well-curated collection of 1,319 problems in elementary mathematics. This benchmark is specifically designed to evaluate multi-step reasoning in foundational math tasks. Problems typically involve two to eight sequential operations, relying primarily on basic arithmetic performed over multiple intermediate steps.
MATH-500 is a challenging benchmark comprising competition-level problems drawn from diverse high school mathematics domains, including Prealgebra, Algebra, and Num- ber Theory. For consistency with previous research, we adopt the same 500-problem subset originally curated by OpenAl for evaluation.
AMC 2023 contains 40 mathematical problems, covering algebra, geometry, number the- ory, and combinatorics. The American Mathematics Competitions (AMC), organized by the Mathematical Association of America (MAA), are prestigious contests designed to de- velop wobblem-solving skills and identify mathematical talent. For evaluation, we used 40 questions from AMC 23 in LIMO.
24

---

Published as a conference paper at ICLR 2026
AIME 2024 comprises 30 challenge problems selected from the 2024 American Invita- tional Mathematics Examination (AIME). This prestigious contest evaluates participants' mathematical reasoning abilities across diverse domains, including arithmetic, algebra, counting, geometry, number theory, probability, and other secondary school math topics. A distinctive feature of the AIME is its answer format: all solutions must be integers between 000 and 999 (inclusive). Each problem is categorized by difficulty level (1-5) according the Art of Problem Solving (AoPS) scale. Beyond these three math problems, also conducted evaluations on scientific questions.
AIME 2025 comprises 30 challenge problems selected from the 2025 American Invita- tional Mathematics Examination (AIME).
OlympiadBench OlympiadBench is an Olympiad-level bilingual multimodal scientific benchmark dataset that aims to challenge and evaluate the advanced capabilities of Large Language Models and Large Multimodal Models. It features 8,476 problems sourced from mathematics and physics competitions at the Olympiad level, including those from the Chinese college entrance exam. Our experimental evaluation selects the same subset of 675 samples as used in LIMO, allowing for direct rule- aile-based evaluation of the generated answers.
SCIENCE BENCHMARKS:
GPQA is PhD-level benchmark consisting of high-quality questions spanning physies, chemistry, and biology subdomains. Notably, domain experts with PhDs in these fields achieved only 69.7% accuracy on this dataset. For experiments, we specifically select the highest quality subset, known as GPQA Diamond (composed of 198 questions).
PROGRAMMING BENCHMARKS:
HumanEval is proposed by OpenAl, containing 164 hand-crafted (to avoid data leakage) Python programming tasks focusing on basic algorithms, each with function signatures, docstrings, canonical solutions, and unit tests.
BigCodeBench is designed as a read-weold-orienteed benchmark, which includes 1,140 tasks requiring interactions with 139 libraries and diverse function calls.
LiveCodeBench is newly proposed benchmark dataset designed to evaluate the capabil- itics of large language models in code generation and related tasks. It aims to mitigate issues such test set contamination found in existing benchmarks by emphasizing scenar- ios beyond code generation, ensuring high-quality problem sources, adequate test cases, and balanced difficulty levels. The dataset comprises problems sourced from well-known competitive programming platforms like AtCoder, LeetCode, and CodeForces, collected from specific time windows. Our evaluation is based Bevehode which con- tains 880 programming problems collected from May 2023 to January 2025.
F COMPUTATION SOURCE
In our experiments, 8 x 80g memory H100 was used to perform evaluations.
G MORE LRM DESCRIPTIONS.
In this work, we validate the effectiveness of DEER across 12 reasoning models. The evaluated models include: Qwen3-1.7B, Qwen3-4B, Qwen3-8B, Qwen3-14B, Qwen3-32B, DeepSeek-R1- Distill-Qwen-1. 1.5B, DeepSeek-R1 --S-seelRRR-Distil---eeee 7B, DeenSeet-RI--Distll---eeeee -eeooooooootmtto---na------
DeepSeek- All
R1 RI-Distill-Qwen--2B, QwQ DeepSeek-R166718 and models in the DeepSeek-B RI-Distill-Series were supervised fine-tuned using reasoning data gener- ated by the DeepSeek-RI RI model. The Qwen3-1.7B, Qwen3-4B, Qwen3-8B, and Qwen3-14B mod- els were trained using a method known as Strong-to- -roaak Distillation. Trained via reinforcement learning, the non-distilled models QwQ-32B and Qwen3-322 demonstrate competitive performance on reasoning benchmarks, matching that of DeepSeek-R1-oe R1-671B. Due to computational constraints, implemented quantized version of Deepseek-R based on KTransformers (kveache ai 2025).
25

---

Published as a conference paper at ICLR 2026
H COMPUTATIONAL COST ANALYSIS
In this section, we provide theoretical analysis to demonstrate that DEER effectively reduces com- putational costs. Let L denote the total length generated by the original CoT method, and a represent DEER's is compression ratio relative to L, such that DEER generates sequence of length aL. Then, we define & as the number of answer induction triggers within these aL tokens of reasoning and the average length generated per answer induction, which is typically small constant. Dur- ing transformer inference, the primary computational overhead stems from attention calculations, which constitutes main focus. Assuming the generation process employs key-value caching technology, each new token only needs to compute attention with the cached key-value pairs.
H.1 COMPUTATIONAL COST ANALYSIS ON TIME
For the original CoT method, the computational cost is:
T = 0(1) + 0 +
(58)
For our DEER, The computational cost comprises two components: al forward passes in the main reasoning chain and km forward passes for answer inducing.
First, we calculate the cost of the main reasoning chain:
aL
al(aa++)) =0 1) (a²
T main Σ t=
(59)
Next, for the computational overhead during answer inducing, we first calculate the time cost of single inducing. Suppose the j-th answer inducing is triggered at position Pj. yielding cost of:
m(m - -1)
Ssingle Σ (ps 1) PS
Σ ii ( Pj
(60)
2
Assuming the inducing positions Py are uniformly distributed over the interval [0, aL), the average inducing position is Elpy] xe aL Hence, the total cost of answer inducing is:
aL + m(m - 1) O(k aL) + O m²)
Cinduce se k
(61)
2
2
Even in the worst-case scenario where most trigger points pN cluster near the end of reasoning, the average inducing position is Elpy] = aL. The total cost of answer inducing is:
m(m
Cinduce aL+ +
O(k aL) O(k m²)
(62)
As the length each answer inducing m is negligible compared to the reasoning length L, we have:
Cinduce Fs O(k: m aL)
(63)
Finally, the total cost of DEER is:
CDBER
Cmain + Cinduce = 0(a2 + O(k ab)
(64)
DEER reduces the quadratic term from O(L2) to L() while only introducing a linear term O m LL). Since m < L in long chain-of-thonn th-tuuughtt reasoning, the savings from the quadratic term reduction far exceed the overhead of the additional linear term. This analysis effectively explains superlinear speedup phenomenon observed Section 4.4
H.2 COMPUTATIONAL COST ANALYSIS ON MEMORY
The memory overhead analysis can be decomposed into two components: primary memory con- sumption from the KV cache and additional overhead from parallel decoding operations.
26

---

Published as a conference paper at ICLR 2026
Peak Memory Reduction. The dominant memory overhead in modern LLM inference stems from the storage of attention keys and values the KV cache, whose size scales linearly with the pro- cessed sequence length. Standard Chain-of- Thouuhh (CoT) approaches necessitate maintaining KV cache for all tokens, resulting in memory complexity of (T.). Through early termination at po- sition o where < 1, DEER effectively reduces the peak sequence length during inference from L to aL. Consequently, the peak KV cache memory consumption is reduced from (L) to O(a)).
This memory reduction proves partieularly valuable when processing long-context reasoning tasks. Beyond reducing peak memory requirements for individual requests, this approach enables systems accommodate increased concurrent requests under identical memory constraints during batch processing, thereby enhancing overall throughput.
Additional Overhead for Parallel Decoding. The proposed parallel decoding variant, which per- forms answer induction forward passes concurrently with main reasoning, introduces minimal addi- tional memory overhead. This efficiency is achieved through prefix caching and sharing mechanisms implemented in modern inference frameworks such vLLM. When multiple reasoning branches share a common prefix sequence, the corresponding portions of their KV caches require only single storage in physical memory through technologies such as vLLM's PagedAttention.
During parallel decoding, the answer induction branch incurs virtually no additional KV cache over- head, as fully leverages the KV cache already computed by the main reasoning branch. The only marginal additional memory requirement arises from storing limited number of tokens represent- ing the answer induction branch's 's decoding state.
For code generation tasks, our implementation incorporates specific optimizations whereby only the initial tokens are generated for confidence estimation. This design choice represents an imple- mentation detail rather than a methodological contribution. Experimental validation confirms that utilizing partial answer tokens for carly-cxit confidence calculation remains effective for coding tasks.
I INVESTIGATION OF REASONING TRANSITION MONITORS
In Section 3 of the main text, experiments reveal that the choice of Reasoning Transition Monitor exerts subtle effects on DEER, primarily manifested in how the number of potential early- exit opportunities affects the final generation length. In this section, we investigate the underlying connections between linguistic marker-based and entropy-based monitoring approaches.
Table 10 presents comparative analysis of average token entropy between linguistic markers and other tokens across multiple datasets and models. Our findings reveal that linguistic markers exhibit significantly higher entropy compared other tokens, suggesting that the linguistic marker-based approach inherently targets high-entropy positions where multiple candidate actions exist.
Additionally, we compute cosine similarity scores between consecutive tokens in the final layer's hidden state representations, comparing linguistic markers with their adjacent tokens against reg- ular token pairs. The similarity metric serves as an indicator of the model's reasoning coherence: high similarity reflects continuous, coherent reasoning processes, whereas low similarity signals the occurrence of reasoning transitions. The results presented Table TT demonstrate that linguis- tic markers exhibit substantially lower similarity scores, indicating disruptions in representational continuity.
Collectively, these experiments provide compelling evidence that large reasoning language mod- els do not undergo uncertain states silently; instead, they explicitly express uncertainty through language. The external linguistic markers leveraged by DEER constitute direct manifestations of internal state transitions, thereby providing strong empirical support for the theoretical foundations of our approach.
27

---

Published as a conference paper at ICLR 2026
Accuracy of Vanilla COT
Accurscy of BEER (Ours)
Generation Length of Vanile COT
Generation Length DEER (Ours)
Acurao 560
Vanile 2144 DEEB: 9L.0 54.
Average: MCMe500
52.9
4122
5215.0
WATH 500
4661
100 Averoge:
Visillu 6032 BEER elag
JRM 2004
76.7
323302
2014
5214
20/77
1343.
00
2008
1.78
1.78
128
1.38
1.70
40
140
(b) Experimental
models.
Figure 10: Experimental results of DEER compared to Vanilla CoT across Qwen3-Serie models of varying sizes on MATH-500 and AIME 2024.
OlympiadBench
AIME24
Qwen3-328
30
441
19
Qwen3-148
37
54
401
19
Qwen3-88
36
52
369
R1-Distill-78
28
69
286
DETE Bl Voelll coT
bECA Vevils CoT
XEER 6 Vovila CoT
BEER X Voniie CoT
Figure 11: More detailed experimental results of DEER compared to Vanilla CoT. v denotes correct answer, and denotes an incorrect answer.
J INVESTIGATION INTO THE REASONS BEHIND DEER'S THRESHOLD ROBUSTNESS
In Section 4.3 of the main text, demonstrate DEER's robustness the threshold À through experiments across various models and datasets. In this section, we investigate the underlying source of this robustness. We analyze the confidence scores of induced answers at all potential exit positions across three models on three mathematical reasoning datasets, calculating the proportion of scores falling within three distinet intervals. Specifically, 0-0.9 represents the low-confidence interval, 0.97-1.0 represents the high-confidence interval, and 0.9-0.97 constitutes the error-prone gray zone.
The results presented in Table T2 reveal that the model's confidence distribution exhibits a pro- nounced polarization phenomenon. The vast majority of cases concentrate at either the highly confi- dent or insufficiently confident extremes, with minimal presence in the intermediate range (the error- prone gray zone). When method induces the model to generate final answers, the confidence scores follow a distinctive U-shaped distribution, with remarkably low probability mass between 0.9 and 0.97. This phenomenon indicates that when the model possesses sufficient certainty about an answer based on its preceding reasoning chain, it generates the answer with exceptionally high probability (typically exceeding 0.99). Conversely, when uncertainty exists, the assigned probability drops substantially.
Furthermore, we observe that all three models exhibit higher proportions of high-confidence scores compared to low-confidence scores on simpler problems (GSM8K); While on more challenging problems (AIME24), the proportion of low-confidence scores exceeds that of high-confidence scores. This observation further validates the rationality of the DEER method: the confidence assigned to trial answers accurately reflects whether the existing reasoning sufficient to solve the problem. Consequently, confidence scores are generally lower on difficult problems, leading to many failed early-exit attempts in the initial stages. This pattern also explains DEER's s varying performance across different problem difficulties.. On simpler problems, the model demonstrates sufficient confidence, resulting better compression effects. On challenging problems, the model becomes more cautious, yielding weaker compression but maintaining satisfactory accuracy. This adaptive behavior shows that DEER naturally balances computational efficiency and solution quality based problem complexity.
28

---

Published as a conference paper at ICLR 2026
Table Comparison of Vanilla, DEER, and DEER-PRo across multiple models and datasets. Acc accuracy (%), Len average tokens, CR compression ratio.
GSMSK
MATH
AMC
AIME
GPQA
Overall
Method
Ace
Len
CR
Acc
Len
CR
Acc
Len
CR
Acc
Len
CR
Acc
Len
CR
Acc
CR
DeepSeek-RIIDDE RI-Distill-l Ri--iiiiil---een--555
Owen--.BennBB
Vauilla
76.1 1,617
100%
69.0
6,018
100%
52.5
8,819
100%
23.3
13,702
100%
7.1
13,029
100%
45.6
100%
DEER
74.7 984
60.9%
67.8 2,497
41.3%
6000
5,496
32.3%
23.3
9,557
69.7%
12.1
5,762
44.2%
47.6
55.7%
DEER-PRo
77.3 1,062
65.7%
70.0
2,891
48.0%
62.5
5,701
64.6%
26.7
10,390
75.8%
14.5
6,820
52.3%
50.2
61.3%
Qwen3-4B
Vanilla
94.1
2.175
100%
92.2 4,767
100%
87.5
7,443
100%
63.3
11.916
100%
46.5
9,294
100%
76.7
100%
DEER
94.5
1,250
57.5%
92.6
3,214
67.4%
87.5
4,906
65.9%
63.3
9,327
78.3%
47.5
3,275
35.2%
77.1
60.9%
DEER-PRo
94,5
1,301
59.8%
93.0
3,517
73.8%
92.5
5,153
69.2%
65.0
9,651
81.0%
49.2
3,750
40,3%
78.8
64.8%
Qwen3-1.7B
Vanilla
90.1
2,045
100%
85.6
5,160
100%
70.0 8.637
100%
30.0
13.758
100%
35.9
9.271
100%
62.3 100%
DEER
90.3
1,066
52.1%
85.6 2,463
77.7%
70.0
4,673
54. 1%
30.0
7,943
57.7%
43.
3,549
38.3%
63.9
50.0%
DEER-PRo 1,261
61.7%
87.2 2,702
52.4%
75.0 5,143
59.5% 35.0 8,644
62.8%
3,960
42.7%
66.5 55.8%
Table 3: Experimental results on programming tasks, Acc = accuracy (%), Tok. average tokens,
CR compression ratio.
HumanEval Tok.
BigCodeBench
LiveCodeBench
Overall
Model
Method
Acc
CR
Acc
Tok.
CR
Acc
Tok.
CR
Acc
CR
RI-Distill- Series
Vanilla
91.5
3,861
100%
44.5
5,459
100%
56.0
9,109
100%
64.0
100%
32B
DEER
93.9
1,254
32.5%
46.1
1,929
35.3%
56.6
3,677
40.4%
65.5
36.1 %
Vanilla
89.0
4,039
100%
40.9
4,806
100%
52.7
9,259
100%
60.9
100%
14B
DEER
90.9
1,000
24.8%
40.7
1,583
32.9%
52.1
4,000
43.2%
61.2
33.6%
Vanilla
78.6
5,666
100%
26.1
8,516
100%
38.4
10,482
100%
47.7
100%
7B
DEER
78.6
913
16.1% %
25.2
1,605
18.8%
40.3
2,582
24.6%
48.0
19.9%
Qwen3 Series
Vanilla
93.3
3,277
100%
44.6
5,072
100%
73.4
8,203
100%
70.4
100%
14B
DEER
93.9
1,118
34.1% 1%
44.3
792
15.6%
74.1
5,437
66.3%
70.8
38.7
Vanilla
85.4
3,904
100%
37.9
6,994
100%
64.7
8,871
100%
62.7
100%
8B
DEER
87.8
793
20.3%
41.1
608
8.7%
65.1
4,257
48.0%
64.7
25.7%
Vanilla
91.5
3,768
100%
36.1
7,804
100%
64.7
8,789
100%
64.1
100%
4B
DEER
92.7
1,050
27.9%
37.1
826
10.6%
63.5
5,626
64.0%
64.4
34.2%
Vanilla
83.5
3,580
100%
25.7
6,151
100%
51.7
9,447
100%
53.6
100%
1.7B
DEER
84.1
2,236
62.5%
28.3
2,104
34.2%
51.4
8,425
89.2%
54.6
62.0%
K
MORE EXPERIMENTAL RESULTS
More experiments across Model Sizes on Qwen3. across model sizes and reasoning difficulty in Fig. 10 consistent with the findings presented in Section
The performance of the Qwen3-series models
Performance on SoTA Reasoning Models.
We evaluated DEER's 's effectiveness on two state- of-the-art reasoning models: Qwen3-32B (rep- resenting dense models) and Deepseek-RI 671B (representing MoE models). To fully leverage their reasoning capabilities, we set their maxi- mum sequence lengths to the officially recom- mended 32k and 16k, respectively. The impact of max length will be further discussed in the next section. Due to computational constraints, we im- plemented a quantized version of Deepseek-RI based on KTransformers (kveache ail 2025). Fig. 12 provides close look DEER's performance two challenging datasets, AIME and MATH.
Accurscy of Vonille COT
Generation Length of Vanille COT
Accurocy BEER (Ound)
Goneration Length of DEBR (Ours)
11511
6586-0
7223
CONEE ME Accu Aecurao
5054D
Figure 12: Performance on SoTA models.
29

---

Published as a conference paper at ICLR 2026
Table 4: Additional threshold sensitivity experiments across more models and tasks.
Qwen3-14B
GSM8K
MATH
AMC
Vanilla
95.1
93.8
95.0
0.80
96.0
93.8
93.8
0.85
95.7
94.4
93.8
0.90
96.1
93.8
95.0
0.95
96.0
94.0
95.6
0.97
95.7
93.8
94.4
Qwen3-8B
GSM8K
MATH
AMC
Vanilla
94.9
91.2
87.5
0.80
95.2
91.4
88.8
0.85
94.9
92.0
90.0
0.90
95.5
92.8
91.3
0.95
95.3
93.2
92.5
0.97
95.3
93.0
92.5
The results show that DEER maintains competitive aceuracy (with R1 making only additional егror on each dataset) while significantly reducing sequence length by 10.4% 35.7%.
Performance Trends across More Model Sizes and Benehmarks. To provide more compre- hensive demonstration of DEER's effectiveness and facilitate comparison for researchers, we present experimental results on seven reasoning benchmarks and eleven large reasoning language models. Fig. 13 compares the experimental results between DEER and vanilla CoT, demonstrating that the conclusions drawn the main text of the paper hold consistently across more benchmarks and additional models.
In addition to popular reasoning models, we also evaluate DEER on less commonly used models. -ee.---tttoo--aaaa Nano-8B-vl consistently exhibits low
mentioned in the Limitations section, confidence in generating intermediate answers, resulting in a significantly lower early stopping rate during evaluation compared mainstream models (Qwen3-8B: 80%, RI R1-Distill--wen--75 85%, Llama-3. Mamnotron-Nano-8... 55%). Consequently, as shown in Table 5, the improvement is limited. Nevertheless, DEER still effectively mitigates overthinking in this model, as evidenced by its ability to prevent subsequent reasoning steps from altering correct answers into incorrect through early stopping.
in reasoning efficiency for Llama-3. Neemotron-Nano-ST.
Performance with Different Decoding Configurations. As the configuration of DeepSeek-Ri. Distill-Series models recommends maximum length of 16k (16,384), we evaluate Qwen3-14B under the same setting in the main experiments to maintain setup consistency. In practice, this length sufficient for most real-world applications. In addition, to ensure experimental stability and reproducibility, we employ greedy decoding in the main experiments. Nevertheless, provide more comprehensive assessment of DEER's performance. we further conduct experiments on larger variants of the Qwen3-series models (8B, 14B, 32B) using the officially recommended decoding strategy (max len 32768, top 0.95, temperature = 0.6). Fig. g shows that DEER remains significantly effective under these configurations, demonstrating the robustness of approach.
Performance with Different Multi-Token Confidence Averaging Methods. In the main text, mentioned adopting the geometric mean strategy for calculating multi-token answer confidence scores. as it better aligns with the multiplicative nature of joint probability computation in language models and exhibits higher sensitivity to low probability values. this section, we supplement our analysis with comparative experiments using arithmetic mean calculation (DEER-AM), employing the same early-exit threshold of 0.95. The results in Table demonstrate that DEER-AM exhibits significant decrease in accuracy compared to DEER-GM, while achieving marginal improvements in compression ratio. This indicates that the arithmetic mean dilutes the contribution of low-valued tokens, resulting in overall inflated confidence scores and consequently leading to premature in- correct exits. Therefore, we recommend using the geometric mean for estimating true confidence scores.
30

---

Published as a conference paper at ICLR 2026
with different reasoning transi- tion monitors. DEER(W) denotes transition via Wait, DEER(A) via Altenatively, and (EER(Ent) via entropy threshold. Chunk Size denotes the length (token numbers) of one reasoning chunk (thought), and Chunk Num denotes the number of reasoning chunks.
Table 5: Results on MATH-500 PrepsSek-RI-Distill-Pee
Method
Accuracy
Tokens
Chunk Size
Chunk Num
Exit Ratio
Exit Acc.
Vanilla
88.6
3815
DEER(W)
89.6.1.0
2572.32.6%
259.5
14.7
87.6%
93.4%
DEER(A)
90.8,2.
2775.27.3%
719.8
5.3
54.8%
91.2%
DEER(Ent)
90.2.
2339
38.7%
183.7
20.8
90.2%
93.0%
Table 6: Comparison of Vanilla, DEER-W, and DEER-Ent across multiple models and datasets. Acc accuracy (%), Len average tokens, CR compression ratio.
GSM8K
MATH
AIME
GPQA
Overall
Method
Acc
Len
CR
Ace
Len
CR
Acc
Lem
CR
Ace
Len
CR
Acc
1.en
CR
Acc
CR
DeepSeek- SeepSeek-RI-Diiee RRI-Distill-wenns
Vanilla
89.6
1,484
100% 87.4 3,888
100%
78.8 6.792
100%
41.7
13,765
100%
23.7
10.247
100%
64.2
100%
DEER W 90.6 917 61.8%
89.8 2,143
55.5%
85.0 4,451
65.5%
49.2
9,839
71.5%
31.3
5,469
53.4%
69.2
61.5%
DEER Ent 90.8 876
39.0%
89.2 2,261
58.6%
85.0
4,072
60.0%
48.4
8,961
65. 15:
29.6
5,037
49.2%
68.6
58.4%
Qwen3-14B
Vanilla
95.1
2,047
100%
93.8 4.508
100%
95.0 7.139
100%
70.0
10,859
100%
60.1
7,339
100%
82.8
100%
DEER 95.3
840
41.0%
94.0
3,074
68.2%
95.0
4.763
66.7%
76.7
7,619
70.2%
57.6
2,898
39.5%
83.7
57.1%
DEER-FM Ent 96.1
803
39.2%
93.8
2,979
66.
1%
93.3
4,903
68.7%
73.3
7,128
65.6%)
58.1
2,818
38.4%
82,9
55.6%
Qwen3-8B
Vanilla
94.9
2,245
100%
91.2 5,216
100%
87.5 7,986
100%
65.0
12,110
100%
51.5
9,145
100%
78.0
100%
DEER 95.2
1,071
47.7%
92.6
2.732
52.4%
92.5
4,392
55.0%
61.7
8.796
72.6%
52.5
3,111
34.0%
78.9
52.3%
DEER-Ent 95.8 1,037
46.2%
93.6
2,789
53.5%
91.3 4,003
50.1%
63.3
8,328
68 8%
51.5
3,248
35.5%
79.1
50.8%
Error Bars with 95% Confidence Intervals. To demonstrate the statistical significance of DEER's accuracy gains, we conducted multiple experimental runs on two models and calculated emor bars with 95% confidence intervals. Specifically, we performed four independent runs on GSM8K, MATH, and GPQA benchmarks. Given the limited sample sizes of AMC23 and AIME24, increased the number of experimental repetitions to eight for these datasets. The results pre- sented in Table confirm that the accuracy improvements achieved by our method are statistically significant.
L CASE STUDY DETAILS
In Fig. 13 we provide examples of results MATH-500 visually demonstrate the effectiveness of DEER. The design of DEER ensures that it follows the same reasoning process as the vanilla CoT method before early exiting. Both methods arrive at the correct answer during the first reasoning step, as shown in the green box. The difference lies in the fact that our method exits early after evaluating the confidence of the trial answer as sufficiently high, thus producing the correct result. In contrast, the vanilla CoT method proceeds to the next reasoning action. After double chubleecheeking and switching reasoning approaches, the model becomes trapped in an endless cycle of verification due to inconsistent answers from the two approaches, ultimately failing to provide a final answer. In addition, Fig. 14 15 16 provides additional generated examples to more comprehensively demon- strate the effectiveness of DEER's 's carly-exit mechanism and illustrate the underlying mechanisms of the approach.
Figure 17 shows the detailed process of DEER applied on mathematical example. It can be ob- served that, at each reasoning switch point ("Wait" token), DEER generates a trial answer and evaluates its confidence. The change in confidence is consistent with the reliability of the current reasoning chunks and trial answers. This shows that LRMs implicitly know when to leave early, and method is simple and effective to realize such potential of the model itself.
31

---

Published as a conference paper at ICLR 2026
Table 7: Comparison of Vanilla, DEER-GM (Geometric Mean), and DEER-AM (Arithmetic Mean) across multiple models and datasets. Acc accuracy (%), Len = average tokens, CR compression ratio.
GSM8K
MATH
AMC
AIME
GPQA
Overall
Method
CR
Ace
Len
CR
Acc
Len
CR
Len
CR
Len
CR
Ace
CR
Vanilla
89.6
1,484
100% 87.4
3,858 100%
78.8
6.792
100%
41.7
13,765
100%
23.7
10.247
100%
64.2
100%
DEER GM 90.6 917
61.8%
89.8 2,143
55.5%
85.0
4,451
65.5%
49.2
9,839
71.5%
31.3
5,469
53.4%
69.2
61.5%
DEER-AM 90.2
832
56.1%
88.2 1,879
48.7%
80.0
3,872
57.0%
43.3
8.095
58.8%
22.6
4,116
40.2%
64.9
52.2%
Qwen3-14B
Vanilla
95.1
2,047
100%
93.8 4,508 100%
95.0
7.139
100%
70.0
10,859
100%
60.1
7.339
100%
82.8
100%
DEER-GM 95.3 840
41.0%
94.0
3,074
68.2%
95.0
4.763
66.7%
76.7
7,619
70.2%
57.6
2,898
39.5%
83.7
57.1%
DEER-AM 95.3
39.6%
92.4
2,620
58.1%
90.0
4,513
63.2%
6,933
63.8%
2,508
34.2%
78,9
51.8%
Qwen3-8B
Vanilla
94.9 2,245
100%
91.2 5,216
100%
87.5 7,986
100%
65.0
12,110
100%
51.5
9,145
100%
78.0
100%
DEER-GM 95.2 1,011
47.7%
92.6
2.732
52.4%
92.5
4,392
55.0%
8.796
72.6%
52.5
3,111
34.0%
78.9
52.3%
DEER AM 94.9
972
43.3%
92.0
2,522
48.4%
87.5
3,899
48.8%
56.7
7.697
63.6%
49.7
2,950
32.3%
76.2
47.3%
M RELATED WORK DETAILS
The advent of Open-Al ol (OpenAl 2025) established test-time scaling (Snell et al.) 2024)
pivotal research direction in the LLM community. This approach enhances LLMs" slow think- ing capabilities, enabling breakthroughs in complex problem solving. The recent open-sourcing of DeepSeek-RI (DeepSeek-Al et al. 2025) has further intensified interest in locally deployed reason- ing models. However, two critical challenges have emerged: 1) excessively long CoT generated significantly degrades inference efficiency, and 2) growing empirical evidence (Chen et al. [0256] Team al. (2025)) reveals their susceptibility to overthinking tinue reasoning beyond the point of optimal output. /Zhang et al.] (2025c) introduces a novel bench- mark named SI-Bench test the performance of LRMs on simple tasks, evaluating the overthinking issues of these LRMs. Following the taxonomy of efficient reasoning established in (Sui et al., 2025 Wang et al. 2025a). we categorize related work into three classes: post-traning based, prompt-baseee and output-based based efficient reasoning methods.
phenomenon where models con-
Post-training based efficient reasoning methods use supervised tin-ttnnigg Yu ct al. 2024 Kang
et al.
2025; Xia et al.. 2025 Ma et al.
2025b) Munkhbat et al., (025 Zhuu et al. 2025: Liu et al.)
2024
Han et al. 20244] Qiao et al.
2025
Yu et al. (025) with variable-length CoT data or incor-
porate length rewards (Team et al.
2025b
Luo et al. 2025a Aggarwal & Welleck 2025 Arora &
Zanette 2025 Yeo et al. [025 Shen et al. 2025b Qu et al. 2025| Cui et al. 2025 Dai et al. 2025
Liu et al., 2025a Tu et al. 22255 Wang et al. 2025c Dumitru et al. 2025
Li et al. 2025a Jiang
et al. 2025a] Zhang et al. 2025b) in reinforcement learning to enable the model to adaptively gen- erate chains of thought of different lengths. However, these methods often require large amount of computational resources and face challenges in dataset construction. Recently, some work (Hao
2024 Shen al. 2025c Cheng & Van Durme 2024 Dang et al. 2025 (Shen et al.) 2025a Su et al.
al.
2025 Tan et al. 2025; Saunshi et al.) (025) Zhang et al. 2025d) has shown that using latent representations to replace explicit textual reasoning steps allows reasoning models be more effi- cient. However, such methods often require extensive-epoch SFT on carefully curated datasets Hao
ct al.
2024 Xu et al. 2025d), leading to overfitting on the output format and consequently compro- mising the model's 's inherent expressiveness and generalization ability.
Prompt-based efficient reasoning methods (Han et al. 2024, Xu al. 2025b Lee et al. 2025
Renze & Guven, 2024: Chen et al.) 2024) use varying prompts to enforce reasoning models to generate concise CoT with less unnecessary reasoning steps. Especially, (Aytes et al. 2025 Chuang et al. 2024 2025 Ong et al.) assign different prompts to queries based on their difficulty, thereby adjusting the length of the CoT generated by reasoning models. We also explored the performance of method combined with prompt design in Tab. demonstrating further reductions in the length of reasoning chains while maintaining considerable accuracy.
Most of the Output-based efficient reasoning methods focus on optimizing the best-of-N sampling for LLMs, such as pruning low-quality samples (Xie et al., 2023: [iao et al.) (225) and implement-
ing early stopping (Li al. 2024 Manvi et al. 2024 Aggarwal et al. 2023) when multiple samples
32

---

Published as a conference paper at ICLR 2026
Table 8: Experimental results on the Qwen3-series models under the officially recommended set- tings (max = 32768, top-p = 0.95, temperature = 0.6).
GSMSK
MATH-500 AMC23 Tok.
AIME24 Tok.
AIME25
OlympiadB
Overall
Budget
Method
Acc
Tok.
Ace
Tok.
Ace
Acc
Acc
Tok.
Acc
Tok.
Acc
CR
Qwen3-8B
Vanilla
95.7
2246
93.8
5368
93.8
9424
70.0
16717
65.0
17880
67.9
11025
81.0
100%
32k
DEER
95.5
981
94.0
3227
95.0
5898
75.8
12465
63.3
15135
67.0
9075
81.8
68.0%
Qwen3-14B
Vanilla
95.7
1699
94.8
4800
95.0
6837
75.0
14347
76.7
16437
68.7
9992
84.3
100%
32k
DEER
95.8
933
95.0
3301
96.3
6299
74.2
10896
76.7
15014
68.9
8263
84.5
77.6%
Qwen3-32B
Vanilla
96.0
1714
95.8
4609
98.8
7209
83.3
12874
78.3
15292
69.3
9775
86.9
100%
32k
DEER
95.8
992
95.4
3325
98.8 5617 84,2
11531
78.3 13981
69.8
8671
87.1
79.6% %
Table 9: Accuracy performance on reasoning benchmarks with 95% confidence intervals.
Model
GSM8K
MATH
AMC23
AIME24
GPQA
Vanilla (ds-7B)
0.897 [0.891, o 902] 0.877 [0.869, 0.884]
0.794 [0. 707767, 0.821]
0.425 [0.400, 0.449]
0.247 [0.203, 0.29
DEER (ds-7B)
0.904 [0.89, 0.912]
0.897 [0.883, 0.911]
0.856 (0.835, 0.878)
0.492 [0.463, 0.520)
0.299 [0.257. 0,341]
Vanilla (Qwen3-14B)
0.948 (0.942, 0.955]
0.938 (0.932, 0.943]
0.938 [0.918, 0.957]
0.708 [0.660, 0.757]
0.596 [0.571, 0.621]
DEER (Qwen3-14B) 0.955 [0.949, 0.962] 0.942 (0.936, 0.948] 0.953 [0.940, 0.967] 0.754 [0.718, 0.791] 0.587 [0.566, 0.608]
achieve self-consistency. However, following the introduction of advanced reasoning models like R1, there is less reliance on best-of-N sampling methods, as these models exhibit strong reason- ing capabilities independently. Very recently, two concurrent works share similar motivations with ours. Zhang et al. (2025a) also proposes to terminate early based on trial answers, but requires an additional probe model to determine the correctness. They focus on enhancing the verification capa- bilities of the probe model, whereas our method explore how to enable the model to oof-dettrmmiee when exit early and integrate seamlessly into existing reasoning logic. MM et al. (2025a) prompts reasoning models to directly output final answers during decoding, but only achieves better per- formance in the low-budget regime or being adapted to best-of-N methods compared to baselines, which limits the applicability and generalization. [Song et al. (2025) periodically compresses the KV cache by retaining KV cache that receive high importance score to accelerates inference by leverag- ing the semantic sparsity of reasoning paths. Diang et al. (2025)) uses teacher model to perform skill-aware step decomposition and content pruning, and then distills the pruned reasoning paths into student model. |Huang et al. (2025) projects the steering direction onto the low-dimensional activation manifold and intervenes the activations to reduce thinking tokens.
N USE OF LLMS
In the preparation of this manuscript, Large Language Models (LLMs) were employed as auxiliary tools for Language Polishing. During the final stages of manuscript preparation, L.MSs were uti- lized to refine the language of selected passages, including grammar checking, sentence structure optimization, and expression standardization. This process was limited to linguistic improvements and did not involve the generation or modification of any substantive academic content, including research insights, data analysis, or conclusion derivation. It should be emphasized that all core argu- ments, research methodologies, experimental designs, data analyses, and conclusions presented in this paper were independently developed by the authors. LLMs served solely as language processing aids, and the authors assume full academic responsibility for all content.
33

---

Published as a conference paper at ICLR 2026
Table 10: Token Entropy for Linguistic Markers and Other Tokens.
Qwen3-8B Linguistic Markers Other Tokens
gsm8k 0.901
0.438
math 1.058
0.385
gpqa
1 1.269
0.500
DS-7B
Linguistic Markers
Other Tokens
gsm8k
1.550
0.658
math
1.753
0.565
gpqa
1.241
0.510
Table 11: Hidden States Cosine Similarity between Linguistic Markers and Other Tokens.
Qwen3-8B Linguistic Markers
Other Tokens
gsm8k 0.262
0.543
math
0.237
0,493
gpqa
0.240
0.509
DS-7B Linguistic Markers
Other Tokens
gsm8k
0.306
0.608
math
0.247
0.530
gpqa
0.231
0.505
Table 12: Confidence interval distribution (%) across tasks for different models.
Qwen3-14B
0-0.9
0.9-0.97
0.97-1.0
gsm8k
38.92
5.95
$5.06
math
49.53
4.83
45.46
aime
77.20
2.45
20.35
Qwen3-8B
0-0.9
0.9-0.97
0.97-1.0
gsm8k
35.31
5.34
$9.12
math
45.27
4.58
49.98
aime
78.61
2.39
19.00
DS-7B
0-0.9
0.9-0.97
0.97-1.0
gsm8k
26.54
5.29
68.17
math
34.09
5.46
60.45
aime
80.90
1.41
17.69
34

---

Published as a conference paper at ICLR 2026
Table 13: Experimental results on more types of reasoning models and reasoning benchmarks. "Ace" denotes accuracy, "Tok" denotes token count, and "CR" denotes compression rate. 1 indicates that higher values are better, while y indicates that lower values are better. The best results are highlighted in bold.
CR.
100%
72.4%
100%
71.9%
100%
61.1 1.11%
100%
56.6%
100%
71.9%
100%
65.0%
100%
62.3
100%
68.5%
100%
58.6%
100%
84.0%
100%
88.55
Overall
Acct
69.0
73.2
65.4
69.3
56.5
62.2
38.5
40.0
78.9
80.6
77.1
79.0
71.9
73.8
70.2
72.2
55.8
58.4
75.0
76.5
65.5
69.0
|
CR.
100%
68 8%
100%
72.1%
100%
53.4%
100%
44.2%
100%
60.5%
100%
39.5%
100%
34.0%
100%
35.4%
100%
38. 3%
100%
84.2%
100%
93.8%
SCIENCE GPQA-D
Tok.
7,181
4,943
6,731
4,856
10,247
5,469
13,029
5,762
6,893
4,167
7.339
2,898
9,145
3,111
9.294
3,275
9,271
3,549
7,320
6,163
8,074
7.576
Accf
56.1
64.1
52.0
56.6
23.7
31.3
7.1
12.1
65.2
64,7
57.6
51.5
52.5
46.5
47.5
35.9
43.4
63.1
64,1
41.9
47.5
CR.
100%
73.0%
100%
72.5%
100%
63.3%
100%
53.2%
100%
80.696
100%
81.2%
100%
78.8%
100%
83.2%
100%
76.9%
100%
89, .9
100%
87.5%
Olympiad
Tok.
7,334
5,351
7,908
5,736
8,563
5,420
11,200
5,960
6,438
5,189
8,692
7,060
9,487
7,479
9,098
7.569
9,437
7,257
8.546
7,639
7,321
6,407
Acct
55.7
57.8
$2.6
$5.0
47.3
52.6
28.0
32.0
63.4
67.9
62.5
67.4
59.3
62.4
59.3
64,7
52.2
52.6
63.2
65.2
54.3
60.7
CR.
100%
80.5%
100%
82.3%
100%
56.8%
100%
64.2%
100%
87.5%
100%
90.6%
100%
95.3%
100%
91. 91.8%
100%
83.0%
100%
94.3%
100%
89.6%
AIME25
Tok.
11,075
8,913
12,304
10,125
12,767
7.257
14,450
9,281
12,446
10,893
12,286
11,135
12,835
12,229
13,112
12,039
13,943
11,579
12,300
11,598
13,192
11,820
Acct
43.3
46.7
36.7
36.7
26.7%
36.7
13.3
10.0
65.0
66.7
63.3
66.7
54.2
60.0
48.4
55.0
26.7
36.7
46.7
50.0
35.0
36.7
CR.
100%
72.1%
100%
72.4%
100%
71.5%
100%
69.7%
100%
76.3%
100%
70.2%
100%
72.6%
100%
78.3%
100%
57.7%
100%
93.3%
100%
90.6%
AIME24
Tok.
10.293
7,424
11,211
8,115
13,765
9,839
13,702
9,557
11.374
8,682
10,859
7,619
12,110
8,796
11.916
9.327
13,758
7,943
10,821
10,097
10,821
9,755
MATH
Acct
56.7
63.3
31.7
68.4
41.7
49.2
23.3
23.3
73.3
76.7
70.0
76.7
65.0
61.7
63.3
63.3
30.0
30.0
66.7
70.0
56.7
66.7
CR
100%
9%
100%
64.88 4.
100%
65.5%
100%
62.3%
100%
65.4%
100%
66.7%
100%
55.0%
100%
65.9%
100%
54.1 1%
100%
85.1% 1%
100%
87.9%
AMC23
Tok.
5,354
4,252
6,545
4,240
6,792
4,451
8,819
5,496
7.627
5,753
7.139
4,763
7,986
4,392
7,443
4,906
8.67
4,673
6,792
5,782
6,153
5,408
Acct
87.5
95
82.5
85.0
78.8
85.0
52.5
60.0
95.0
97.5
95.0
95.0
87.5
92.5
87.5
87.5
70.0
70.0
92.5
95.0
90.0
90.0
CR.
1005E
9%
100%
67.5%
100%
55.5%
100%:
41.5%
100%
77.0%
100%
68.2%
100%
52.4%
100%
67.4%
100%
47.7%
100%
73.6%
100%
78.9%
MATH-500
Acct Tok.
3,736
2,425
3,815
2,577
3,858
2,143
6,018
2,497
4,440
3,418
4,508
3,074
5,216
2,732
4,767
3,214
5,160
2,463
4,508
3,316
3,794
2,995
89.2
90.4
88.6
89.8
87.4
89.8
69.0
67.8
94.4
94.2
93.8
94.0
91.2
92.6
92.2
92.6
85.6
85.6
93.8
94,6
91.2
91.4
Seep Sibee--R-Disill--One DirtT--Drlll--een--22 Qweit--wen-222
DeepSeek- ME-K--R--Dssiil--- Qw-n---en--
Deep-Sek-- D----Diill--- Sis----illl--Qen----. Qwin-I-wnn--.
CR.
100%
68. 16
100%
71.3%
Qwen-TR
100%
917 61.8%
100%
60.9%
100%
46.1%
100%
41.0%
100%
47.7%
100%
57.5%
100%
52.1%
100%
68.5%
LJamo-3.1-Neoon Wew.oroonn-anoo-BB-..
100%
91.0%
GSM8K
Seek-See--R--Diiee Cil-RR-Diisil-QQue
Acc? Tok.
1.202
819
1,458
1,040
1,484
1.617
984
1,668
769
2,047
840
2,245
1.071
2.175
1,250
2,045
1,066
1,427
977
1,618
1,473
Vanilla 94.3
95.1
Vonilla 93.9
DEER 93.3
Venilla 89.6
90.6
Vanilla 76.1
74.7
96.3
96.2
95.1
DEER 95.3
94.9
95.2
94.1
94.5
90.1
90.3
Vanilla 96.7
96.3
89.2
89.8
Owen3-32B
Owen3-14B
Qwen3-8B
Qwen3-4B
Owen3-1.7B
QwQ-32B
Llama-
Method
DEER
DEER
DEER
Venilla
DEER
Vonilla
Vanilla
DEER
Nenilla
DEER
Vanilla
DEER
DEER
Venilla
DEER
35

---

Published as a conference paper at ICLR 2026
Senate committee has 5 Democrats, Republicans, and Independent. In how many ways they sit around a circular table if all the members of each party all sit next to each other? (Two seatings are considered equivalent one is a rotation the other.) DEER
Question:
Answer:
Vanilla CoT
[Slow thinking]
[Slow thinking]
Okay, I have this problem about a Setate committee with 5 Democmes Republicams, Independent They need to sround circular table, all members figine many diffierant ways memions searings of the other. Hmms, skay, let me break this down.
luve this dhout Scrune with Demactuss 5 circuler table, the members each party have st next each other.
Republicass, Independent They
have
need lappen. probicms rotatin
Therefore, the total number of anungemens the number of ways arringe the blecks mullipiie by the namber of ways 5: 11 (120 1) 14400
the parele within cach
Finst, since it's a circeiar table, the number of arrangmmnns usullly less than striggtt line because rotrions considered same.
block. that would 35an8
Wast. hold on. is that all! Let me dmublo-checs So. we lave three blucks: D. R. I. Armnge them anound the ubll: (I-1)) 22 Then, within each block, arange the memberss 5: for D, for R. and I! for So. yes. 2 5! 11-2- 120 28500
So, let me think. There are three partic: Democras, Republicars, and Independemss Each party is group that needs to be seated together. So. incead of thinking of individaals can think of thece block:: D (Democrats), (Repullicams and (Iniqpendent) Ench block las be togethes, the problem reduces ananging these three blocks table
But wait, amother thought since talle cirodlrr does dinection mattor? Like, clockowise vs, coumertlacioive in circular permutations, samerites anargements that mee manee innges are coneilerod difficeat unice speciliie otherwise.
sumillaal-
So, for three blocks, it's 21 distinet arringements.
comined
Bul within each black, the mamiers can be amargee themsolves, For the Democrats, there Sauilurl, Republican they be ways. The Independent just one person, that bluck.
again thene another way appecach problem" Mayhe by considering the circulur amangemess linear arangement where fix one person's positon to eliminate rotational symmetry. somilteds
Iuu
amaged
51 only way amane
But since we've fiood the Democrats, the remaining sears in line, number
Therefore, the sotal number of amungement is the number ways to the blecks muliplial by the namber of ways the people within each block. So, that would 21 (5) * 11) 120 14400 28500.
Republicun black Indopendent Then,
(since
blucks:
Repubikcan bluck, they
can arrnged ways, independent
thinn
Early Exit!
So, the total number of arangemnnss would be (Gx the fivel Demarrad) 21 51 I1= 2 120 240
[Conclusion]
Wast, that's difforent
Himm, which
Senate commintee
partie:: Democrats (D), Republicans
Walt, actually if we
Demeeralss sent, wetee
fixing
(R), and Independent (T), Since they must together, treat each party as vingle Nock.
wont hut the entire block Demoertss. the number ways to amange
blocks 21 the R and 1), and withis euch block, it's S1 for and for So, 2! 5)* I!- 120 240 But that sceoe too low bucess exelier we hud 285000.
1. "*Ammninn the Bloock** Around circultr rable, the number of ways amange blocks 14(3-11
Wait, which approsch comeet" Let think.
2. ** Amanging waysia Republicans can amanged is (15t)) waysin- Indoperaleni is single persen, to there's 110 way.
Bi Democrats can amanged (istii
Repetition
Wait so which approach comeet! Les me think.
3. TTeal Arnangements" 11; Multiply the a snnggements the black by the arangements witl each block'aa Vilmes intims 5t tnimes Viinnc 120 litimes
-omineed
28, 0]
which approsch camont" Lat
"ssswee"* (ooood]288nng
[No Conclusion]
Token number: 870
Token number: 16384
Figure 13: Comparison of generated content samples between DEER and Vanilla CoT on MATH-
500. Both DEER and vanilla CoT arrive at the correct answer during the first reasoning step, as shown in the green box. The difference lies in the fact that DEER exits early after evaluating the confidence of the trial answer as sufficiently high, thus producing the correct result.
36

---

Published as a conference paper at ICLR 2026
Question:
The coordinates of parallelogram are (5, 3), (6. 8), (7, 4) and $(x, y)$ and $x 7$. What the value $x + y
Answer:
DEER
Vanilla CoT
Okay, so have this problem where need find the coordinates of the fourth vertex of parallelogram. The given points are (5, 3). (6, 8). (7, 4), and (x. y) with the Then, need find the value of Him,, let me think about how to approach this. remember that parallelogram, opposite sides equal and parallel. That means the midpoints of the diagonals should be the same, So, can find the midpoint of one diagonal, it should be equal the midpoint of the other
Okay, so have problem where need to coordinates of the fourth vertex of parallelogram. The given points are (5, 3). (6. 8), 17. 4), and ix, with the condition that x Then, need to
condition that
value Hmm, let me think about how to approach Anknfirt that parallelogram, opposite sides equal and parallel. That means the midpoints should be the same, So, if can find the midpoint of one diagonal, should
the diagonals
equal to the midpoint of the other
diagonal.vvynl.e me label the points to make clearer. Let's point A is (5, 3), point B is (6, 8), point Cis (7, 4) and figure out which points are connected to each other. Since it's a parallelogram, the order of the points matters think the points should be to and back A. I'm not entirely sure, so maybe should consider different possibilities.
diagonalArinle' me label the points to make it clearer, Let's say point A is (5, 3), point is (6, 8). point is (7, 4), and point (x. y). Now, need to figure out which points connected to each other. Since it's parallelogram, the order of the points matters. I think the points should be order, so
point DX yl.
connected order,
back to I'm not entirely sure, so maybe I should consider different possibilities.
to
<omitted>
Let try another approach.ym/nAnttte
property
Let me try another approach miinnnthhere property of parallelogram that the diagonals bisect each other. So, the midpoint of diagonal
parallelogram that the diagonals bisect each other. So, the midpoint of diagonal AC should be the same as the midpoint diagonal
should the same
midpoint of diagonal BDininnet me calculate the midpoint of AC first. Point A (5, and point is (7, 4). The midpoint
<omitted>
Midpoint ((S x\/2 (3 Wn/2iinnnMiippoi of BC: Point 8
formula ((x1 x2)/2, (y1 y21/2). So, midpoint AC ((5
72/2, + 4,/2) = (13/2, 12/2) (6.5. 6).nnnSetting midpoints equalAnin(S
a) paint
4. Midpoint
+ 71/2 (3 44/2) = (12/2, 7/2) (6. 3.5).
<omitted>
xx/2 6.5 and (3 yl/2 6.nnnnooiving the first equation:
Midpoint is ((5 + x1/2 (3 Wa2.-nnnMiddpoin BC: Point is 6) and point Cis (7, 4), Midpoint is (6 73/2. (8 4)/2)
(5 xl/2 6.5 =>
13 x 8.vninooovingg the
second equation: (3 yi/2 => 3 y 12 =>
(13/2, 12/2) (6.5, GAnnnStttiing midpoints equal/nVnn(5
9nnnnOkay, this gives
and y 9, which satisfies 17.
-x/2 6.5 and yw/2 = 6.vn\nnolvvng the first equation:
So, the fourth point is (8. 9), and x y
(5 + x)/2 6.5 => 5 ++x = 13 #> x 8ininnalling the y== mminkkay, this gives 8 ynd which satisnis 8 = 17.
Wait, let me verify this. the points are A(5.3), B(6.8), C(7,4), and D(8,9), does this form a porallelogiam??yivieett check the vectors. <omitted>
equation:
y1/2
So, the fourth point is (8, 9), and </thinks
These aren't equal either. Hmm, that's confusing AninWaitt maybe made another approach. <omitted>
To find the coordinates of the fourth vertex of the parallelogram, use the property that the diagonals of parallelogram bisact each other. Vnnun1, *Calculate the midpoint of diagonal BC: Paints (6, 8) and
assigning the points. me try
Hmm, these aren't equal. but according to the vector addition, D should be (8,9). So, why vectors AD and BC not equal?unknWait. maybe check other pair sides. Vector BC are not equal, but vector AB and vector DC are equal. <omitted>
that's problem./ninWWai
4)An Midpoint formula: [Wleeft\/ffaad + 7H2), Wfrrc|8 4H22Wright; [Wett( 3J22), 6\vright) (6.5, vnnn2 "Set the midpoint of diagonal AD equal to the midpoint of BC-*"nn Let D be (x ylAn Midpoint of AD:
MMAeet()ffreeS + x|2), Wraac( WHih)rrgght Equate to (6.5, 6)An
WW/ffaac|5 + xH2) = 6.5 WAighhtrrrw
These aren't equal, but in a parallelogram, be equal. So, that's a problem.\nhyiWait, but according to the midpoint method, it's parallelogram. So, maybe I'm missing something. comitted>
pairs should
5 WRightarrow
B\))1n -V/ifraa yl12 6
WRightamoo 3 + y Wiightaroow y 9W..nnn...
"Calculate Wi >/): Vix +y 8
"Answer""" (17)oved(17)V
No answer
Token number: ~800
Token number: 16384
Figure 14: Comparison of generated content between DEER and Vanilla on MATH-500.
37

---

Published as a conference paper at ICLR 2026
Question: Point $A$ lies somewhere within or on the square which has opposite corners at $(0,0)$ and $(2,2)$. Point SBS lies somewhere within on the square which has opposite Answer: corners at points S(4,2)$ and $(5,3)s. What the greatest possible value of the slope of the line containing points $A$ and $BS? Express your answer as a common fraction. Vanilla CoT
DEER
Okay, so have problem where need to find greatest possible slope of a line connecting two points, A and B. Point A is somewhere inside on square with oppasite corners (0,0) another square with opposite corners at (4,2) and (5,3).
Okay, this problem where need to find greatest possible slope of line connecting two points, A and B. Point A is somewhere inside or on square with opposite corners (0,0) (2,2).
(2.2).
inside on
is inside on another square with opposite corners at (4,2) and (5,3). need to figure out the maximum slope possible between any two points visuallize the squares. The first square has corners at (0,0)
need figure out the maximum slope possible between any two points
these squares!Annniins visualize the squares. The first square has corners at (0.0)
these squares VinnFirst,
me
and (2.2). Similarly, the second square has opposite corners at (4,2) and (5.3). Hmm, so square
and (2,2). Similarly. the second square has opposite corners (4,2) (5,3). Hmm, so square bit smaller me figure out its sides. The distance between (4.2) and (5,3) sqri[[5-an ((5(4))))2 2 (3-2)*2)
smaller.
me figure out its sides. The distance between (4,2) and (5,3)
is sqri((S 2)*2 (3-2)=2] sqri(1 length sqrt(2), rotated degrees relative to the axes. Wait,Wait, actually, no. the opposite corners are (4.2) and (5,3), then the sides comitted>
sqrt(2).
sqrii1 1] sqrt(2). So, it's square with side length sqrt(2), rotated degrees relative to the axes WalnWai,, actually. no. If the opposite corners are (4,2) and (5,3), then the sides not aligned with the <omitted>
square with
aligned with
But wait, that achievable? Because point A is in the first square, A (2.0), which corner, and point
But wait, is that achievable? Because point in the first square, so A is (2,0), which
and point corner of the second square. So, connecting (2.0) to (4,3) would give slope of (3 Dj/(4 2) 3/2. But is maximum?
(4.3), which is a corner of the second square. So, connecting
(4,3) 3), which
(2,0) to (4.3) would give slope of 0)/(4 - 2) = 3/2. But
that the maximum?
</thinks>
To find the greatest possible slope of the line containing need maximize expression VC Vifracly B y A]xx B x x_ W. Inln- Point W A W lies within
Wait, maybe can get a steeper slope by choosing points that are not at the corners. Because if we can have larger y8 yA with smaller x8 xA, that would give steeper slope.
points WA
W B
W (0.0) W) and W. (2.2) the square with opposite corners
The minimum y WV-coordinate for W A W is W. (1) and the maximum W W-coordinate
<omitted>
Wait, but hold Let me think again. Maybe we don't (4,3), somewhere else, we can get a steeper slope. <amitted>
is Win- Point WM B W lies within
the square with
(2,0)
oppasite corners W. (4.2) and (5,3) W. The
maximum Wy (0-coordinate for W. B W is W W and the minimum W W)-coordinatee VM Winnnno maximize the slope, we at W. (4,3) W. The slope is thent'nn///onhttexsssloo Bifrcc/Bi2nnnkjjjmnnHooeoee
But wait. there a way to have larger slope? example, if at (2.2) and is at (4,3). Then, the slope is (3 2)/(4 2) = 1/2, which is less than 3/2.ninAiterrative
choose W.
W (2.0) W and W. W
i is at (0,0)
Wfrac[3 0/4 closer inspection, the square for WC B W actually
upon
and at (5,3), then the slope (3 0)/55 0) 3/5, which is less than 3/2.
diamond with corners at WM (4,2) W. W (5,3) W. WM (5,2) W.
<omitted>
and (4,3) W. The point W (4,3)
indeed corner
Alternatively, paint A is at (x. yA) where x then point B would have to be at (x 2, yB). But since the second square least
this square. Therefore, the maximum slope is
Areeaable. greatest possible slope is W (Mrra(3)22 W.brrnibbowed/ddrresssBi.
x=4, <amitted>
least
'gold_answer answer": "\(rac33H21"
No answer
Token number: ~1000
Token number: 16384
Figure 15: Comparison of generated content between DEER and Vanilla on MATH-500.
38

---

Published as a conference paper at ICLR 2026
5 65$is equivalent to 13. If we add parentheses in Question: various locations, we can change this value. For example, 9+6=6-9+6-5 If we only add parentheses (and not rearrange the order of the terms), what is the minimum possible value this expression this problem, we cannot change addition subtraction into multiplication. For example, $ (1 (1+2+3(-4)+5++ $ not valid placement of parentheses./nnnneenn \nnnEnter your answer as a single value.",
The expression $$1 + +
6= 5-) 2
obtain? (For the purposes of
Answer:
DEER
Vanilla Co
Okay, so have this math problem here: the expression is 2 3-4 =5 and it's equal to 13. The task is to add parentheses various places change rearrange the terms or turn the operations into multiplication. need to find the minimum possible value this expression can obtain by adding parentheses. Hmm, interesting. InisFiisst, let me make sure understand the problem correctly.
Okay, so have this math problem here: the expression is 2- 3 5 and it's equal to 13. The task is to add parentteeees various places change rearrange the terms or turn the operations into multiplicatio. need to find the minimum possible value this expression can obtain by adding parentheses. Hmm. interesting AnknFirst, let me make sure I understand the problem correctly. can only add parentheses, which will change order in which operations are performed. but can't move the numbers around or change the plus and signs into multiplication division. So, example, can do something like + 2) 3-4 + 5 + 6, but can't 1*2+3) - + 5 because that would involve multiplication, which allowed.
only add parentheses, which will change the order in which operations are performed, but can't move the numbers around or change the plus and signs into multiplication
division. So, example. 6, but can't 11(2-)) 4 + 5 +66 because that would involve multiplication, which isn't allowed.
can do somethiig
2)
<omitted>
comitted
Yep, that's correct. So, the original value Aninniterraatively.. group +2)
Yep, that's correct. 13 the original wewllllrilleee group 2) (3
2 3, -1,-1 5 4,4 6 Then, So, 13.yn'nnltermaaiively
6),
= 3, 3- -1, + 4,4 6 Then 10
1. group 1
3-4 4 5) So, 2 Then,
13 group 1 (2 3.4 13.rr/HHmm,
6o.
13..mnynHmm,
Then,
seems like 3 is the lowest can
far. But me think
seems like is the lowest can get far. But let me think there's another way.kry/What I group Let's compute that 15 -9. So, that's -9, Wait, that's way lower than 3. that allowed?
there's another wayknknWhat if group 2- (4 5 compute that:
+
Then
Then,
15 -9. So, that's 9. Wait, that's way lower than 3. that allowed?
</think>
Wait, hold The original expression is 2 3 group -9.
that would be subtracting
find the minimum possible value the expression WV1 2 + 3 4 =5 5W by adding parentheses, we can strategically group terms maximize the impact of the subtraction. iningy grouping the terms after the subtraction, we can create larger number to subtract, significantly reducing the overall value. For example, grouping W4 60 together/yivnkiiil + 2 3 (4 5 6) 6 15 Iynt. the minimum possible value is MM\oooxd
<omitted>
the subtraction, it's +5 +6. So, group +5 +6, that would be changing the operations after the subtraction, but can't rearrange terms. So, that allowed? camitted>
original expression,
Alternatively, group (2 +5 +6), before. 1
+12-13 VntnAltermattieely group (1 +2 +3 -4 +5)
Endless exhaustive search!
Token number: ~1500
Token number: 16384
Figure 16: Comparison of generated content between DEER and Vanilla on MATH-500.
39

---

Published as a conference paper at ICLR 2026
Question:
The coordinates of parallelogram are (5, 3). (6. 8), (7, 4) and $(x, y)$ and $x 7$. What is the value of $x y$?
Answer:
Okay, have this problem where need find coordinates ofe Eourth
of' para parallllogaam The given points 3), 8),
(x. y) with the condition that x 7. Then, I need to find the value of y. Hmm, let me think about how approach this. First, I remember that in parallelogamm opposite sides are equal and purailel. That meams the midpoints of the disgoals should be the same, So, it'l find the midpoint of diagonal, should equal the middoiint Let me label the points to make clearer. Let's point is (5, 3), poin. B (5. S), puini C (7. 4), and poin Dis (s, y) Now, I meed to figure out which points connected each other. Since it's parallclogaam the onter of the points matters think the points should be connected order entirely sure, so maybe should consider different possibilities
other diagoral.
Allerntively, another way to appreach this is by using vectors. In parallelogmmm (he vector from ond point anothur should be equal to the vector from another point to the next, So, for example, vector AB should he equal to vactor TC, and vector AD should be equal to vector BC: 8). So,
Let try
vectr AB, DC, then vector DC should also be 5) Point is (4. and point (7 4) So, veator DC is (7 x, 4,4- -y) Setting this equal to (1, S), we gettwin? = and -y Solving finst equstion: 7-x x-
puint
(6 5,8 3) (l.5). IFvector
equal vector
Solving the second equition: y S 5-5
<Iaduced trial answers: (beved(6 (-1)--
Confidence: 0.7344
Continue thinking
Wait, but the problem statis that 7, and here x which less than That can't be right. So, mayhe assigned the points incorootly. Perfaga the order of points isn't A, D. Mayhe different order. Let me try another approach. Another property of'a panillelogram that the diugomals biseci each other. So, the midpoint of di'diguual AC should be the same the midpuint of diagonal RD..
Let me caleulate the midpoint of AC fine. Point is (5, 3) and puint C 4) The midpoint formula is ((xl x2y2, (yl y2y2). So, midpuini of AC is (15 + 7V22, (3 + 4y-) - (12/2, 7/2) - (6, 3.5).
Now, midpoint of should also (6, 3.5). Point Rt is (6, and point y) midpoiint of
x322, yizy, Setring this equal
to (6, 3. 55))nin66 1 xy2 Solving the first equation (6 xy/2 m so 6- in 12 soo x 6 WninSolving the sccond equation: (8 + +y2 = 3.5 uo 8 + in uo
and (8 yX22 3.5.
Again, ligtt and y -1, but supposed to greater diagonal.
Hmm, that's conflicting, Maybe need to consider diffienent pair points
<Tnduced trial unswert; (boxed(10)
Confidence: 0,5312
Continue thinking
Wail, perhips assumed the wrong disgunal. Maybe the disgonals are AD and BC insteed AC and BD, Let me that. point
Midpoint AD: Point
xY2, (3 +y/2) Midgoint of BC: Point B (6, S) and point C is (7, Midpoint ((6 7)2, (8 4y2) (18/2, 12/2)= (6.5, Seiting mispoinis equillainttS 1 xy2 - 6.5 and (3 yX2 6.
y). Midpoint
StaeeSlivnn the second oquation: (3 +V22 + 12 =2 Okay, this gives -8 and =9 9, which satisfies x 7. So, the fourth point is 9), and y 8 1 17.
Solving fins equitio: (5 x)2 6.5
<Induced trial auswers; (boedd
Confidence: O. 9993 Exit!
</hink>>
To find the coordinates of the fourth veries of the parallelogram, we use the property that the dingenuls a parillelogmm bisect each other. (7, **Caleultee the midpoint of disgonal BC:** Points B (6, (7,4),n Midgoinnt formula: (iileettiiiieee (6 + 7] Wffae 44) (2)
(eee(ffme(33)) (21. Biright) (6.5, 63)).
2. 2. **Ser the midpaint of disgonal AD equil the mi midpoint of BC: Lit Di (s. y) Midpoint of AD: (e0let +5+ Sfrac (5 (2) Riightuow
yi (2iiright)))) Equate (6.5,
WRightrrow 81)) (0 y2
WRightarow 5+y y (Rightrrow y 96).
CCaleulate WXx yty. - 1VX 8-9 176).
"5 "Answer" (17)9)
Figure 17: An example demonstrating LRM's implicit ability to sense the emergence of pearl reason- ing. When the model's reasoning content is insufficient support the elicited answer, the confidence remains at a low level, as demonstrated by the first two confidence values in the figure. Conversely, when the model has provided adequate and sound reasoning as justification, the confidence reaches high levels, potentially approaching 1, as shown by the final confidence value in the figure.
40

---

Published as a conference paper at ICLR 2026
Question: Define\nn Mp= Vssum Vinty (ifrac(1](k"2) \|sum_ (k= VinVyt (3. a way to ([T 13 Winfty \1sum_ (k= 1) Winfiy Vifrac[IKC + k)33)\1jin terms of $p$ and $9.$
2) \ Viuaad V\text(and) Viquad 9=
Answer:
DeepSeek-RI-Diee RI--RstiDl----e- Disillill-----e----2 32B
Length
Okay, so have problem where inced express double sum Witsum I) 1j*Mndty Neam Ik 11 Qintty Vituae [3] 10 3313)% terms Hiplli and Wight, where up- - Visum [k = 11-iiiy Idra [1] (k22)1) and Wig Yeur k Windyy [1 (123) Hmm, lot me think about how approach this, minl'ins, I know that Mit)) is the famous Dasel problem, which equals fettrac
16) and (igh) is the Riemann zeta approumeticy 2.20... But don't tiak need the values; instead, need relate double double sum it's over positive integers 1ijl lilkl, and the term Wettrac (1) kr3j Mayhe
function which known Agery's
sum these sertes oooking can change variables to sampliify this Let me sot 1ipo -+ 223. Thes for each fixed Vally 1i90 cas range from to ugo 199, and 9ik a- So, pertuggs I can rewrito the double sum single sum over Mall) where each term the sum over light from to Vin 1ig
bytidra (1) (a
write that downn' (ialisum () 1yndinly tsum Nauss (j- 1y 11 sifiee (1]
iindly lifrac [1] 1233) Youm Io Mintyy that makes sanse bocause the smallest (0il)) can
408
(wlice 10j 10)) VK 1930. and goes to undiity Now, for each Maae, the inaer sum is just adding tr [1] (103) total of hip 19 times So, the inner sum simplities to Wiltrac (n- Mandyy Virac
write this mn ( the double sum becomes (aa
11 (er3)
//n3///s/olallmm that
manageable. Let (I (m"2)
in 2/ tilef
(n] (n"3) 3) lifrr 3) tright) (aam U2n
Vitree [1] (ara) fanght/aaifallaa felaYes, the's correct. So, this equal toclalali witteh Youn (n 2) lifrac [3) (o linght) Viett Noun [n 21 Minnfy lifecc II (a leight/all///nin Dun know that lyp limm In - "Kinfil Vitrac [1] far 2010 and lite Yiar (n 1) "Minty
ifrrett I (1%) So, if subrrctt the VKn 10) terms from both series, can express the
starning from Vin 20) mnn compute that/
sumd aallllllllyy (nliamm tiifit (1) tar333 q- (ifra [1 (33 q- IniiiaannS,, substincing back into our expression alall p linght)- Weft q (right)
Vindyy (Vitac (m22) p Vitroc (112) p- I'altf alaSSiilalty, for second sum sum/aaaai//jataau [a
1-q p- Trin
</thinks
SnlesSo, the double sum simplifies to Mp glit. Therefore, the answer in' [ni - Unnl
15
QwQ-32B
so need to find
the double lylisum jinuuy Neuum 1) "inntyy Viine -k"3/ terms of (ipll)) and approach winfiin
(ighl) where (ppll is remember that double sums can sumetimes be simplified by changing variables or switching the onder of summation. Mayhee can let Vop j KI0), so that for each Hin the serms where kij k all) contribute to the sum. That might help me rewrite the double sum single sum over (uall). with each multiplied by the number pairs WG, KP0 that add
11k and Highl sum WL 310, Imm.
think about
(imil)) ''n me that. Let's 'kpn 1 ki). Then for each Von ligeq 20ly (since (Kjs) and (ugat) are leest 1) the number pains 100), kF-) such that lij k- gil Hiu 19). Far examppl,, when Vaa 29), there's only one pair (1.1), when Vi 301, there are two pains (1 1,21 and (2.1), and so on, So the double sum can be rewritten as solaatniniismmm
(n=2)" infracin 1) (n'33in)) Jnin Wait, that righ?? Let me check. Each term (ifffrce [1) 1y33)1) for each pair 1KG. kot)) would be grouped by =j 250, for each Harld dn in (113) the entire double sum becomest uan (uiiaum (nr untty
contribation in a/ okay. New need to express this in temms of (igll) and light) Let me see, Let's firs write out the sumciiin (mliisum ( Winfty Iefrac (n- 1f (m"3) - hoam, (nniy lilehh (ifrace) (n 3) Wffe (1) (3 lright) y Noar (oe2) Shinfy Sleft infre () - (ifeee (n'3) split that
(orl) contributes
each (ffifeee (1) [ 12/3)1)) Therefore,
387
tright Juistai
simplifies Infrec ( (m²2) lium (m=2)
difference (I for Walliee Nennoow notice that these are just the calls of the series for (kpl)) and Wejl). Since Wip
separate
C (n-2)
hoam, (leil) We-1y"iie poliniy [I (k-5po), then Setaam fe-2y ty- Winnty Wine Il (e -p (ffaa (1) (1-2) p- 199 Similarly. 1igg
Vsum (k-1 Winity (ifac|]) (K(3))), WCeumm Vinyy lifrac (n"3] lifre (3) (1-3) Wi).ww/Therefin substituting back expression (uupp (q 11- </think>
p- ginl Jinn
Let's
cansidering the suca ii(a -j For each hife Ngog 209, there tie- 19)) pairs HiG kys) such 1ij all). This transforms the double sum into single
the above thought process provide the result. The double
sum funiiaaailuiiiammm 3- 1 Whiniyy toum (k-1 Plinty lifee 100 + ky Houm (o- tiliiill tifmeja- (a- 13 He jatttajjaaaaaaaiiiin this into two
sopurate suns sattslaaaiiii af suisum (n- 2) mundyy Wtent lifiae 2) ofie (erS) leight) y (leth voum (n-2) (yl2)t lotune (ur2) Wright )- series for (ppli) and light) we subtract first comms//aaafflllllee p-1 (right) )- bieefl q- lright ) p- glall/ywhhhi the double sum simplifies lighbooed (p- qi1))iin
260
Wiettr Usum (n-2) "iinty (ifrac1) (ar3) liight yabl RiReengizzngg
the
Answert* hoxod ip ql'eel
</think>
TinnTo express the double sam Witamm G- 11% Youm (k 1p%innf Sffee (1) (6 37331% in temns of Uilll and Mee%) we start by chonging variables. Let life 2i)) For each tee figg 201, the number of pairs hij k99 such that vij + k nil) is o(n- Fily This allows two separate
rewrite the double sum astrinisfielleem
(o=2) "iiniy lifrac
(/r3//////aeess we split
sume (uittam (n-2)"Winfly Wilef (ifrae (I (inell)) (n linght yoll] menenngniing these as the tails the series (ipp)) and (eell), we bavertstriiaallln mimiiiin lifee (1) (r p- ligund (aad) squd harm. (n-2) by (Iaa)(
128
(rr3) 4--
SuSubsttiiui these the expression gives D) (-(q- 1) qini//aaaauss the duuble sum simplisess (i -120.
Figure 18: An example demonstrating the presence of more than one (/think) tokens in QwQ-32B. For both models, the green thinking chunk is sufficient to draw the correct conclusion. However, QwQ-32B proceeds with additional summary (red chunk) and generates its own (/think) token. Based on all the above content, it arrives at the conclusion.
41


Reviews:
[{"review_id": "ViaEqs0fDk", "reviewer": "Reviewer_LEHd", "summary": "Large reasoning models often produce excessively long reasoning sequences, leading to computational inefficiency. To address this issue, the paper proposes DEER, a method that detects transition points during model reasoning, based on linguistic markers or entropy, and prompts the model to generate trial answers at these points. A confidence evaluation mechanism is then applied to decide whether to stop further reasoning and produce a final answer or continue generating additional thoughts.", "questions": "n/a", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-\tThe proposed method is simple and effectively reduces the number of output tokens in practice.\n-\tThe experiments are comprehensive, covering a wide range of models (DeepSeek-R1-Distill-Qwen series, Qwen3 series, QwQ-32B, and DeepSeek-R1) across 10 benchmarks.", "weaknesses": "-\tMore details about the branch-parallel acceleration strategy (Section 3.3) are needed. The current description lacks clarity.\n-\tThe technical novelty is relatively limited. Using linguistic markers or entropy to identify reasoning transitions is not entirely new, as similar ideas have been well explored in prior and concurrent works [1-6]. It would be beneficial to include a discussion of these related approaches.\n-\tThe paper lacks an evaluation of the quality of reasoning steps. It remains unclear whether early exits lead to oversimplified reasoning or disrupt the reasoning flow. A more detailed quality analysis would strengthen the work.\n\n[1] Yan, Hang, et al. \"Mur: Momentum uncertainty guided reasoning for large language models.\" arXiv preprint arXiv:2507.14958 (2025).\n[2] Wang, Shenzhi, et al. \"Beyond the 80/20 rule: High-entropy minority tokens drive effective reinforcement learning for llm reasoning.\" arXiv preprint arXiv:2506.01939 (2025).\n[3] Fu, Yichao, et al. \"Efficiently Scaling LLM Reasoning with Certaindex.\" arXiv preprint arXiv:2412.20993 (2024).\n[4] Agarwal, Shivam, et al. \"The unreasonable effectiveness of entropy minimization in llm reasoning.\" arXiv preprint arXiv:2505.15134 (2025).\n[5] Huang, Jiameng, et al. \"Efficient reasoning for large reasoning language models via certainty-guided reflection suppression.\" arXiv preprint arXiv:2508.05337 (2025).\n[6] Vanhoyweghen, A., Verbeken, B., Algaba, A., & Ginis, V. (2025). Lexical hints of accuracy in llm reasoning chains. arXiv preprint arXiv:2508.15842.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "M6rGYnUWE1", "reviewer": "Reviewer_gfWw", "summary": "This paper proposes DEER, a training-free method for eliciting efficient reasoning from LRM by dynamically early-exiting CoT generation. The authors argue overthinking harms both latency and accuracy in long CoTs. Instead of using fixed heuristics, DEER watches for reasoning transitions (linguistic markers like “Wait” or entropy spikes), briefly induces a trial answer, and computes a geometric-mean confidence from token probabilities. If confidence exceeds a threshold, it stops thinking and outputs the answer. A robust variant, DEER-Pro, averages multiple inductions and MAD-calibrates confidence. Across 10 benchmarks and 11 models, DEER cuts reasoning length while achieving higher accuracy over the vanilla LRM.", "questions": "Can this training-free method for efficient reasoning be adapted to be a training-based method to further improve efficiency and accuracy?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The proposed method is a training-free and plug-and-play approach for eliciting efficient reasoning from LRMs, which has clear advantages over training-based methods.\n2. The experiments demonstrate that the method improves efficiency and accuracy simultaneously.\n3. The method is well-motivated and clearly presented.", "weaknesses": "1. Confidence may not always serve as a reliable signal for early exit. Prior work [1] has shown that explicitly encouraging reflection (such as by appending tokens like “wait”) can help the model identify and correct earlier mistakes. In contrast, DEER’s reliance on confidence may lead the model to terminate reasoning prematurely: it could be highly confident yet incorrect, losing the opportunity to self-correct in later reasoning steps.\n2. It remains unclear how DEER and DEER-Pro achieve higher accuracy than the vanilla model in Table 1 despite substantial reductions in token length. Without a detailed explanation, it is difficult to justify the improvement.\n3. The fairness of the reported comparisons is uncertain. DEER-Pro employs a parallel decoding strategy, which inherently introduces additional computational overhead compared to single-path decoding methods. This difference complicates claims of efficiency and may limit the validity of direct, apples-to-apples comparisons with baseline models.\n\nReferences\n1. s1: Simple test-time scaling", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "viBnQQtrx3", "reviewer": "Reviewer_Ax2Q", "summary": "Summary\n\nThis paper proposes DEER (Dynamic Early Exit in Reasoning), a training-free framework that allows large reasoning models (LRMs) to dynamically terminate the chain-of-thought (CoT) generation when the model is already confident enough in its answer. The method monitors reasoning transition points through linguistic or entropy-based signals, induces trial answers at these points, and uses token-level confidence scores to decide whether to stop reasoning early. The authors also introduce DEER-Pro, a robust variant using multiple answer inducers and calibrated confidence aggregation.\nExperiments across 10 reasoning benchmarks (math, science, and programming) and 11 models (1.5B–671B parameters) show substantial token reduction (19–80%) and accuracy improvements (up to +5%). The method is efficient, plug-and-play, and demonstrates strong robustness to thresholds and model scales.", "questions": "None", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Clear Motivation & Insightful Observation:\nThe paper convincingly identifies the “overthinking” problem in modern reasoning LLMs and empirically verifies the existence of pearl reasoning — points where further CoT expansion is redundant or even harmful.\n\nSimple Yet Effective Approach:\nDEER is training-free, easy to integrate, and works well across different reasoning models. It leverages confidence signals during inference — a practical and theoretically grounded design.\n\nComprehensive Experiments & Strong Results:\nEvaluations cover diverse tasks (GSM8K, AIME, GPQA, BigCodeBench) and model families. DEER consistently outperforms baselines such as CoD, Dynasor-CoT, and SEAL in both accuracy and efficiency.", "weaknesses": "The paper uses a limited number of backbone models, and it remains unclear how well the proposed method performs on closed-source reasoning models.\n\nMathematical reasoning benchmarks typically use pass@k metrics to reduce randomness and improve robustness, but this paper does not adopt that evaluation standard.\n\nThe authors do not include ablation studies to verify how each component or module of the proposed method contributes to the overall performance improvement.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)