Deep Think with Confidence
Authors: Yichao Fu
Xuewei Wang
Hao Zhang
Yuandong Tian
Jiawei Zhao
Venue: ICLR 2026 Poster (2026)
Keywords: Large Language Model Reasoning
Primary area: generative models

Abstract: Large Language Models (LLMs) have shown great potential in reasoning tasks through test-time scaling methods like self-consistency with majority voting. However, this approach often leads to diminishing returns in accuracy and high computational overhead. To address these challenges, we introduce \textbf{Deep Think with Confidence (DeepConf)}, a simple yet powerful method that enhances both reasoning efficiency and performance at test time. DeepConf leverages model-internal confidence signals to dynamically filter out low-quality reasoning traces during or after generation. It requires no additional model training or hyperparameter tuning and can be seamlessly integrated into existing serving frameworks. We evaluate DeepConf across a variety of tasks and the latest open-source models, including Qwen3 and GPT-OSS series. Notably, on challenging benchmarks such as AIME 2025, DeepConf@512 achieves up to 99.9\% accuracy and reduces generated tokens by up to 84.7\% compared to full parallel thinking. Our code is available at https://github.com/facebookresearch/deepconf

Published as a conference paper at ICLR 2026
DEEP THINK WITH CONFIDENCE
Yichao Fu Xuewei Wang', Hao Zhang', Yuandong Tian', .Jawei Zhao't
'Meta AI, PUCDD
"Equal contribution
Project Page: jiaweizzhao. github. io/deepoonff
ABSTRACT
Large Language Models (LLMs) have shown great potential in reasoning tasks through test-time scaling methods like self-consistency with majority voting. However, this approach often leads diminishing returns in accuracy and high computational overhead. To address these challenges, we introduce Deep Think with Confidence (DeepConf), simple yet powerful method that enhances both reasoning efficiency and performance at test time. DeepConf leverages model- internal confidence signals to dynamically filter out low-quality reasoning traces during or after generation. It requires additional model training or hyperpa- rameter tuning and can seamlessly integrated into existing serving frameworks. We evaluate DeepConf across variety of tasks and the latest open-source mod- els, including Qwen3 and GPT-OSS series. Notably, on challenging benchmarks such as AIME 2025, DeepConf@511 @5 achieves up 99.9% accuracy and reduces generated tokens by up to 84.7% compared to full parallel thinking. Our code is available http:://ggtuuu..coo//cchoorrrree
Accuracy AIME (Offline)
Generated AIME 2025
(Online)
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92.7
Accursty (5)
02
87.4
87.5
3.23
82.3
Tool Counts
2.37 (-40.9%)
76.9
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Figure I: Up: DeepConf on AIME 2025. Down: Parallel thinking using DeepConf.
Work done during internship Meta FAIR.

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Published as a conference paper at ICLR 2026
INTRODUCTION
Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities, particularly when equipped with methods that enhance their performance during test-time inference. A promi- nent technique is self-consistency, which samples multiple reasoning paths and aggregates final answers through majority voting (Wang al. 2023). This type of approach, also known as parallel thinking, significantly improves reasoning accuracy but incurs substantial computational overhead: generating numerous reasoning traces per query scales inference overhead linearly, limiting prac- tical deployment (Xue et al., 2023). For example, improving pass@) accuracy from 68% to 82% using standard majority voting on AIME 2025 requires 511 additional reasoning traces per question using Qwen3-8B, consuming 100 million additional tokens.
Moreover, parallel thinking with majority voting exhibits diminishing returns pertons--perforancce often saturates or degrades as the number of traces increase (Chen et al. 2024a). A key limitation is that standard majority voting treats all reasoning traces equally, ignoring quality variations (Pal et al. 2024 Wang et al. (2025a). This can lead to suboptimal performance when low-quality traces dominate the voting process.
Recent work has leveraged next-token distribution statistics to assess reasoning trace quality (Geng) al. 2024, Fadeeva et al.) 2024] Kang et al.] 2025). Higher prediction confidence typically cor- relates with lower entropy and reduced uncertainty. By aggregating token-level statistics such as entropy and confidence scores, existing methods compute global confidence measures across an entire trace to identify and filter low-quality traces improve majority voting performance (Kang
ct al. 2025).
However, global confidence measures present several limitations in practice. First, they may obscure confidence fluctuations at local reasoning steps, which can provide sufficient signals for estimating trace quality. Averaging across entire tokens in a trace mask critical reasoning breakdowns that occur at specific intermediate steps. Second, global confidence measures require generating complete reasoning traces before they can be calculated, which prevents early stopping of low- quality traces.
We introduce Deep Think with Confidence (DeepConf), simple yet effective test-time method that combines parallel thinking with confidence-aware filtering, based on local confidence mea- surements. DeepConf operates both offline and online modes, identifying and discarding low- confidence reasoning traces either during or after generation. This approach reduces unnecessary token generation while maintaining or improving final answer accuracy.
We evaluate DeepConf across multiple reasoning benchmarks (AIME 2024/2025, HMMT 2025, BRUMO25, GPQA-Diamond) and models (DeepSeek-8B, Qwen3-8B/32B, (0T-00)-20B/1200B Through extensive experiments averaged across 64 repetitions per setting, we demonstrate that DeepConf achieves superior reasoning performance while requiring significantly fewer generated tokens compared to standard majority voting.
In offline mode with access to all reasoning traces, DeepConf@512 achieves 99.9% accuracy on AIME 2025 using GPT-OSS-1208 (no tools), saturating this benchmark compared to 97.0% for cons cons@512 512 (majority voting) and 91.8% for pass@1. 1. online mode with real-time generation control, DeepConf reduces token generation by up 84.7% compared standard parallel thinking while maintaining or exceeding accuracy. Fig. highlights our key results.
CONFIDENCE AS AN INDICATOR OF REASONING QUALITY
Recent work has demonstrated that reasoning trace quality can be effectively estimated using metrics derived from the model's internal token distributions (Kang et al.) (025). These metrics provide model-intrinsic signals for distinguishing high-quality reasoning trajectories from erroncous ones without requiring external supervision.
Token Entropy. Given a language model's predicted token distribution P. at position i, the token entropy is defined as:
H: =
Σ Pi(g) log P.U),
2

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Confidence
Bottom 10% Confidence
Confidence
2000
2200
Frequency
Cuenei
Requency
1309
Careil
1500
Ouent
1200
denfidence
Figure 2: Confidence distributions for correct vs. incorrect reasoning traces across different metrics. Data from HMMT25: 30 problems, 4096 traces each.
where P.()) represents the probability of the j-th vocabulary token. Low entropy indicates peaked distribution with high model certainty, while high entropy reflects uncertainty in the prediction.
Token Confidence. We define token confidence C2 as the negative average prooprbbabylityy of the top-k tokens at position i:
C₁
= log P.(),
==1
where & denotes the number of top tokens considered. High confidence corresponds to peaked distri- butions and greater model certainty, while low confidence indicates uncertainty in token prediction. Note that the top-k tokens used for confidence computation may differ from those used for next to- ken sampling (specified in Table We compute confidence using the top-20 token probabilities.
Average Trace Confidence. Token-level metrics require aggregation to assess entire reasoning traces. Following Kang al.] (2025), we employ average trace confidence (also termed self- certainty) as trace-level quality measure:
N
Cavg
ΣC, C
(3)
where N is the total number of generated tokens. As demonstrated in Fig. 2 average trace fidence effectively distinguishes between correct and incorrect reasoning paths, with higher values indicating greater likelihood of correctness.
Despite its effectiveness, average trace confidence has notable limitations. First, global aggregation obscures intermediate reasoning failures: few high-confidence tokens can mask numerous low- confidence segments, potentially hiding critical errors. Second, this approach requires complete traces for quality assessment, preventing early termination of low-quality generations and resulting in computational inefficiency.
3 DEEP THINK WITH CONFIDENCE
In this section, we present how to leverage confidence more effectively to improve both reasoning performance and thinking efficiency. We target two primary scenarios: offline and online thinking. Offline thinking leverages confidence to enhance reasoning performance by evaluating and aggregat- ing information from completed reasoning traces. Online thinking incorporates confidence during token generation to improve reasoning performance and/or computational efficiency in real-time.
3.1 CONFIDENCE MEASUREMENTS
To address the limitations of global confidence measures like self-certainty, we introduce several alternative confidence measurements that capture local intermediate step quality and provide more fine-grained assessment of reasoning traces.
Group Confidence. We quantify the confidence of intermediate reasoning steps using group fidence. Group confidence provides a more localized and smoother signal by averaging token confi- dence over overlapping spans of the reasoning trace. Each token is associated with sliding window
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group G; consisting of n previous tokens (e.g., 1024 2048) with overlapping adjacent win- dows. For each group Gú, group confidence defined as:
Cc.
Σ Co
C,,
GG
AEG;
where [G;] is the number of tokens in group Gi-
Estimating reasoning trace quality requires aggregating signals from group confidence. We ob- serve that intermediate steps with extremely low confidence in a trace can significantly affect final solution correctness. For instance, when confidence drops sharply during reasoning with repeated low-confidence tokens like "wait", "however", and "think again", disrupts reasoning flow and leads to subsequent errors.
Bottom 10% Group Confidence. To capture the effect of extremely low confidence groups, propose bottom 10% group confidence, where trace confidence determined by the mean of the bottom 10% of group confidences within the trace:
Obottom-10 (t))
CGp GjEG.
Σ
(5)
GG
where G2 is the set of groups with the lowest 10% confidence scores. Empirically, we find that 10% effectively captures the most problematic reasoning segments across different models and datasets.
Lowest Group Confidence. We also consider lowest group confidence, which represents the con- fidence of the least confident group within reasoning trace-4 special case of bottom 10% group confidence. This measurement estimates trace quality based solely on the lowest confidence group:
Cleast (t)
min Ca,-
(6)
G₁EG
where G is the set of all token groups in the reasoning trace. We discuss how lowest group confidence improves reasoning efficiency in online thinking scenarios.
Tail Confidence. Beyond group- based measurements, we propose tail confidence, which evaluates reasoning trace reliability by focusing the final portion. This metric is motivated by observations that reasoning quality often degrades toward the end of long chains of thought, and final steps are critical for correct conclusions. In mathematical reasoning, final answer and conclusion steps particularly important: traces that start strong but end weakly may produce incorrect results despite promising intermediate reasoning. Tail confidence Ciall is defined as:
Caa (1)
1
Σ C₁ TET
T
where Tia represents a fixed number tokens (e.g., 2048). Fig. 2 compares different confidence measurements, illustrating that both bottom 10% and tail confidence metrics better separate incorrect and correct trace distributions compared to mean confidence methods, suggesting these metrics are more effective for trace quality estimation.
3.2 OFFLINE THINKING WITH CONFIDENCE
We now describe how to apply various confidence measurements to improve reasoning performance in offline settings. In offline thinking, reasoning traces for each problem have been generated, and the key challenge is aggregating information from multiple traces to better determine the final answer. While recent work proposes advanced methods for summarizing and analyzing reasoning traces using LLMs, we focus on standard majority voting approaches.
Majority Voting. In standard majority voting, the final answer from each reasoning trace con- tributes equally to the final decision. Let 7 be the set of all generated traces, and for each f e T, let answer(t) be the answer string extracted from trace The vote count for each candidate answer is:
V(a) = Σ [(answer (t) a),
TET
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Token Confidence
V/ Zajis loge where logR() one top-k logprobs
mettinn your proile exep Step
Pythagomonn frmmusil
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Tail Confidence
BVgICx-K=1/ G
Cy- Cogl where last tokens K, total tokens N
thi probiom Step aggrora tiple toiniieeipp pipla gencrsted
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Σ
10%
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K66) 17
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Ce16
Bottom 10% of all Cp
high 90%
Iheifiollansen 105
The Einil Enswer
V(a) = 15 (17 13)/
Lowest Group Conf: Giowest min Co; 6,30
The frist C-11
Average
Casy 1/4 2ers G
The firal aroweris C-0
Trace Confidence Measurements
Confidence Fittering
Conf-Weighted Majority Voting
Figure 3: Confidence measurements and offline thinking with confidence.
where 1{-} is the indicator function. The final answer is selected as the one with the highest vote count:
arg max V(a).
Confidence- Weighteed Majority Voting, Instead of treating each vote equally, weight each final answer by the confidence of the associated trace. For every candidate answer a, we define its total vote weight as:
V(a) = Ec. ((anwerr))))) a),
EET
where Ct is the trace-level confidence chosen from the confidence measures discussed above. We select the answer with the highest weighted vote. This voting scheme favors answers supported by high-confidence traces, thereby reducing the impact of uncertain or low-quality reasoning answers.
Confidence Filtering. We apply confidence filtering in addition weighted majority voting to control concentration on high-confidence reasoning traces. Confidence filtering selects the top-1) percent traces based on trace confidence, ensuring only the most reliable paths contribute to the final answer. We provide two options across all confidence measurements: 7 10% and 17 90%.
The top 10% option focuses on highest confidence scores, suitable when few reliable traces are ex- pected to yield accurate results. However, relying very few traces risks incorrect answers if the model exhibits bias. The top 90% option offers a more balanced approach, maintaining diversity and reducing model bias by including broader range of traces. This ensures alternative reasoning paths are considered, especially when confidence distributions tend to be uniform. Fig. provides illus- tration for confidence measurements and how offline thinking works with confidence. In addition, Alg. provides the details of the algorithm.
3.3 ONLINE THINKING WITH CONFIDENCE
Evaluating confidence during online thinking enables real-time estimation of trace quality during generation, allowing dynamic termination of unpromising traces. This approach is particularly valu- able in resource-constraing constrained environments or when quick responses are necessary. The lowest group confidence metric be effectively applied in this online setting. We can halt trace generation when token group confidence falls below a critical threshold, ensuring such traces would likely be excluded during confidence filtering.
5

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Published as a conference paper at ICLR 2026
Question: the
Online Generation
Offline Warmup
solutionsx.)
6,
Ce. >
Confidencd Fitering
Trace
100
whare
G₁
Coy S
sfforsome
stopping threshold
posttiun inneger
G,
Ca.
Trace
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Walt, ma double check previou resuits... thinkaggein obout
plpmmtoe trites ganuratedd by
again...r
takemindee
Figure 4: DeepConf during online generation.
We propose DeepConf-low and DeepConf-high. two algorithms based on lowest group confidence that adaptively stop generation and adjust trace budgets during online thinking. The approach in- cludes two main components: offline warmup and adaptive sampling.
Offiiee Warmup. DeepConf requires an offline warmup phase to establish the stopping threshold for online determination. For each prompt, generate Ninit reasoning traces (c.g.. Ninit 16). The stopping threshold is defined as: s = Percentilc1oo-p((CCC : i Twamup }), where T Tarmuu represents all warmup traces, C. is the confidence of trace and is the desired keeping ratio. Specifically, DeepConf-low uses top 10% (corresponding to the 90th percentile) and DeepConf- high uses top 7 90% (corresponding threshold ensures that during online generation, traces are terminated when their confidence falls below the level that retains the top 17% highest- traces from the warmup phase.
the 10th percentile) uniformly across all settings. This
Adaptive Sampling. In DeepConf, employ adaptive sampling across all methods dynami- cally adjust the number of traces generated based on problem difficulty (Xue et al. (202)). Difficulty assessed by consensus among generated traces, quantified by the ratio of majority vote weight (ā) to total vote weight Σ. V(a): 3 Σ. Viaj t is preset consensus threshold. If < т, the model does not reach consensus for the current problem, and trace generation continues until fixed trace budget
v(a)
met. Otherwise, trace generation halts, finalizing the answer with existing traces.
Since we use lowest group confidence, a sufficiently large warmup set yields an accurate estimate of the stopping threshold 8; consequently, any trace terminated online has group confidence < and would be excluded by the offline filter. Thus the online procedure approximates the offline sowest-group-confidencc policy, with accuracy approaching offline accuracy as Ninit increases (see Appendix C.2) We illustrate the online generation process in Fig. 4 In addition, Alg, provides the details of the algorithm.
4 EXPERIMENTS
4.1 EXPERIMENTAL. SETUP
Models. We evaluate five open-source reasoning LLMs from three model families: DeepSeek- 8E (uuo et al. 2025). Owen3-8B, Qwen3-32B (Yang al. 2025a), GPT-OSS-20B and GPT- OS5B120B (OpenAl, 2025). These models are recognized for strong mathematical reasoning and long-chain-of-thuugh performance, are fully open-source for reproducibility, and cover multiple parameter scales to test robustness. Complete generation hyperparameters and prompting templates are provided in Appendix
Benchmarks. We evaluate on five challenging datasets: AIME24 Art of Problem Solving 2024a b). AIME25 (Art of Problem Solving 2025a b). BRUMO25 bru 2025), HMMT25 (HMMT)
DeepSeck-SB refers the Qwen3-8B model distilled from the DeepSeck-RI (0528) model: https:// hnggrranfaee.ccd/pppeeeae/eeeeaa

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Published as a conference paper at ICLR 2026
Algorithm 1: Offline Thinking with Confidence
Impuls: Prompt I2, number of traces N. lilterigg threshold y, confidence meaurement ((t)
Inirialize trace set T <- 6, confidence set for i 1 to N do Generate trace t, for prompt P. calculate trace confidence C, = C(t+), and add (4,, (T, end for
Select tog- 9/ percent of traces hased on trace confidence C., compute V (a) for all answers a Final answer with highest weighted
arg max, V(a)
Algorithm 2: Online Thinking with Confidence (DeepCoof-lowwhighh
Inputs: Prompt
budget initial Nun. filtering threshold v) consensus threshold
Offline Warmup:
Perform Algorithm ! Jusing
Nii traces with lowest group confidence
Compute threshold x Percentilejon (Co, Ci, Phr.... -xx, 1) where we keep top-yff confident traces
Initialize trace set T +- (fo. E1.... .t.) get vote values (a) for all answers o, majority answer
Online Generation:
while (V(a) E. V(a)) < and [T] < B do do Generate nexi token i and calculate group confidence Ccs, for group G; Co; s: stop generating trace 1, otherwise: token trace
while geaerating
end while
Add trace to T. compute trace confidence Cz, update vote counts (()), and majority answer end while
return & and stop generation
2025), , and GPQA (Rein et al. 2024). The first four are high-difficully mathematical competition problems, while GPQA comprises graduate-level STEM reasoning tasks. All benchmarks are widely adopted in recent evaluations of top reasoning LLMs (e-g.. Grok-4 (xAI (005), Qwen3 (Yang et al., 2025a), GPT-5 (OpenAl 2025)) and featured in the MathArena leaderboard (Balunović et al. 2025).
Baselines. We adopt celficonsit (Wang et al. 2023) with majority voting as our primary base- line. Each LLM samples T' independent reasoning paths and selects the final answer via unweighted majority voting, as formalized in Sec. 3.2
Experimental Settings. For each problem, we establish a common sampling frame by pre- generating pool of 4,096 complete reasoning traces, serving as the foundation for offline and online evaluations. Offline experiments resample a working set of size K (c.g., K=512) from on each run and apply the specified voting method. Online experiments similarly resample working set to drive on-the-fly generation with early stopping, ensuring consistent sampling across methods.
We report four key methods: (i) Pass @1 (single-trace accuracy), (ii) Cons @ (unweighted majority- vote accuracy with K traces), (iii) Measure@K K (confidence-weiigheed majority-vote accuracy), and (iv) Measure+top-7$66 @ K, which retains the top 1/% traces by confidence within the sampled work- ing set before applying weighted majority voting (we use 1) E {10, 90})). The specific confidence measure varies by setting. We also report total generated tokens. All metries are averaged over 64 independent runs with fresh resampling; unless noted, tokens are counted end-to-end for all gener- ated traces, with early- early-terminated traces contributing only tokens produced before stopping.
For online evaluation, we instantiate DeepConf-low and DeepConf-high using Lowest Group Con- fidence (Eq. 6) with an overlapping window of 2,048 tokens. Each problem begins with - complete traces for offline warmup: we then set run-specific stopping threshold minkeTi Ct. where Tepp contains the top-percentile traces by confidence (1==10 for DeepConf-low, 9=90 for DeepConf- Sec. 3.3). During generation, traces whose current group confidence falls below are terminated early; completed traces are aggregated with confidence-weighted majority voting and generation stops adaptively once consensus or budget K is reached.
For offline evaluation, we benchmark three kinds of trace-level confidence from Sec. 3.1 (i) Average
Trace Confidence (Eq. 3). (ii) Bottom-10% Group Confidence (Eq. [5) and (iii) Tail Confidence over the last 2,048 tokens (Eq. 7). For each metric we report Measure K and Mcasure+top-176 % @ K with
M (10, 90), where the top-7/% cutoff is recomputed within the sampled set on every run (Sec. 3.2
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Table 1: Benchmarking confidence measurements in offline setting. Accuracy (%) reported. Cons@512 and mean @512 denotes majority voting and average mean confidence using 5 512 traces. All experiments are repeated 64 times.
Model
Dataset
Pass @
Cons @512
Mean @512
Bottom- 10 Conf
Tail Conf @512
@ 512
Retention Ratio
90%
10%
90%
10 %
AIME24
83.0
86.7
86.7
86.7
93.3
86.7
93.3
AIME25
76.9
82.3
82.3
81.0
87.5
81.3
87.4
DeepSeek-8B
BRUMO25
80.0
93.2
93.3
93.3
93.3
93.3
93.3
HMMT25
58.1
69.6
69.9
69.9
79.5
69.9
83,9
GPQA-D
62.8
72.5
72.5
71.2
70.6
72.8
74.0
AIME24
80.6
85.3
85.7
86.0
90.8
86.8
89.4
AIME25
71.7
80.1
80.0
80.1
80,2
80.1
80.2
Qwen3-32B
BRUMO25
78.0
93.3
93.3
93.3
93.3
93.3
91.2
HMMT25
51.9
63.3
63.3
63.2
63.3
63.4
62.9
GPQA-D
68.9
72.2
72.3
70.0
70.0
72.8
72.5
AIME24
91.9
96.7
96.7
96.3
96.5
96.7
97.4
AIME25
91.8
97.0
97.1
96.9
98.1
97.8
GPT-OSS-122 120B
BRUMO25
75.6
86.7
86.8
85.3
82,9
89.9
89.4
HMMT25
78.9
92.9
92,9
92.9
90.5
92,9
88.9
4.2 OFFLINE EVALUATIONS
We present offline results with three models on five datasets at voting size K-512 in Table We compare the following: Pass@1 single-trace accuracy; Cons@512 unweighted majority voting with 5 312 traces; Mean Conf@511 = confidence- wewieenneewwwwteedddd majority voting using average trace confidence (Eq. 3): Bottom- 10% Conf@ 512 and Tail Conf@ 512 confidence-weighted majority voting using (i) the mean of the lowest 10% group confidences (Fq. 5 and (ii) the mean confidence over the final 2k tokens (Fq. respectively. The 90%/10% subcolumns indicate the retention ratio in confidence filtering: we retain the top 17% highest-confidence traces within the sampled set before voting. For example, with K-512 and 1=1,% we keep approximately 51 traces for voting.
Overall, confidence-awarc weighting with filtering consistently outperforms majority voting (Cons@512) across most settings. Filtering with 10% yields the largest gains, with notable im- provements like DeepSeek-8B on AIME25 (82.3% + 87.4% and Qwen3-32B
AIME24 (85.3% + 90.8%); GPT-OSS- even reaches 99.9% on AIME25. Both local (Tail and Bottom- 10%) and global (Average Trace) confidence measures show promising results in identifying confident traces. However, filtering involves important trade-offs: while aggressive filtering 101) maximizes ac- curacy gains in most cases, it can sometimes hurt performance due model overconfidence on incorrect problems (e.g., GPT-OSS-120B) In such cases, conservative filtering (7-90%) provides safer option. Substantial improvements over pass @ I observed across all methods, confirming the value of ensemble approaches. Detailed confidence measure comparisons are in Appendix C.4
22.5
35.0
50.0
07.0
90.0
80.0
12
167
123
207
10: Veting Budget
157
Voting Budget
Veting Burget
Vettng Budget
Figure 5: Offline accuracy with Lowest Group Confidence filtering (DeepSeek-SB) on AIME24, AIME25, BRUMO25, and HMMT25. The 77% variant retains only the top 17% highest-confidence traces before wonfidencc--eiihtee majority voting.
We then show that Lowest Group Confidence is also effective. Fig. reports offline results using Lowest Group Confidence (Eq. 6 capture the least-confident token group (window size 2,048)
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within each trace. Within each sampled working set we retain the top 77% highest-confidence traces and then apply confidence-wend -eeihhtd majority voting. Across AIME24, AIME25, BRUMO25, and HMMT25 with DeepSeck-SB, retaining the top 1=10% yields consistent gains over the best curacy achieved by majority voting: +0.26 to +9.38 percentage points (average +5.27), and large improvements over single-trace (or no voting) accuracy (+10.26 +20.94 percentage points; aver- age +14300.. The conservative 17-00% setting matches or slightly exceeds the best majority-voting accuracy on all four datasets ( (+0.16 to +0.57 percentage points; average +0.29) while still provid- ing substantial improvements over single-trace accuracy (average +9.31). These results motivate the online variant: focusing on the least-confident segment reliably identifies traces with localized reasoning breakdowns, providing a strong signal for offline filtering and natural stopping criterion during online generation. Beyond these results, we ablate the retention rate v/ Appendix and present the full offline results in Appendix D
Table 2: Benchmark DeepConf in online setting. Accuracy (%) and tokens (x10*) at voting size budget 512 for Majority Voting and DeepConf (high/low).
Model
Dataset
Cons 512
DeepConf-high
DeepConf-low
Token
Acc
Token (4 %)
Acc
Token (A %)
Acc
AIME24
3.55
86.7%
1.45 (-59.0%)
86.7%
0.78 (-77.9%)
92.5%
AIME25
4.01
82.3%
2.37 (-40.9%)
81.4%
1.24 (-69.0%)
86.4%
DeepSeek-8B
BRUMO25
3.56
93.3%
2.17 (-39.2%)
93.3%
1.07 (-70.0%)
93.3%
HMMT25
4.49
69.8%
3.43 (-23.5%)
70.0%
1.60 (-64.4%)
77.6%
AIME24
2.00
84,8%
0.88 (-56.0%)
86.4%
0.66 (-66.8%)
89.5%
AIME25
2.43
80.1%
1.61 (-33.7%)
80.2%
1.14 (-52.9%)
80.2%
Qwen3-32B
BRUMO25
2.17
93.3%
1.37 (-37.1%)
93.3%
0.96 (-55.7%)
92.4%
HMMT25
2.76
63.4%
2.24 (-18.8%)
63.6%
1.55 (-43.8%)
64.5%
AIME24
2.66
96.7%
1.20 (-54.6%)
96.7%
0.53 (-79.9%)
97.0%
AIME25
3,23
97.1%
1.42 (-56.0%)
97.0%
0.49 (-84.7%)
97.9%
GPT-OSS-120B
BRUMO25
2.68
83.8%
1.81 (-32.6%)
84.0%
0.73 (-72.8%)
83.4%
HMMT25
4.09
92.8%
2.78 (-32.0%)
93.0%
0.97 (-76.2%)
92.0%
4.3 ONLINE EVALUATIONS
We evaluate accuracy-cost trade-offs of the online algorithm by varying the budget E (32, 64, 128, 256, 512), where cost counts all generated tokens, including partial tokens from early- stopped traces. Following Sec. 3.3 we perform a warm-up with Nmna=16 traces to set the stopping threshold using Lowest Group Confidence (LGC) of window size 2k: we set over the top-7/% warm-up traces by confidence (1) E (10, 90}} and then terminate any new trace once its current group confidence drops below After each new trace completes,
reapply the same threshold for filtering so that the procedure matches the offline version of LGC filter while saving the cost of early-stopped traces. We consider two online variants: DeepConf-low (1)=1%% and high (7=90%)) which continue sampling until the consensus 2 (we use r=0.95) or the budget cap K is reached. We compare with budget-only variants (always running to cap H) and more in Appendix C.
Table 2 shows the performance of the adaptive sampling version of DeepConf at the voting-size budget of K 5122 on DeepSeek-8B, Qwen3-32B, and GPT-OSS--20B. Compared with the majority voting baseline, DeepConf-low reduces tokens by 43-79% across AIME24, AIME25, BRUMO25, and HMMT25. While matches or improves accuracy in most cases (e.g.. DeepSeek-Sa 8B AIME24: +5.8%), it experiences accuracy drops in a few settings (e.g., Qwen3-32B BRUMO25: -0.9%). The more conservative DeepConf-high saves 18-59% tokens on these sets while maintaining ac- curacy incurring only minimal performance degradation. Fig. 6 visualizes the token reduction patterns for GPT-OSS-1200 showing how DeepConf achieves substantial computational savings (i.e., up to 85.8%) while preserving competitive accuracy across different math reasoning tasks.
Fig. compares DeepConf with majority voting on DeepSeek-8B. DeepConf methods show clear efficiency advantages while maintaining equal accuracy: DeepConf-low achieves token savings of 62.88% and DeepConf- 47.67% compared to the majority voting at the same accuracy levels. In terms of performance, DeepConf's behavior mirror the offline setting: 10% (low) filtering yields

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the highest accuracy gains in most cases, though it may occasionally result in accuracy drops specific datasets (e.g., GPT-OSS- 120B on HMMT25 in Table 2). These results support our design: using the least-confident segment to gate traces provides strong, local signal for early stop, and the adaptive consensus stop further saves tokens without sacrificing accuracy. Besides, we provide an
ablation of the warm-up size Ninit in Appendix C.2 and the full online results in Appendix F
Token Courte te 305
AIMEZ4
AIMEZ5
BRUMO25
HMMT22
1-12
1.01
2.78
(-70.0%
0.53
654.6%)
0.40
143 (36.0%1
(72.8%)
97
Figure 6: Generated tokens comparison across different tasks based GPT-OSS-120B
AIME24
AIME25
BRUMO25
HMMT FEB25
92.6
20.0
92.0
62.0
#Tokons (2
#Tokens (1c8)
TTokees (1c8)
DespContion
DespConi-ign
Majorit telling
Figure 7: Accuracy vs. generated tokens for online Lowest Group Confidence filtering (DeepSeek- 8B) on AIME24, AIME25, BRUMO25, and HMMT25. High/low means keeping the traces with top 90%/10% confidence for voting.
5 RELATED WORK
This section focuses on confidence estimation, which is most central our approach. For a broader review of literature test-time scaling and efficient reasoning, please refer to Appendix A Confi- dence estimation techniques offer a complementary direction by directly quantifying the reliability of model outputs. A growing body of work proposes metrics such as token-level entropy and uncer- tainty scores (Fadeeva et al. 2024), self-certainty based on KI. divergence from a uniform distribu- tion (Kang et al. and specialized confidence tokens leamned during fine-tuning (Chuang al., 2024). In the same spirit, Dynasor (Fu et al. 2024) uses semantic entropy (Farquhar et al., 2024) as confidence signal. These signals have been applied to re-ranking (Jain et al.) 2024), selective generation (Ren et al., 2023). and abstention in high-stakes domains (Han et al., 2024). ) and they consistently exhibit better calibration than raw sequence probabilities (Geng et al.) 2024). Waag & Zhou (024) applies confidence at the answer position to elicit model reasoning ability without prompting. Recent work further employs various confidence metrics as reward signals for reinforce-
ment learning (Zhao et al. 2025 Zuo et al. 2025) (Zhang et al.) 2025 Prabhudesai et 2025 Gao ctt al., 2025) Agarwal et al. 2025), , showing improved model performance. Yang Holtzman| (2025) note that entropy drops late in generation, and earlier branching yields higher quality samples.
Integrating confidence into test-time reasoning provides a way to assess the quality of individual traces before aggregation. Recent results with global confidence, which is computed at the sequence level and applied post hoc to rank or select among completed candidates, show that combining multi-sample reasoning with confidence-
selection can outperform majority voting while using fewer generated tokens (Kang et al.) 2025). In contrast, DeepConf relies on a lightweight local confidence signal that is updated along each trajectory and triggers only-the-fly pruning of low- confidence traces, yielding more token-efficient parallel generation and higher accuracy.
CONCLUSION
We present DeepConf, a simple yet effective method that significantly enhances both reasoning performance and computational efficiency in ensemble voting scenarios. Through extensive exper- iments across state-of-the-ait reasoning models and challenging datasets, DeepConf demonstrates substantial accuracy improvements while achieving meaningful token savings, with consistent ben- efits observed across model scales from 8B to 120B parameters. We hope this method shows the potential of practical and scalable solution for efficient L.M reasoning.
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7 ACKNOWLEDGMENTS
This work was primarily conducted during Yichao Fu's internship at Meta FAIR. We gratefully acknowledge the Meta FAIR team for providing the essential computational resources and infras- tructure that made this research possible. We also thank the open-source community for developing and maintaining the foundational models and serving frameworks utilized in our experiments.
REPRODUCIBILITY STATEMENT
We provide full implementation details to facilitate reproduction. Section presents complete al- gorithmic descriptions with pseudocode (Algorithm 222 All hyperparameters are documented in Tables II 12 (Appendix [G), including model-specific generation settings, warmup configurations, and filtering thresholds. Source code with detailed vI..M integration instructions is available at and supplementary materials. Experimental pro- tocols, including 64-run repetitions and evaluation procedures, are detailed in Section 4.1 Dataset sources and prompt templates are specified in Section 4.1 and Appendix G
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A EXTENDED RELATED WORK
A.1 TEST TIME SCALING
Current LLMs increasingly succeed by allocating very large amounts of reasoning at inference, a paradigm we call test-time scaling (Snell et al. [024] Welleck al. 2024). Along one axis, Chain- of-Thought (Wei et al. 2022) depth is scaled by lengthening a single reasoning trajectory through more thinking steps; representative models include ol (Jaech et 2024), DeepSeek RI (Guo al. 2025). Kimi K1.5 (Team et al. 2025), Qwen3 (Yang et al. 2025a), and Grok-4 (xAl 2025), which typically rely on large-scale RL with lots of samples, as well as simpler fine-tuning approaches such as STILL-2 (Min et al. 2024), s [Muennighotf et al. 2025). and LIMO (Ye et al. 2025). Along complementary axis, parallel generation scaled by increasing the number of trajectories and aggre- gating them: Self-Consistency (Wang et al., 2023) and Best-of-N (Brown al. 2024 Irvine al., 2023) sample multiple candidates and select via voting or a score, while REBASE (Wu et al. 2024) expands breadth with tree- strustrrut exploration. To optimize these allocations, DVTS (Beeching al.) and DORA (Wang et al. (225c)) introduce adaptive PRM-guided search and direction strategies to maximize accuracy under fixed compute budgets. Chen et al. (2024a) analyze parallel generation in compound Al systems. These two axes can be combined to trade compute for accuracy under deployment constraints, and they underpin many recent reasoning- systems.
A.2 EFFICIENT REASONING
Test-time scaling for reasoning seeks better accuracy-compute trade-offs through adaptive sampling and richer aggregation. On the parallel axis, Early-Stopping Self-Consistency (ESC), Didaiiulty-Adaptive Self-Consistency (DSC), Reasoning-Awan Self-Consistency (RASC), Adaptive-Consistencyy Dynamic Voting, and Dynasor achieve more efficient self-consistency by reducing the required sample count while preserving accuracy (Li et al. 2024; Wan et al. 2025 Aggarwal et al. 20233 Xue et al. 2023] Fu et al.) 2024; Wang al.] (025b). On the Cee-h axis, efficient CoT fine-tuning methods elicit shorter, more efficient chains (Chen et al. 2024b Luo et al., 2025 Hou al. 2025), whereas Dynasor-CoT (Fu al.) 2025) and DEER (Yang al., 2025b) optimize inference without additional training. Other works refine aggregation: ranked vot- ing (Wang et al., 2025a) collects ranked candidate lists for more nuanced preference aggregation, liklihhoddweiihhee scoring (Soft-SC) (Wang et al. 2024) leverages model probabilities when no single answer dominates, and verffcatioonaugmmented voting filters logically inconsistent paths using external tools (Toh et al.] 2024). Complementarily. |Hassid et al. (2025) show that preferring shorter CoT chains among multiple samples can improve accuracy. DeepConf leverages local confidence to improve accuracy by filtering out low-confidence traces; in online generation, it further performs early termination when local confidence drops below threshold, reducing token usage.
B FUTURE WORK
We believe several promising directions emerge from this work. First, extending DeepConf to inforcement leaminng settings could leverage confidence-basee early stopping to guide policy ex- ploration and improve sample efficiency during training. Second, addressing cases where models exhibit high confidence on incorrect reasoning paths, which a key limitation observed in our ex- periments. Future work can also explore more robust confidence calibration techniques and uncer- tainty quantification methods to better identify and mitigate overconfident but erroneous predictions.
C ABLATION STUDY
C. ABLATION ON CONSENSUS THRESHOLDS
We ablate the consensus threshold in online Algorithm 2 using budget-only (not using (V(a)/E. V(a)) < T to do early stopping) as baseline in Table 3 warmup traces, check modal agreement before each new trace generation and stop generat- ing more samples for this problem the agreement exceeds т. We evaluate on Qwen3-32B with AIME24. 7=0.95 achieves optimal balance: it preserves accuracy exactly while saving
After generating N1
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15.4% tokens at B = 32/512 (DeepConf-low) and 22.0% (DeepConf-hipp highh. Conser- vative r=1.0 weakens savings without accuracy drop. More aggressive thresholds (T=0.90, 0.85) increase savings up to 69.6% but cause accuracy drops in DeepConf-low (e.g.. - -0266pp at 0=0900, while DeepConf-high maintains perfect accuracy even at r00-55, showing greater robustness. Be- cause DeepConf-high already retains a larger pool of traces by design, changing т has a smaller influence on the final vote. Besides, Token savings are larger at B = 512 than at B = 32 because adaptive stopping only applies after the Ninit 16 warm-up traces. At B 512 it can truncate up to the remaining 496 generations, whereas at B = 32 it can eliminate at most 16. As a result, the same rate of early terminations translates into far greater relative token reductions at higher budgets. Overall, 0-0.95 offers the best tradeoff, cutting tokens by over half with zero accuracy loss.
Table 3: Ablation on adaptive thresholds (Qwen3-32B @ AIME24). We report accuracy and token
usage at voting budgets B {32, 512). Accuracy deltas percentage points (p.p.) and token deltas are percent changes, both measured relative to the budget-only bascline (no adaptive early stopping) the same B. Token counts are shown in scientific notation.
B 32
B 512
Accuracy (A p.p.)
Tokens (A %)
Accuracy (A p.p.)
Tokens (A %)
Baseline
87.50%
1.23e7
86.35%
1.94e8
1.0
87.50% (+0.00)
1.03e7 (-16.5%)
86.35% (+0.00)
1.29e8 (-33.4%)
High
0.95
87.50% (+0.00)
9.59e6 (-22.0%)
86.35% (+0.00)
8.79e7 (-54.7%)
0.90
87.50% (+0,00)
8.88c6 (-27.7%)
86.35% (+0.00)
7.13e7 (-63.2%)
0.85
87.50 (+0.00)
8.39e6 (-318%%
86.35% (+0.00)
6.01e7 (-69.0%)
Baseline
87.92%
1.05e7
89.48%
1.40e8
1.0
87.92% (+0.00)
8.97e6 (-15.0%)
89,48% (+0.00)
8,94e7 (-36.3%)
Low
T 0.95
87.92% (+0.00)
8,92e6 (-15.4%)
89.48% (+0.00)
6.62e7 (-52.8%)
0.90
87.66% (-0.26)
8.13e6 (-22.9%)
89.43% (-0.05)
5,14e7 (-63.4%)
0.85
87.45% (-0.47)
7.75c6 (-26.5%)
89.17% (-0.31)
4.26c7 (-69.6%)
C.2 ABLATION ON WARMUP SAMPLING SIZF.
Table 4 compares warmup sizes Ninit E {8, 16, 32} with the budget-only online DeepConf method voting budget B 512 under the DeepConf-low setting (top 1/ 10% by confidence). Across models and datasets we observe that: Increasing Nmn stabilizes the empirical confidence distribu- tion used set the threshold s and, in practice, generally makes online accuracy closer the of- fline baseline (smaller Acc)): however, the threshold-accurade relationship is model- and dataset- dependent and need not improve monotonically. On tokens, the net effect driven by two forces: (i a larger fixed warm-up cost because all Nini traces run to completion and (ii) the post-war warm-up carly-termination
rate over the remaining Bi traces. As these forces trade off, total token us- age is also not necessarily monotone in Numi- Empirically, |ACc across warm-up sizes is small (typically < 1.0 p.p.). We therefore adopt -16 as a balanced default: sufficiently close to the offline baseline while avoiding excessive warm-up overhead.
C.3 ABLATION ON FILTERING PERCENT.
Table 5 investiggaee the effect of varying the keeping percentage for filtering method using Lowest Group Confidence metric (group size 2,048). The retention ratio sweeping from top 90% to top 10%. For each model-dataset pair, we sweep voting sizes E (1...., 512) in the offline setting and report the best accuracy attained. Across DeepSeck-8B, Qwen3-8B, and Qwen3-32B, more ag- gressive filtering (smaller top percentages, retaining fewer traces) generally yields higher accuracy in most cases, though the optimal 7) can vary by dataset. For instance, top 10% frequently achieves the best performance, but top 25% or top 50% may be optimal for certain model-dataset combina- tions, indicating that the ideal filtering threshold depends task characteristics. Mechanistically, the filter preferentially discards low-confidence (and often incorrect) traces, concentrating the vote on higher-confidence evidence and thereby improving accuracy average.
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Published as a conference paper at ICLR 2026
Table 4: Impact of warmup size Nini fixed voting budget B 512 (online, DEEPCONI-LOW).
Each online cell reports Accuracy (%) with A in p.p. and Token usage (x10²) with relative A in %, both described as relative to the offline baseline B 512 (keep top 1j = 10%: lowest group confidence). Boldface marks the warm-up size whose online accuracy is closest to the offline baseline (smallest |AAco]. The last column, labeled Offline, reports the baseline (Accuracy/ Token) at B 512.
Model
Dasaset
Nui
Nan
Nuii
Offline
AIME24
92.2% /1 (-54,99)
92.5% (488/151 (-57.4%)
92.9% 1.54 (-57.1%)
93.3%
AIME25
86.0% (-1.4) (:51.75%)
56.4% (4091/ 1.85 (-53.8%)
86.7% (-0.7) (-538%)
87.3% 74.01
DeaySerk-8R
BRIMOSS
93.3% (+0.0) 1.63 (-54.1%)
93.15 (-0.0/ 1.55 (-56.5%)
93.4% (40.1)/ 1.54 (:56.9))
93.3% 3.55
GPOA
7188% (-0.1)/490 (1)///33335))) (-50,39%)
71.7% (40.2)4.75 (-52.1%)
71.9% (-0.0) /478 (-51.8%)
71.9% 1996//9.99 19.92
HMMT22
76.8% (-2.2)/2.05 (:54,498)
77.6% (-1.51/191 (457.498)
78.2% (-0.S) 1,89 (-57.8%%
79.0% /4.49
AIME24
89.2%
(.0.)/1.433 (-28.22))
89.5% (-061/1400 (:2,775))
90.1% (-0.1) (.31)/1199930..... (-30.2%)
90.1% /2.00
AIME22
1.72 (-29.2%)
(-0.01/
80.1% (-0.1) (:30.75))
80.2% /2.43
Qwen3-332 32B
BRUMOS5
92.8% (+0.1) 1.53 (-29.5%
92.45 (-0.3) (:31,499)
92.4% (-0.3) (:31,49)
92.8% /2117
GPOA
72.9% (+0.31/5.87 (:21.11)
73.0% (-0.31 5,77 (:22.616)
72.9% (+0.2) (.72)///5//4299990/ (-22.9%)
72.71% 77.44
1IMMT25
63.4% (+1.0)/ (-29.%)))
64.5% (-0.8) 1,90 (-3.3%)
64.6% (+0.2) (-31.5)))
64.4% /
ATME34
86.5% (-0 (..52//1.533344.
86.5% (40.2) /1 (-35,39)
8677%
(-0.1)1.51 (-35.9%)
86.7% 2.332
ATMF25
(-33.99))
(-0.2) 1.78 (-35.6%)
78.29
(-35.39)
77.9% /2.77
Qwen3-8B
BRUMOSS
(+0.2)/ 1.67 (-34,4%)
82.7% (-0.3)/ 1.63 (-35.9%)
82.9% (+0.5) 1.63 (-36 196)
82.4% 22.54
GPQA
65.1% (-0.4)/499
/4-92 (-34.19))
65.25 25 (-0 3) 4.822 (-35 (-35.5%)
65.3% (-0.2) 4,81 (-35.5%)
65.5% 77.47
HMMT35
62.3% (-0.8) 1158 (-36,258)
62.7% (-04)/ 1154 (-33.55%)
630% (-0.3) / 1,94 (-37.5%)
63.15%73.30
Table 5: Best accuracy (%) across different filter sizes using Lowest Group Confidence with group
size 2048
Model
Dataset
Maj-
Top900
Top75
Top50
Top25
TTop10
AIME24
86.7%
87.2%
87.7%
88.9%
91.8%
93.3%
DeepScek-8B
AIME25
82.6%
82.7%
82.8%
83.6%
85,9%
87.4%
BRUMO25
93.2%
93.3%
93.3%
93.3%
93.3%
93.4%
HMM125
69.6%
69.9%
70.3%
73.4%
75.4%
AIME24
81.4%
82.1%
82.2%
84.9%
86.9%
86.7%
Qwen3-8B
AIME25
82.6%
82.7%
81.8%
79.5%
79.4%
77.9%%
BRUMO25
81.5%
81.8%
82.3%
83.3%
83.3%
82.4%
HMMT25
60.15
60.3%
60.2%
60.6%
61.6%
63.1%
AIME24
87.8%
88.3%
88.9%
88.9%
89.1%
90.2%
Qwen3-32B
AIME25
80.5%
80.4%
80.5%
81.0%
81.5%
80.9%
BRUMO25
93.3%
93.3%
93.3%
93.3%
93.3%
92.8%
HMMT25
63.4%
64.0%
64.5%
66.7%
67.3%
64.4%
C.4 ABLATION ON CONFIDENCE METRICS
In this offline ablation, we report the accuracy at voting size B- = 512 for each model-dataset pair (Tables 6 7 g and 9). We compare aggregation rules that differ only in how they compute per-trace confidence score and whether they do filtering before voting. Maj. represents standard majority voting without confidence weighting. Mean computes the average trace confidence over the entire trace and uses it weight votes. L(w) denotes Lowest Group Confidence with group size w. B(q%) represents Bottom Percent Confidence, which retains the bottom 4% least confident groups and computes the average confidence from these selected groups for voting weights. For positional confidence computation, Hcad(q%) calculates confidence using only the first 9% of tokens in each trace, while Ta) computes confidence from the last 9% of tokens. Tail(2k) uses fixed window of the last 2,048 tokens regardless of the total trace length. The @17% suffix indicates filtering mechanism that retains only the top 17% of traces ranked by confidence before applying the respective voting method. For example, Mean @ 10% first selects the top 10% most confident traces and then applies wewffiennce-eeighie voting, while Tail 990% keeps the top 90% of traces based on tail confidence before voting.
Across models and datasets, head-based confidence has weak correlation with final correctness and typically matches plain majority voting; applying head-based filters even hurts average, reflecting that early tokens are dominated by setup, paraphrase, and exploratory planning with little discrimina- tive signal. By contrast, tail- and based signals frequently yield gains. Notably, on DeepSeek- 8B AIME25, a tail variant reaches 89.6% with only an 8B model, and on GPT-OSS- 120B AIME25, TTil((k) @ 10% attains 99.9%. Conceptually, the Lowest Group Confidence (LGG)) metric is an ex-
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Published as a conference paper at ICLR 2026
treme case of Bottom-Perree Perceet confidence (it takes the minimum sliding groups), yet remains competitive: over 23 model-dataset pairs, LGC (2k window) with a 10% filter averages 84.4%, compared to 84.0% for Bottom-109 @ 10% and 84.0% for Bottom-50% @ 10%, and higher than Mean 10% at 83.9%. Tail-focused variants are especially reliable defaults, with Tail(10%) 10% and Tail(2k) @ 10% averaging 84.6% and 84.5% respectively. Overall, local confidence signals, in- cluding tail, bottom, and lowest, are not inferior to global average trace confidence and, on average, deliver equal or better accuracy across settings.
Table 6: Accuracy (%) at voting size 512. Maj.=majority; Mean: average trace confidence;
@ @re=keep top 77% by confidence. Head (10%): first 10% tokens.
Model
Datasct
Maj.
Mean
Mean 85 10
Meane
Head (10%)
Head (10%)Ø
Head (10%)]990
AIME24
86.7%
86.7%
93.3%
86.7%
86.7%
86.7%
86.7%
AIME25
82.3%
82.3%
88.6%
80.7%
82.2%
81.1%
80.9%
DeepSeck-8B
BRUMO2S
93.2%
93.3%
93.4%
93.3%
93.2%
91.2%
93.2%
HMMT25
84.3%
69.6%
GPQA
72.5%
72.5%
71.6%%
72.7%
72.5%
70.7%
72.5%
AIME24
80.1%
80.1%
86.7%
80.5%
80.1%
80.5%
80.0%
AIME25
82.66%
82.7%
74.0%
82.1%
82.7%
73.8%
82.4%
Qwen3-8B
BRUMO25
80.9%
11.0%
82.9%
81 9.9
80.95 9%
82.3%
80.9%
HMMT25
60.0%
60.0%
62.2%
60.0%
60.0%
59.2%
60.0%
GPOA
63.8%
63.8%
63.9%
64.3%
63.8%
63.6%
64.1% 14.1%
AIME24
85.3%
85.7%
93.2%
86.5%
84.1%
86. 1%
AIME25
80.1%
80.0%
82.0%
80.0%
80.1%
77.4%
80.2%
Qwen3-32B
BRUMO25
93.3%
93. 3%
93,
93.3%
93.3%
92.6%
93,2
HMMT25
63.3%
63.3%
62.4%
63.3%
63.3%
59.0%
63.2%
GPQA
72.2%
72.3%
73.3%
72.6%
72.2%
72.2%
72.2%
AIME24
96.7%
96.
90.7%
96.7%
V6.75
96.7%
96.7%
AIME25
95.3%
95.3%
94.0%
94.8%
95.4%
94.9%
94.8%
GPT-
BRUMO25
87.3%
87 47.4%
87.7%
87.5%
87 87.3%
88.2%
87.4%
HMMT25
89.9%
89.7%
86.5%
89.2%
89.9%
89.0%
89.7%
AIME24
96.7%
96.7%
96.7%
96.7%
96.7%
97.7%
96.7%
GPT-OSS-1208
97.0%
97.9%
97. 97.9%
97.1%
BRUMO25
86.7%
86. 8%
85.7%
87.6%
86.7%
85.9%
86.7%
HMMT25
92.9%
92.9%
80.3%
93.0%
92.9%
90.6%
93.0%
Averuge Acc.
83.0%
83.0%
83.9%
83.1%
83.0%
81.9%%
82.9%
Table 7: Accuracy (%) at voting size = 512. @y=keep top 17% by confidence. Tail (2k): last 2,048 tokens; Tail (10%): last 10% tokens.
Model
Dutaset
Tail (10%)
Tail (10%)@ 10
Tail (10%) 90
Tail (2k)
Thil (2k) (13))110
Tail (2k)@90
AIME24
86.7%
93.3%
86.7%
86.7%
93.3%
86.7%
81.6%
DeepSeck-8B
BRUMO25
93.3%
93.3%
93.3%
93.3%
93.3%
93.3%
HMMT25
69.9%
84.0%
69.9% 9%
69.9%
83.9%
69.9%
GPQA
72.8%
72.7%
72.8%
AIME24
80.3%
87.1%
80.7%
80.4%
86.7%
80.7%
AIME25
82.8%
75.6%
82.9%
82.7%
75.7%
82.7%
Qwen3-8B
BRUMO25
80.9%
81.6%
81.6%
80.9%
81.4%
81.5%
HMMT25
60.0%
64.1%
60.0%
60.0%
63.8%
60.0%
GPQA
63.9%
64.1%
64.2%)
63.8%
65.7%
64.44%
AIME24
86.0%
12.1%
87.1%
85.9%
89.4%
86.8%
AIME25
80.0%
86.6%
80.1%
80.0%
80.2%
80.1%
Qwen3-32B
BRUMO25
93.3%
92.1%
93.3%
93.3%
91. 2.%
93.3%
HMMT25
63.4%
62.7%
63.4%
63.4%
62.9%
63.4%
GPQA
72.3%
73.2%
72.7%
72.4%
72.5%
72.8%
AIME24
96.7%
96.7%
96.7%
96.7%
96.7%%
96.7%
AIME25
95.5%
94.7%
95.7%
95.7%
95,9%
96.1%
GPT-OSS-200
BRUMO25
87.3%
88.0%
87.1%
87.3%
84.6%
87.1%
HMMT25
89.7%
85.3%
89.9%
88.2%
89.8%
AIME24
96.7%
97.4%
96.8%
96.7%
97.4%
96.7%
AIME25
97.3%
99.4%
97.6%
97.4%
99.9%
97.8%
GPT-OSS-120B
BRUMO25
87.9%
85.6%
89.9%
89.4%
89.9%
HMMT25
92.9%
87.4%
93.1%
92.9%
88.9%
92.9%
Average Acc.
83.1%
84.6%
83,4%
83,2%
84.3%
83,3%
D SCALING BEHAVIOR FOR OFFLINE DEEPCONF
The offline method applies confidence filtering followed by confidence-weightee majority voting
(Sec. 3.2 under two retention settings using Lowest Group Confidence. We evaluate across 5 model
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Table Accuracy (%) at voting size 512. Maj. majoortty L(x)=Lowest Group Confidence with sliding window of tokens; @n keeps the top 17% by the Lowest-confidence.
Model
Dataset
L(ST2)
L(K)
L2K)
L(512)e
L(KK)er
L22Ke
L@2K)
AIME24
86,7%
7%
86. 7%
86.7% 7%
92.8%
93.1%
93.3%
86.7%
AIME25
82.3%
82.2%
82.3%
82.2%
86. 9%
87.1%
87.3%
81.0%
DeepSeck-SB
BRUMO25
93.2%
93.3%
93.3%
33.3%
33.3%
93.3%
93.3%
93.3%
HMMT25
69.6%
69.9%
69.9%
69. 99.
77.3%
77.8%
79.0%
69.9%
GPQA
72.5%
72.5%
72.5%
72.5%
71.7%
71.7%
71.9%
72.5%
AIMEZ4
80.1%
80. 156
80.1 %
80.1%
86. 7%
86.7%
86.7%
80.3%
AIME25
82.6%
82.7%
82.7%
82.6%
74.2%
76.6%
77.9%
82.7%
Qwen3-8B
BRUMO25
80.9%
80.9%
80.9%
80.9%
81.9%
82.3%
82.4%
81.5%
HMMT25
60.0%
60.
60.0%
60. 0%
62, 8%
63.
63.
60.0%
65.5%
AIME24
85.3%
35.3%
85.2%
85.6%
87.3%
86.8%
90.1% 1%
86,218
AIME25
80.1%
80.0%
80.0%
80.0%
78.5%
82.6%
80.2%
80.1%
Qwen3-32B
BRUMO25
93.3%
93.3%
93.3%
93.3%
92.8%
93.3%
HMMT25
63.3%
63.3%
63.4%
63.4%
62.6
64,7%
64.4%
63.44%
GPQA
72.2%
72.3%
72.4%
72.4%
73.5%
72.8%
72.7%
72.8 72.8%
AIME24
96.7%
96.7%
76.7%%
96.7%
93. 33.3%%
93.3%
95.
96.7%
AIME2S
95.3%
95.4%
95.4%
95.4%
66.2%
96.2%
96.0%
95.5%
GPT-OSS-20B
BRUMO25
87.3%
87.3%
87.3% 3%
87.3%
67.6%
87, 4%
87.6%
87.4%
HMM125
89.9%
89.8%
89 8%
89. 9%%
90.1 1%6
90.2%
89. 89.5%
89. 99.9%
AIME22
96.7%
96.75
99.7%
97.2%
96.7%:
AIME25
97.0%
97.0%
97.0%
9%
97.44%
97.8%
98.0%
97.0%
GPT-OSS-1200
BRUMO25
86.7%
86.7
86.8%
86.8%
85.5%
86.3%
85.8%
86.8%
HMMT25
92.9%
92.9%
93.0%
92.9%
92.6%
92.0%
92.0%
93.1%
Average
83.0%
83.0%
83.0%
83.0%
83.5%
84.0%
84.4%
83.1%
Table 9: Accuracy (%) at voting size 512. Maj.=majority;
confidence
within a 2,048-token sliding window; @1) keeps the top 17% by the Bottom-confidence.
Model
Dataset
Maj.
@(10%)
B(10%)@00
B(10%)
((50%)
B(50%)
B(50%)
AIME24
86.7%
93.3%
86.7%
86.7%
93.3%
86.7%
86.7%
AIME25
82.3%
87.5%
81.0%
82.2%
88 4%
81.1%
82.2%
DeepSeck-8B
BRUMO25
93.2%
93.3%
93.3%
93.3%
93.3%
93.3%
93.3%
69.6%
GPQA
72.5%
70.6%
71.2%
72.2%
71.4%
72.3%
72.5%
AIME24
80.1
86.7%
80.3%
80.1 1%
86.7%
80.4%
80.1
AIME25
82.6%
76.4%
82. 7%
82.7%
74.3%
82.6%
82.7%
Qwen3-8B
BRUMO25
80.9%
83.3%
81.8%
80.9%
83.0%
82.1
81.0%
HMMT25
60.0%
63.2%
60.0%
60.0%
62.6%
60.0%
60.0%
GPQA
63.8%
62.7%
60.8%
63.4%
64.1%
63. 33.
63.6%
AIME24
85.3%
90.8%
86.0%
85.5%
92.8%
86.2%
85.7%
AIME25
80.1%
80.2%
80.1%
80.0%
80.2%
80.0%
80.0%
Qwen3-32B
BRUMO25
93.3%
93.3%
93.3%
93.3%
93.3%
93.3%
93.3%
HMM125
63.3%
63.3%
63.2%
63.4%
62.4%
63.3%
63.3%
GPQA
72.2%
70.0%
72.3%
72.5%
71,90
AIME24
96.7%
96.5%
96.5%
96.6%
96.6%%
96
96.7%
AIME25
95.3%
95.01
95.2%
95.3%
94, 11%
95.1
95.
GPT-OSS-20B
BRUMO25
87.3%
87.5%
86.6%
88.0%
HMMT25
89.9%
89.8%
89.8%
AIME24
96.7%
96.5%
96.3%
96.615
96.6%
96.6%
96.6%
AIME2S
97.0%
98. 1%
96.9%
97.0%
98.4%
97.4
97.1%
GPT-OSS-120B
BRUMO25
86.7%
82.9%
85.3 35.3%
86.4%
85.1%
86.7%
86.7%
HMMT25
92.9%
90.5%
92.9%
92.9%
84.8%
93.0%
92.9%
Average Acc.
83.0%
84.0%
82.6%
83.0%
84.0%
83.0%
83.0%
totaling 20 experimental settings, and for each method we vary B {1..... 512]. The results are presented in Fig.
configurations and 4 datasets (AMM22WALMEE21BRUUOSSHHM
Keeping Top 90% consistently matches or slightly outperforms unweighted majority voting with low variance (-0.21% ~ +0.73% avg. +0.17%).
Keeping Top 10 % yields notable gains on most datasets (12/20 settings; +0.26% ~ +9.38%), with
drops the remaining eight (-4.99% -0.31%); the overall average improvement is +1.22% These regressions arise from rare cases where confidence concentrates on an incorrect answer ("con- fidently wrong").
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Both settings substantially outperform the single-sample baseline (B=1;ie. voting): Top 90% delivers consistent margins (+3.83% ~ 16.88%, avg. +10.57%), while Top 10% provides even larger gains (+5.26% +20.94%, avg. +11.62%).
Overall, Top 90% is safe choice when stability is paramount, whereas Top 10% offers higher aver- age performance with occasional regressions. These results demonstrate the reliability of the offline method using Lowest Group Confidence across diverse model scales and mathematical reasoning benchmarks. We additionally report results on GPQA-Diamond in Appendix
AIME24
AIME25
BRUMO25
HMMT. FEB25
860
Despseck-R1
92.5
01.0
91.
913
8235
55.0
85.0
37.5
60.5
81.
50.
Qwen3-c 88
83.0
00.0
75.3
13.0
16.5
730
15.0
Qwen3-328
873
60.3
825
80.0
GPT-SS--2008 GPTOSS-2088
87.5
02.0
250
81.0
75.0
121
12'
20
30'
202
15"
10'
107
18
05.0
00.0
85.0
46.3
94.0
93.
02.0
75.
20.
123
127
10'
70
15
107
Voiing Budget
Voling Budget
Voslng Budget
Wiing Badgel
Keep Tpp
Majorty by Vesing
todrg
Figure 8: Scaling behavior: Models's Accuracy vs voting size for different methods on different models and datasets using offline method with Lowest Group Confidence
E SCALING BEHAVIOR FOR ONLINE DEEPCONF
We evaluate accuracy-cost trade-offs in an online setting in Fig. 9 where cost counts all generated tokens, including partially generated tokens from carly-stopped traces. Each problem warm- uped with Wimit=16 traces to calibrate the consensus threshold 7 (Sec. 3.3): We set to the 90th percentile for the DeepConf-low (top-10%) setting and the 10th percentile for the DeepConf- high (top-90%) setting; trace is stopped on the fly once its current group confidence falls below 7. Aggregation over completed traces always uses confidence filtering plus srafidence-weighhee majority voting. We compare DeepConf with majority baseline at two perspectives.
At matched budget. We compare the adaptive DeepConf-high and DeepConf-low with majority voting at the voting budget of 512 in TT) Across models and datasets, DeepConf-lowe yields the largest cost reductions, which is about 43-84% fewer tokens than majority voting at B=512, while usually matching improving accuracy (e.g., DeepSeck-SB/AIME224 777.9% tokens, +5.8 pp; Owen3-32B/ANl 324B/A/E/2 -6..%% +4.7 pp). DeepConf-high is more conservative, saving roughly 16- 59% with accuracy essentially unchanged. Notable exceptions for DeepConf-low include Qwen3- 8B/AIME25 ( (-4 4.44 pp) and a few <I pp drops on GPT-OSS BRUMO/HMMT; on low still saves 55-65% with mixed (within pp) accuracy shifts. Overall, DeepConf-Ne offers
20

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Published as a conference paper at ICLR 2026
the best efficiency-accurace trade-off, while DeepConf-high is the safer choice when minimizing accuracy changes is paramount.
Table 10: Benchmark DeepConf in the online setting. Aceuracy (% and tokens (x10*) at voting size 512 for Majority Voting and Adaptive DeepConf-(highlll on AIME24, AIME25, BRUMO25, HMMT25, EPQA-Diamons (where available;
only for DeepSeek/Qwen).
Model
Datasct
Maj. @512
DespCon--ighe5122
DospConf-low0522
Tok
Acc
Tok (A%%
Acc
Tok (4.%)
Acc
AIME24
86.7%
1.45 (-59.0%)
86.7%
0.78 (-77.9%%
92.5%
ATME25
4.01
82.3%
2.37 (-40.9%)
81 4%
1.24 (-69.0%)
86.4%
DoepSock-8B
BRUMO25
3.56
93.3%
2.17 (-39.2%)
93.3%
1.07 (-70.0%)
93.3%
HMM125
4.49
69.8%
3.43 (-23.5%)
70.0%
1.60 (-64.49%)
77.6%
GPQA-D
9.92
72.5%
6.90 (-30.4%)
72.4%
3,46 (-65.19) 158)
71.7%
AIME24
2.32
80.0%
1.33 (-42.8%)
80.4%
0.90 (-61.1%%
86.5%
AIME25
82.5%
1,99 (-28.19))
82
1.31 (-52.7%%
Qwen3-8B
BRUMO25
2.54
81.0%
1.74 (-31.4%)
81.7%
1,15 (-54.7%%
82.7%
HMM125
3.10
60.0%
2.59 (-16.6%%
60.0%
1.67 (-46.258)
62.7%
GPQA-D
7.47
63.7%
4.94 (-33.9%)
63.8%
3.31 (-55.7%)
65.2%
AIME24
84.8%
0,88 (-56.0%))
86.4%
0.66 (-66.818)
AIME25
2.43
80.1%
1.61 (-33.7%)
80.2%
1.14 (-52.9%%
80.2%
Qwen3-32B
BRUMO25
2.17
93.3%
1.37 (-37.1%%
0.96 (-55.7 7%))
92.4%
HMMT25
2.76
63.4%
2.24 (-18.8%)
63 6%
1,55 (-43.88%)
64.5%
GPQA-D
7.44
72.2%
4.16 (-44.1%%
72.9%
3.21 (-56.918)
73.0%
AIME24
5.57
96.7%
3.07 (-44.8%)
96.7%
1.11 (-80.0%)
95.7%
AIME25
3.18 (-49 2.5)
95.35
80))
GPT-20B
BRUMO25
5.16
87.1%
3.49 (-32.5%
87 2%
1.34 (-74,1%%
87,8%
HMM125
8.16
89.9%
6.03 (-26.0%)
90.3%
2.17 (-73.4%
89.4%
AIME24
2.66
96.7%
1.20 1.54 (-54.6%)
96.7%
0.53 (-79.9%)
97. 97.0%
GPT-120B
AIME25
97.1%
1.42 (-56.0%)
97.0%
0.49 (-84.7%)
97.9%
BRUMOZS
2.68
83.8%
1.81 (-32.6%)
84.0%
0.73 (-72.8%8)
83.4%
HMMT25
92.8%
2.78 (-32.0%)
93.0%
0.97 (-76.25%
92.0%
At Comparable Accuracy. We compare adaptive DeepConf (early termination when the modal an- swer reaches 2 0.95 confidence, otherwise continuing to the budget cap) against budget-only Deep- Conf (which always runs the full budget cap) under two filtering regimes: High retains the top 90% confidence traces, while Low retains only the top 10%. We conduct experiments across budget sizes B E {32, 64, 128, 256, 512] on ALME24/IIEE2//BUUO///EE
datasets (Fig. 9
Benchmarked against majority voting baselines, adaptive DeepConf-low typically achieves 19- 96% token reduction while maintaining matched accuracy, whereas adaptive DeepConf-high de- livers 13-84% savings with near-equivalent performance. However, several exceptions exist within the B E [32, 512) range where matching majority voting accuracy with reduced to- ken consumption is not achieved: DeepConf-low: [wwn3-8B/AIMEE.
Qwen3-32BBBRRMM025, GPT-20B/AIME24, GPT-20B/BRUM025, GPT-20B/HMMM225, GPT- -BMMME25..
120B/BRUMO25, UPT-120B/HMMT25 DeepConf-high:
Overall, DeepConf-low filtering provides the most substantial efficiency gains in successful cases, while DeepConf-hige filtering represents the more conservative choice when minimizing accuracy degradation critical. Compared to budget-only DeepConf, adaptive DeepConf consistently dom- inates the liken-accuracy Pareto frontier: identical voting ensemble sizes, it consumes fewer to- kens without sacrificing accuracy (e.g., DeepSeek-SB/AIMIE
@512: 0.782 x 108 vs 1.512 x 10 tokens for Low: GPT- H20/HM22B/ @512: 2.782 10 vs 3.679 x 10 for High). Consequently, we adopt adaptive DeepConf as the default configuration when computational efficiency is priori- tized.
F EPQA-DIAMONT RESULTS
We present the performance of our methods applied to DeepSeek-8B, Qwen3-8B, and Qwen3-32B on the GPQA-Diamond dataset in this section. The offline results using Lowest Group Confidence shown in Fig. [0 Our method matches exceeds the majority voting baseline in terms of peak accuracy. On Qwen3-8B and Qwen3-32B, Keeping Top-10% outperforms the baseline, while on DeepSeek-8B, keeping Top-90% roughly matches it and keeping Top-10% performs slightly lower.
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Published as a conference paper at ICLR 2026
AIMEZ4
AIME25
BRUMO25
HMMT FEB25
DeepSock-R1-00
37.5
91.
15.3
03.0
92.0
72.
84.0
91D
760
47.5
Qwen3 -88
46.0
04.0
02.0
78.0
Qwen3-3228
92.0
$1.0
61.5
92.0
05.0
0.0
2.0
2.2
16
23
GPT-20B
90.0
65.0
16.3
09.0
240
01.0
05.0
GPT-1208
22.5
16.3
02.0
95.0
54.3
15
0Tokuns
sudpet-crt only DespCoridon
budlptieelly Despborlingn
DespCartiin
Majer 101
Figure 9: Scaling behavior: Models's s Accuracy vs token cost for different methods on different models and datasets using online DeepConf
DeepSeek-Ri RR-888
Qwen3-88
Qwen3-328
73.0
Accuracy%)
70.0
72.0
GPQA
68.0
66.0
70.0
64.0
68.0
Voting Budget
Budget
Vottng Budget
Keep
Keep Top
Majority Voting
Vocing
Figure 10: Scaling behavior: Models's Accuracy vs budget size for different methods on GPQA- Diamond
Overall, keeping Top-90% represents the safer choice, consistently matching or exceeding baseline accuracy, whereas keeping TTp-100% often achieves larger gains but may occasionally underperform. Relative to generating only one answer per question, both variants provide clear average improve- ments of approximately 6%.
The online method's performance is shown in Fig. Adaptive policies consistently achieve greater token usage reduction at the same voting budget compared to the fixed method. Consistent with the offline results. DeepConf-high generally maintains majority voting accuracy with conserva- tive approach, while DeepConf- pursues larger computational savings but may underperform on DeepSeek-8B. These results align with the findings reported in $4.2 and $4.3
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Published as a conference paper at ICLR 2026
DeepSeek-RLe -R-888
Qwen3-88
Qwen3-328
730
Accurasr
72.0
72.0
GPDA
71.0
70.0
63.5
TTkkns (1e8)
#Tokens (1e8)
TTkeere 11e8]
Sudget-anly
butigel-arly DeepConshigg
CespCrrfhigh
Figure 11: Scaling behavior: Models's Accuracy vs token cost for different methods on GPQA- Diamond
G EXPERIMENTAL SETTINGS
Online CoepConf hyperparameters. Table 12 summarizes the settings used in our runs Ninits y, and the voting budget B with two configurations: DeepConf-low (7=10%% and DeepConf-high (1=90%).
Generation hyperparameters. We list below the per-model decoding hyperparameters used across all experiments. For each model, we fix temperature, top-p, top-k, and the maximum generation length, and we use each model's native tokenizer. A dash (-) indicates that the control is not applicd (e.g., if top-k -, sampling uses only top-p truncation).
Table 1I: Generation hyperparameters used our experiments. Different models use different decoding settings. A dash (-) indicates the option is not applied.
Model
Temperature
Top-p
Top-k
Max seq len
DeepSock-8B
0.6
0.95
64k
Qwen3-81
0.6
Qwen3 32n
0.6
0.95
20
32k
GPT-OSS
130k
GPT OSS 120B
1.0
40
130k
Prompt templates. For Qwen3 and GPT-OSS, append the same instruction every problem prompt: "Please reason step by step, and put your final answer within \boxed[]." For GPT-OSS, additionally keep the provider's 's official system prompt and enable the reasoning effort high setting. For DeepSeek-888 we use the official system prompt and put the problem in the user mes- sage.
In all cases, the final answer is expected to appear inside \boxed(... and is extracted during post- processing, Decoding terminates only when an end-of-sequence token produced the maximum generation length is reached.
Table 12: Hyperparameters for Online DeepConf (Algorithm 20. Nin denotes the number of initial traces used the offline warmup; 1) the filtering percentile to form Trop (we will keep top 7/ traces); is the online consensus threshold; B is the maximum budget (number of traces).
Method
Nun
7 (Top-%)
(consensus)
B (budget)
DeepConf-low
16
10%
0.95
32, 64, 128, 256, 512
DeepConf-high
16
90%
0.95
32, 64, 128, 256, 512
23


Reviews:
[{"review_id": "syNNhrXFIs", "reviewer": "Reviewer_U1LE", "summary": "This paper presents Deep Think with Confidence (DeepConf), a test-time method that improves LLM reasoning accuracy and efficiency by leveraging internal confidence signals without retraining. The method addresses the inefficiency and diminishing returns of standard self-consistency (majority voting) by dynamically filtering or halting low-confidence reasoning traces. DeepConf replaces a single global confidence value with localized confidence metrics computed over sliding windows of tokens:\n- Group confidence: mean of token-level confidence across overlapping windows;\n- Tail / Bottom-10% confidence: highlight locally uncertain regions;\n- Lowest Group Confidence: the weakest confidence window per trace, used for online early stopping.\n\nIn offline mode, DeepConf ranks and filters traces by these scores, applying confidence-weighted voting instead of naive majority voting.\nIn online mode, it adaptively terminates traces early once local confidence falls below a learned percentile threshold and stops sampling once vote consensus exceeds a preset $\\tau$.\n\nAcross math-reasoning and QA benchmarks (AIME’24/’25, HMMT’25, BRUMO’25, GPQA-Diamond) and multiple models (DeepSeek-8B, Qwen3-8B/32B, GPT-OSS-20B/120B), the method achieves strong empirical results without any retraining or extra supervision.", "questions": "1. How does DeepConf compare to semantic entropy and self-certainty in online settings under the same token budget?\n2. Can the authors provide quantitative measures (e.g., AUROC, ECE) showing how well their confidence metrics discriminate correct vs. incorrect traces?\n3. How often do “confidently wrong” traces dominate the vote, and can local diversity or disagreement be incorporated as a second signal?\n4. Can the same percentile thresholds $s$ learned during warm-up be reused across multiple problems from the same domain, or must they be recomputed for every new query?\n5. Would varying the top-k (for confidence) or window size meaningfully affect results?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. Practical impact and simplicity: DeepConf can be deployed immediately without retraining or external calibration. It’s a drop-in improvement to any self-consistency pipeline.\n2. Local vs. global insight: The authors convincingly show that global average confidence can mask local failures while sliding-window metrics like LGC and Tail Confidence capture these weak spots better.\n3. Strong empirical results: Large-scale experiments (5 datasets, 4 models, 64× repeats) demonstrate consistent improvements in both accuracy and efficiency.\n4. Comprehensive ablations: The authors systematically explore the effects of confidence thresholding, consensus level, and warm-up size, providing actionable insights for practitioners.\n5. Presentation: The presentation, visualizations, and overall narrative are coherent and reader-friendly.", "weaknesses": "1. Confidence calibration: The authors treat percentile thresholds ($\\eta = 10 / 90$) as hyperparameters, but the actual confidence scores are not calibrated across models. Reporting AUROC or ECE/Brier scores for trace-level discrimination would provide a more rigorous evaluation of confidence quality.\n2. “Confidently wrong” cases: The authors briefly mention (Appendix D) that models sometimes assign high confidence to incorrect reasoning modes, but there’s no robust mitigation strategy. A hybrid ensemble or diversity-aware weighting could improve robustness.\n3. Hyperparameters: The choice of top-$k$ = 20 and window = 2048 seems arbitrary. An additional ablation varying these values could offer deeper understanding of sensitivity.", "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": "ys3F2ruxdG", "reviewer": "Reviewer_s7Pe", "summary": "This paper introduces Deep Think with Confidence (DeepConf), a test-time method designed to improve the reasoning performance of LLMs. The paper argues that global confidence metrics are flawed as few high confident region can hide critical errors within low confidence segment. It proposes several new, more fine grained metrics such as group confidence and tail confidence, etc to capture local statistics. It then introduces two inference mode, in offline settings confidence filtering and weighted majority voting is applied. In online settings, an offline warmup is required to setup a stopping threshold, and adaptive sampling can be applied based on existing rollout results and partial confidence. The method demonstrates a accuracy improvement compared with majority voting and significant token saving in online settings.\n\nIn short, it is an empirical paper that extends the previous global confidence method with finer granularity to improve the test-time performance on token efficiency and accuracy.", "questions": "1. As for weakness 2: What default, model-agnostic settings do you recommend for these parameters? What minimal selection protocol (and validation budget) do you propose for new tasks/models? if above questions cannot be addressed, please revise the abstract/claims to acknowledge required hyperparameter choices. \n2. Regarding Weakness 3: Can the authors provide the token efficiency metrics taking offline warmup tokens into account? Can the confidence threshold be reused or shared across questions or within a dataset to reduce per-prompt warmup?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Clear Motivation and Problem Framing: The paper provides a clear and intuitive justification for moving from global to local confidence metrics.\n2. The experimental setup is comprehensive: The authors test across multiple model families and scales, on a suite of reasoning and QA benchmarks. The paper also includes detailed ablations on hyperparameters introduced in the method.\n3. The proposed method is practical and simple with multiple variants that can adapte to different downstream need, making it easy and meaningful to integrate into existing frameworks.", "weaknesses": "1. Incremental Novelty: The primary novelty lies in the specific local metrics and the online early-stopping mechanism compared to prior works (e.g., Kang et al., 2025). While effective, the proposed method is an incremental improvement on existing ideas.\n2. Overstated “No Hyperparameter Tuning.” The abstract’s “no … hyperparameter tuning” assertion is not faithful to the method as presented. The method introduces several new parameters that require choices: the filtering ratio, the online consensus threshold, the warmup steps and window sizes. For example, the reported ablations (e.g., Table 5 / Fig. 8) show the optimal filtering percentage varies by dataset and model, implying some form of tuning or at least selection is needed for new settings.\n3. Warmup Cost Not Fully Accounted. The online mode requires an instance-level warmup that generates N full traces before early stopping is even applicable. For common majority-vote budgets e.g. K=32, setting N=16 is a major overhead that should be counted. The current amortized token-saving curves appear to exclude or underweight this cost.", "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": "xAR1I1sCOH", "reviewer": "Reviewer_yu1z", "summary": "Self-consistency with majority voting as a test-time scaling (TTS) strategy can effectively improve LLM reasoning accuracy; however, it multiplies computational cost and shows pronounced diminishing returns. To address this, the paper proposes DeepConf, an efficient, training-free TTS method that leverages a model’s internal confidence to dynamically filter low-quality reasoning paths. Across both offline and online settings, DeepConf achieves superior performance while using substantially fewer resources.", "questions": "1. **Online, extreme-difficulty cases.** When the model generates a long chain-of-thought (CoT), if certain “reflection” segments exhibit low confidence, could early stopping become overly aggressive—filtering out trajectories that might otherwise converge to the correct answer—and thus hurt accuracy? Should the definition of the group (G_i) adapt to the already-produced output length?\n\n2. **Practical guidance on hyperparameters.** What are the recommended defaults and applicable ranges for (G_i), (\\eta), (\\tau), and (N_{\\text{init}})? Is there a simple heuristic or automatic setting strategy for these?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. **Simple and effective with practical value.** Relying only on *Bottom 10% Group Confidence* enables effective adaptive sampling with early stopping and confidence filtering of high-quality reasoning paths. In both offline and online settings, it markedly lowers inference cost while delivering better performance, indicating broad applicability.\n\n2. **Comprehensive and rigorous experiments.** The paper evaluates five mainstream open-source reasoning LLMs from three model families on five challenging benchmarks under two settings. Experimental details are clear and easy to follow. Thorough ablations, across different budgets and hyperparameters--demonstrate the method’s effectiveness, making the evidence methodologically solid.\n\n3. **Clear writing and sound structure.** Centered on confidence and targeting cost-efficient TTS, the paper offers a detailed, comprehensive discussion and comparison of approaches based on internal token distributions and their limitations, and builds a logically coherent, step-by-step case for the proposed method.", "weaknesses": "1. **Limited task generalization.** The evaluation focuses primarily on mathematical reasoning, with little assessment in verifiable settings such as code generation. Adding at least one non-mathematical reasoning benchmark would strengthen claims of generality.\n\n2. **Missing highly relevant strong baselines.** While the paper centers on confidence-based methods and compares unweighted vs. confidence-weighted majority voting, it lacks comparisons with closely related, strong baselines—e.g., ESC [1], DSC [2], and RASC [3]. Including these would improve completeness, better substantiate the method’s effectiveness, and clarify the source of gains.\n\n3. **Missing related work** . The paper omits several classic/recent SOTA parallel-generation approaches under TTS in A.1, such as DVTS [4] and DORA [5].\n\n[1] Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning ICLR2024\n\n[2] Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning NAACL2025\n\n[3] Leveraging Reasoning Paths for Efficient LLM Sampling NAACL2025\n\n[4] Scaling Test-Time Compute with Open Models\n\n[5] Every Rollout Counts: Optimal Resource Allocation for Efficient Test-Time Scaling NeurIPS2025", "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": "pxdtPaGYzw", "reviewer": "Reviewer_2dPu", "summary": "This paper introduces Deep Think with Confidence (DeepConf), a test-time method to enhance the reasoning performance and efficiency of Large Language Models (LLMs) by leveraging internal confidence signals from token distributions. DeepConf filters low-quality reasoning traces either offline (after generation) or online (during generation) using localized confidence measures like group confidence, bottom 10% group confidence, lowest group confidence, and tail confidence. It integrates with self-consistency majority voting, achieving weighted voting and early stopping to reduce computational overhead. Evaluations on mathematical benchmarks (e.g., AIME 2025) and models (e.g., GPT-OSS-120B, Qwen3-32B) claim up to 99.9% accuracy with 84.7% token reduction compared to standard majority voting. The method requires no additional training and is plug-and-play.", "questions": "In addition to the weaknesses mentioned above, I am particularly concerned about the practical computational cost of DeepConf. The reported results are obtained under the setting of K = 512, which seems computationally heavy. It would be important to clarify the average inference cost and compare it with standard decoding. Moreover, how sensitive is the method to the choice of K? How does the performance change when K is reduced to a more realistic range for deployment?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "-  DeepConf demonstrates significant reductions in generated tokens (up to 84.7%) while maintaining or improving accuracy, which is crucial for deploying LLMs in resource-constrained settings. The online mode with adaptive sampling and warmup is a clever way to approximate offline performance in real-time, making it suitable for serving frameworks.\n- Experiments cover multiple models (from 8B to 120B parameters) and challenging benchmarks (AIME, HMMT, BRUMO, GPQA). Results are averaged over 64 repetitions, adding statistical robustness. The ablation on confidence thresholds (η=10% vs. 90%) provides insights into trade-offs between precision and diversity in filtering.\n-  No hyperparameter tuning or retraining is needed, and the method integrates seamlessly with existing parallel thinking approaches. The anonymous code release supports reproducibility.", "weaknesses": "- The paper assumes that higher confidence correlates with correctness (as shown in Figure 2), but this assumption is problematic. Confidence in large models is not necessarily calibrated, and without calibration analysis (e.g., ECE or reliability plots), confidence values cannot be interpreted as correctness probabilities. Moreover, low-confidence traces may still contain valid, diverse answers that are filtered out, potentially causing mode collapse. A more thorough analysis of calibration quality and failure modes (e.g., overconfident wrong answers) would be necessary to substantiate the claims.\n-  While the idea of discarding uncertain reasoning paths during generation makes sense conceptually, the experimental setting (K=512) raises concerns about practicality. The paper does not report the computational overhead or the average inference cost compared to normal decoding. It is unclear how scalable the method is in realistic settings and how strongly the results depend on the choice of K. An ablation or sensitivity analysis on K would be essential to understand the trade-off between accuracy and efficiency.\n- The paper mainly evaluates the method on benchmarks with well-defined ground truth answers. To better assess its generalization ability, it would be helpful to include experiments on open-ended tasks where correctness is less strictly defined. Such evaluation could reveal whether the proposed confidence mechanism remains effective under less constrained, real-world generation scenarios.\nIf the authors can address the above issues, I would be willing to raise my score.", "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)