BARREL: Boundary-Aware Reasoning for Factual and Reliable LRMs
Authors: Junxiao Yang
Jinzhe Tu
Haoran Liu
Xiaoce Wang
Chujie Zheng
Zhexin Zhang
Shiyao Cui
Caishun Chen
Tiantian He
Hongning Wang
Yew-Soon Ong
Minlie Huang
Venue: ICLR 2026 Poster (2026)
Keywords: Large Reasoning Models
Factual Alignment
Knowledge Boundary
Primary area: alignment, fairness, safety, privacy, and societal considerations
TL;DR: We present BARREL, a framework that enhances the factual reliability of Large Reasoning Models by promoting concise, boundary-aware reasoning, allowing models to stay accurate while using “I don’t know” when uncertain.

Abstract: Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with “I don’t know”. Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL—a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

Published as a conference paper at ICLR 2026
BARREL: BOUNDARY-AWALE REASONING FOR FAC- TUAL AND RELIABLE LRMs
Junxiao Yang! .2 Jiizhe Tu', Haoran Liu', Xiaoce Wang', Chujie Zheng',
Zhexin Zhang', Shiyao Cui', Caishun Chen', Tiantian He", Hongning Wang',
Yew-Soon Ong"., Minlie Huang"
The Conversational AI (CoAl) group. DCST, Tsinghua University
2 Centre for Frontier AI Research, Institute of High Performance Computing,
Agency for Science, Technology and Research, Singapore
3 The College of Computing and Data Science, Nanyang Technological University
yangjunx211 (aniggnxx1@@mmaaai gmail com, aihuang inghuu edu.en
ABSTRACT
Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL novel framework that promotes concise and boundary- factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeck-RI -.-cck------sillllll Distill-Llamal while still achieving accuracy comparable models finetuned reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System LRMs.
from 39.33% to 61.48%
INTRODUCTION
Recent advances Large Reasoning Mod- els (LRMs) (Jaech et al.) 2024 Guo et al.]
Currest LRM
Fabricasal
2025 Team 2025) have shown impressive performance in specialized reasoning tasks, especially in mathematics and logic. How- ever, these gains have not led to correspond- ing improvements in reliability. On the con- trary, faithfulness hallucination rates ris- ing (Hughes & Bae 2003), and helpfulness on factual tasks declining (Zhao et al. 2025), raising concerns about the reliabil- ity of these reasoning models.
unknows
Kaowledge
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In this work, we focus primarily on the factual reliability of LRMs, which is cru- cial requirement for many real-world tasks. Factuality of language models involves two aspects: knowing (whether the model holds relevant knowledge) (Huang et al., 2025 Ji et al. (023) and telling (conveying the correct factual information) (Gekhman et al. 2024 Mallen et al. 2022). As shown in Figure [ we want LRMs to exhibit two aspects of factual reliability: (1) Identify both what it knows and what does not know: The model should be able to recognize questions it does not know the answer and respond with "I don't 't know." (Xu et al. 2024a| Zhang et al.) 2024a) (2) Tell what it knows: There a gap
Figure 1: How reliable factual reasoning is expected improve model performance. Left: Current LRMs rarely admit ignorance and often respond inconsistently. Right: Reliable LRMs should acknowledge unknowns and express known facts more consistently.
"Corresooniing author.

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Published as a conference paper at ICLR 2026
between knowing and telling (Saunders et al., [2022) and we want to improve the model's accuracy in expressing the knowledge it has (Zhang et al. 2024b).
However, current LRMs consistently struggle with the two factual reliability goals above. They rarcly acknowledge gaps in their knowledge and often fabricate answers instead, even on questions for which they lack sufficient knowledge. Moreover, their responses be incorrect answers in some instances while correctly responding to similar queries elsewhere (Wang al. 2022). thereby reducing the overall factual accuracy of their responses (Zhao al., 2025).
providdnn
What underlying reasoning behaviors contribute to these observed issues? As shown in Fig- ure 2 our preliminary experiments reveal a variant of the overthinking pattern discussed by Chen et al.] (2024), which we term factual overthinking where large reasoning models (LRMs) consume more tokens when producing factually incorrect answers than when generat- ing correct ones. And we further identify two prevalent pathological reasoning patterns asso- ciated with this overthinking phenomenon. As shown on the left part of Figure 3 one promi- nent pattern is Last-minute Guessing. in which the model, after extensive but inconclusive rea- soning, abruptly commits to an answer in final burst of speculative output-much like a student hastily filling in an answer just before the end of an exam. Another frequent pattern is Second-thought Spiraling, where the model initially identifies the correct answer but continues to over-analyze, ultimately undermining its own correct conclusion.
Thinking Tokens: Correct vs Incorrect Responses
coreet Reepors
5318.5%
Toker Count
-70.0%
+119.0%%
Decpuesc (006/-0wee--3
id Oigrr Llens
Figure 2: Number of reasoning tokens used by LRMs when producing correct versus incorrect answers. We test on TruthfulQA across different types of reasoning models. Details and results on other datasets are listed at Appendix
To mitigate these pathological reasoning patterns, we propose a novel training framework, BARREL (Boundary-Awail Reasoning for Reliable and Factual LRMs). As shown in Figure BARREL trains LRMs to perform concise, deliberative factual reasoning and draw conclusions after it has explored a sufficient number of candidates. Concretely, for known questions, when the model identifies the correct factual answer during reasoning, we want it to maintain confidence in that answer while continuing to explore other possible ones. Once there are no likely candidates, it should halt further reasoning and provide the correct factual answer. For unknown questions, after exploring sufficient number of plausible candidates, it should terminate reasoning and proactively admit its lack of knowledge with uncertainty-awart refusal (e.g.. "Sorry, don't know"). To implement BARREL, begin by employing sampling strategy to probe the model's knowledge boundary. Drawing on the identified pathological patterns, we construct two distinct types of reasoning data, and use Supervised Fine- Tuming (SFT) to instill the corresponding reasoning behaviors in the model. Finally, we adopt Group Relative Policy Optimization (GRPO) using general reliability-bass answers, medium for uncertainty-ave -wware refusal, and low for incorrect answers) without the need for labeling knownlunkkoww further enhancing the model's s ability to generalize in factual reasoning.
reward (high for correct
Our experiments demonstrate that models trained with BARREL can effectively express uncertainty- aware refusal, and mitigate the two pathological reasoning patterns. This capability significantly improves reliability: BARREL boosts the reliability of DeepSeck-R1/ Ri--istill--lamm- to 61.48%, while maintaining an accuracy of 40.7%, which is even higher than the accuracy of 38.3844 08.43% achieved by distillation. Through detailed analysis, refusal. This result also identifies the root cause of models'
from 39.33% %
highlight the critical role of medium level
rewards in promoting uncertainty- inability to admit ignorance to fundamental gap in current RL paradigms: they do not reward refusal. As result, models are incentivized to answer every question, regardless of uncertainty.
Our main contributions are follows:
We discover the factual overthinking phenomenon and point out two pathological reasoning patterns that lead to factual unreliability of LRMs.
To the best of our knowledge. we are the first to explore how LRMs can utilize reasoning to admit ignorance and say "I don't know". Also, we introduce a novel training pipeline to do so.
We emphasize medium-level rewards encourage uncertainty-aware refusal for reliable LRMss
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Published as a conference paper at ICLR 2026
1. Pathological Reasoning Patferns in Current LRMs
Constructed BARREL Reasoning for SFT
GRPO
whi's singing of the gooe Geal
Sreend-thought Spiraling
Auchored Exploration
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ceneeber
Rocalling
Rocalling
Lowed ciretiily evalatt the exidese [..]
trek
t The foot that conss to ased is The Black Eyed Pee. as I...
be The Bllck Eyed Peas. [n]]
C Correct Answer
Correct Answer
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Verifying
Verifying
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1 petestial performers could ixclnde [..]]
one
Weit andher appoadh, Elten [..]
Wet: tobek in was The Ratling Stones-giie [-]
I..1
Second-thouge Spiraling
Exploration
Anchored
Thweridess fssufficinn [..]
Alter J. contireed the Bltack Ryst
GRPO
tiekk
Wrong Answer
Currect Answer
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jaho playal jurre
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Recalling
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MIDAUN
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Araes.. reffe Michee Rasker? No. war, [-]
Guess Guess I
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Uncertainty
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X So the unwerra Bobert O'Seil.
Wrong Answer
Correct Anywer
Josw the ueswez
Figure 3:
The two current reasoning patterns of LRM: Last-minute Guessing, typically associated with unknown knowledge, and Second-thought Spiraling, which occurs despite known knowledge. Right: The BARREL pipeline addresses both cases by correcting overthinking tendencies and constructing SFT data accordingly, further enhanced with GRPO.
Left:
2 RELATED WORK
Knowledge Boundary The knowledge boundary of LLMs refers to the extent of knowledge model possesses or can reliably recall (Li et al.) 2024). Identifying such boundaries is crucial for model safety and reliability and is commonly addressed by confidence calibration (Ren et al. 2023), internal state probing (Ji et al. 2024),, uncertainty estimation (Kapoor et al.] (024), and sampling strategy (Gekhman al. [2024] Xue et al., 2024). To mitigate failures by outbound queries, recent studies have proposed training LLMs to abstain from answering when uncertain, often by generating "I don't know" responses (Cheng et al. 2024) or providing further explanations of the unanswerability (Deng et al. 2024). Our work pushes it further to structured and interpretable rationales about their knowledge boundary.
Factual Alignment Factual alignment aims to improve factuality while preserving instruction- following capabilities in LLMs. Recent work incorporates factuality-awareness into both SFT and RL stages to improve factual accuracy (Lin et al. 2024), or finetuning with DPO to enhance its self- evaluation capability (Zhang et al. 2024b). Other approaches include tine-tuning with refusal- -wwrr datasets encourage appropriate abstention behaviors (Zhang al. 2024a), and RLKE, which guides models to reject uncertain queries based on external feedback signals (Xu et al. 2024a). Similarly, other reinforcement learning strategies have been proposed incentivize models express doubt uncertainty (Stangel et al., 2025| Xu et al. 20244b). Damani et al. (2025) has also explored training LLMs reason with uncertainty using binary rewards. While previous work has primarily focused on non-reasoning models, our research demonstrates how to correct reasoning pathologies to enhance the factual reliability of LRMs.
METHOD
In this section, we introduce the overall framework of BARREL, which comprises three main components: (1) Knowledge Labeling, which distinguishes whether question is known unknown to the model: (2) Reasoning Trace Construction for SFT, which constructs reasoning traces based on the question type and performs SFT to prepare the model to follow this thinking pattern; (3) GRPO Stage, which further enhances the model using a rule-based factual reward. We detail each component below.
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Published as a conference paper at ICLR 2026
3.1 KNOWLEDGE LABELING
We first determine whether a question is known to the target model using the sampling strategy proposed in (Gekhman al., 2024), which is a widely recognized approach (Xue al. [024]]
Li et al. 2024). Let D = { yt ) be factual QA dataset, where each question æ; has ground-truth answer yr- We generate answers with the target model M using K distinct few-shot prompts (P,),= and repeat the sampling procedure L times for every prompt:
yi
M P3 xi)
j j= K, k
After collecting the samples V = { Mi 1ik K. least one sampled answer matches the ground-truth answer under evaluator E.
1== we consider question known to the model at
known, 4 unknown, otherwise.
if 3 such that Fly, v()
(2)
3.2 REASONING TRACE CONSTRUCTION FOR SFT
To address the pathological reasoning patterns identified in our analysis-namely, Last-minute Guessing and Second-though Spiraling-ww we propose targeted method for constructing reasoning trajectories. Based on the type of question, we construct two distinct evidence-growe seeence-grouded reasoning traces T(x;) for question 24, aiming to respectively correct these two faulty reasoning patterns. This construction outlined in Algorithm!] [
To mitigate Second Second-thought Spiraling in known questions, where the gold answer y" with strong evidence e* available, it should begin by retrieving and identifying this answer. It then examines alternative candidates (yj. eÿ) to contrast possibilities. After this anchored exploration, it reaffirms the choice with solid justification and draws confident conclusion favoring the correct answer.
To address Last-minute Guessing in unknown questions, the system adopts similar exploratory strategy: recalls background knowledge and searches on plausible answer-evidence pairs (M/ eÿ) through hypothesizing. However, if it fails to identify a sufficiently supported answer, explicitly acknowledges the uncertainty and ultimately outputs cautious, confirmed rejection-demonstieee demonstrating its ability explore hohb-probability paths without overcommiting or hallucinating.
Algorithm BARREL reasoning trace T (xxa) construction
Input: Question z; and knowledge label 4, gold answer with evidence (y² e²), alternative candidates with poor evidence ey),,,
Output: reasoning trace T(x;)
1: T(r;) + ()
Initialize an empty trace record recalled background facts
2: T(::) += RECALL(
3: 7, 1(known knowledge) then
4:
T(x;) += (y*ee")
Attach gold answer and supporting evidence b Attach distractor answer-evidence pairs Verify the conclusion with strong evidence
5:
T(x;) += (lis G)
6:
T(x,) += CONFRM((")
7:
else (unknown knowledge)
8: T(x;;) += {V),, (2) }
exploring plausible answer-evidence pairs Record uncertainty for guesses
9:
T(x;) += Acknowledge Uncertainty(
10: end if
11:
return T(x:))
> Return the constructed reasoning trace
We construct the reasoning traces by prompting GPT-4 with detailed instructions and BARREL reasoning examples. This approach produces a Long-CoT-stylee reasoning process that aligns with the expected reasoning patterns. Examples of the constructed reasoning traces for both known and unknown questions are shown in Figure 3 and the detailed prompt used for trace construction is provided in Appendix G
Then, we use these data to train the model to emulate boundary- aware and deliberative reasoning patterns using SFT. For each question T4, construct full output of T(x:)llas where a; is
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Published as a conference paper at ICLR 2026
either the gold answer yi (for known questions) incertainty-awar refusal (e.g., "Sorry, I don't t know") for unknown questions. This instills the model with a disciplined reasoning style grounded in traceable evidence and uncertainty-awee aware conclusions. The training objective minimizes the negative log-likelihood:
N ((0) = log Po zi).
(3)
3.3 GRPO-STAGE
Kule-Based Reward Design To train the model generate verifiable and boundary-aware rea- soning trajectories and answers, we employ rule-based reward function. We categorize the model response o into three types, each associated with a distinct reward signal. Given generated answer to question 24, and ground-truth answer yf the reward function R(o,, yf is defined as:
Te:
(o,, v/) 1,
R(o,, vi)
o; contains a valid rejection phrase, = Fs:
(4)
Tw:
otherwise.
This reward function provides general supervision for training the model optimize not only for correctness but also for calibrated uncertainty, aligning with the goals of boundary-aware reasoning. It comprises three components: high reward for correct answer (rx). medium reward for truthful rejection (r,) and a low reward for an incorrect or hallucinated output (rw)) To discourage the generation of unfounded claims, the penalty for an incorrect answer more severe than the outcome of a truthful rejection, thereby incentivizing the model to acknowledge its knowledge boundaries when uncertain. The reward magnitudes follow the order:
Te To Tw
GRPO Training After SFT, the model has learned the pattern of reasoning express uncertainty appropriately and is able to maintain confidence when the answer is correct. Building on the above reward design, we further enhance the factual reliability of the reasoning model using Group- wisse Reinforcement Policy Optimization (GRPO) (Shao et al. 2024). For each labeled input (I,, V 4)) we sample set of G reasoning-answwa trajectories from the current policy ma,..
O (o......o. ........,))...... Te.. 1x)).
Each trajectory 0j includes a reasoning trace followed by a final answer token. GRPO then updates the model parameters to optimize the following clipped reward-weights objective:
(C)
E[x
D (0
loc|
min P3.AA,,, clip (ps.e, () BD [moll mrol(rres]
G
0
where Pi,t
no (e1
is the importance weight at step f,, and D denotes the stepwise KI.
Fe Feaid (..0),0)))))
divergence between the current and old policies. The advantage estimate Á is calculated using reward normalization:
Å (() R
[((o..))) 12)2.
(8)
Or
G
j=1
4 EXPERIMENTS
4.1 SETTINGS
Datasets We use separate datasets for training and evaluation. The training set consists of TriviaQA (Joshi et al. 2017). SciQ (Welbl et al. (017),, and NQ-Open (Kwiatkowski et al.) 2019), covering general ledge, scientific reasoning, and web- based QA, respectively. For evaluation, we sample 1,000 questions from the test splits of each dataset, forming 3,000-questton test set.
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Published as a conference paper at ICLR 2026
Models Due to limited computing resource, primarily utilize DeepSec--R--Disiil-LLmee DeepSeek-RI-Be RI--istill- mistill-Qwen-BB and Qwen3-8B to perform our study.
Baselines ICL: Vanilla Reasoning models with few-shot prompt designed for factual tasks. (2)
In-Context Learning with Refusal Examples (ICL-IDK): Prompting LRMs to claim uncertainty (3) Distill: SFT training using the reasoning path of DeepSeek-FR -1 _ on the training set. (4) Vanilla
prior SFT stage. GRPO: A standard GRPO implementation without uncertainty- based rewards
(5) Ennhabilty-EEhaaeeedd GRPO: We include two variants -Vaiills-Vannllaa GRPO w/ Verbal Confidence and Vanilla GRPO w/ Probing. These methods augment the standard GRPO by employing verbal confi- dence extraction and predictive classifiers, respectively, to improve reliability. Further implementation details for all baselines are provided in Appendix !
We evaluate the correctness of model response by prompting the models to box their final answer as follows, and then utilize string matching to evaluate whether the answer is correct (the model answer appears in any of the candidates). More details are listed in Appendix
Evaluation
Inference Prompt for verifiable Answer
Answer the following question based your knowledge and put your final answer within boxed()- (question)
Metrics A Factual Reliable LRM should provide much assistance possible while making as few errors as possible, such that we evaluate factuality on the test set using three metrics: Accuracy (Acc.), Truthfulness (Truth.), and Reliability (Rel.) (Xu al. 2024a). Let No, Nr, Ni denote the number of correct answers, truthful rejections ("Sorry, don't 't know"), and incorrect answers, respectively, where N =N N, + Nw. The metries are defined as:
No N
Truth. = No + Nr N
Rel. = ans. Truth. + (1-ans.) aas.a...cc where ans. = 1 N, N
Acc.
While the Truthfulness metric (Truth.) considers the notion of truthful rejection, it overlooks the model's answer rate-since a model could achieve 100% truthfulness simply by refusing to answer all questions. In contrast, the Reliability metric (Rel.) provides more robust, weighted, and comprehensive evaluation by jointly considering both the truthfulness of responses and answer rate.
Training Details and Hyperparameters For BARREL-SFI and Distill SFT, ensure that only finetune on correct answers of the known QA set, as finetuning on unknown knowledge could encourage hallucinations (Gekhman al. 2024). In practice, the rewards in GRPO stage defined -.55. More details and parameters are provided in Appendix[]
as re = 1, Tw = 11, and
4.2 MAIN RESULTS
Balancing Accuracy and Appropriate Refusals Our experimental results Table T demonstrate that our method significantly enhances model reliability and truthfulness, while maintaining accuracy. For the baseline methods, the truthfulness and reliability scores consistently remain below 40%. These models rarely acknowledge uncertainty. In contrast, method increases the reliability of DeepSeek-RI 1 -Distil-L-lama-88 from 39.33% to 61.48 .88, while maintaining an accuracy of 40.7%, surpassing the distillation method's 38.43 38.43%. Similar improvements are observed for the DeepSeek- RI-Distill-Qwen-7B and Qwen3-8B. We further compare BARREL with Vanilla GRPO and post-hoc confidence estimation methods (Verbal Confidence and Probing). While Vanilla GRPO lacks the mechanism to express uncertainty. and probing methods often suffer from accuracy degradation due miscalibration when tuned for higher truthfulness (Detailed in Appendix DD. BARREL consistently yields a superior balance for reliability. This highlights the advantage of using RL to teach LRMs to reason and internalize the accuracy-refusal trf rather than relying on external classifiers or heuristic thresholds. For instance, on Qwen3-8B, BARREL achieves reliability score of 71.46% significantly surpassing the Probing baseline of 58.94 58.94%. Table 2 provides examples illustrating how BARREL-trained LRMs mitigate Last-minute Guessing and aecond-thought Spiraling. Overall, our

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Published as a conference paper at ICLR 2026
IriviaQA
SdQ
NQ_open
Avg.
Are.
Truth.
Rd.
Truth.
Acc.
Truth.
Rel.
Are.
Truth.
Abstain
Rel.
DeepSrek- Beteee--R---aee RR--Distill-T-aaa
ICL
35.80
36.10
36.10
31.80
31.80
31,80
10.80
17.30
17.30
26.13
24.35
0.20
28.35
ICL-IDK
35.20
37.50
37.26
33,70
33.70
33,70
15.50
21.60
21.23
28.13
30.87
2.74
30,79
Distill
48.20
48.18
46.60
46.90
46.90
22.90
Vasilla GRB)
$3,50
56.80
$6.80
56.80
31.40
47.50
Conf
45.30
55.17
50.91
38.73
50.33
Prohing
46.20
60.30
58.31
51.90
61.
60.98
58.67
18.37
BARREL
48:40
71.80
66.32
$2,80
69.40
66.64
20.90
70.00
45.89
40.70
70.40
29.70
61.58
SPT only
38.10
55.60
32.54
39,00
53.50 .0)
51.40
18.50
40.20
35.49
31,87
49.77
17.90
46.55
DeeepSelll MKI-LDettlll-Oeeeee
7B
ICL
18:40
20,10
20.07
27,60
27. 27.60
27.60
8.20
8.70
8.70
18.07
18.80
0.73
18.79
ICL-IDK
18.00
22.90
31.30
23.30
23.15
23.93
22.30
22.30
50.00
50.00
50.00
13.90
13.90
28.73
28.73
0.00
28.75
Vartal Conf
21.40
21.70
31.70
38.55
11.80
12.10
12.10
23.83
24.03
Vanilla GRPO w/ Probing
14.80
49.50
37.46
32.40
56.00
54,90
6.60
63.40
31.14
17.93
39,83
41.90
42.28
BARREL
21.70
76.00
46.52
50.60
64.20
62.35
12,50
83.30
33.17
28.27
74.50
46,23
53.12
SPT only
17.00
38.90
34.10
34,00
43. 90
43.04
10.00
33.70
28.08
20.53
31,83
18.30
35.48
Qwen3-8B:
50.20
51,00
50.99
52.60
41.97
51.10
54.90
48.17
$2.90
54.60
$4.67
57.00
57.
57.20
18
46.00
Vanilla GRPO
$1.50
54.90
34.90
63.50
63.55
63.50
33,80
33.90
33.90
50.60
30.77
0.17
50.77
Vinitla GRPO w/ Verhal Conf
52.40
$2.60
$2.60
63.10
63. 10
63.
31.40
31:40
31:40
48.97
49.03
0.06
49.03
Vanulla GRPO w/ Probing
45.80
63.00
00.04
58.20
66.80
66.06
20,90
61.90
45.09
41.63
63.90
22.27
58,94
BARREL
55,50
$6.50
76,89
69.30
79.10
78.14
26.70
75.60
51.79
50.50
80.40
29.90
71,46
SPT only
40.90
57,00
54,41
52.50
65.00 5..0
63.44
19:60
36.60
33.71
37.67
52.87
15,20
50.56
Table I: Comparison of Different Methods on Accuracy, Truthfulness, and Reliability Across Datasets.
All results are multipled by 100.
training method enables LRMs retain relatively high accuracy while expressing uncertainty approximately 50% of the remaining questions, thereby substantially improving factual reliability.
Discussion on the Two Stages of BARREL We can notice from the results in Table 1 that GRPO training is indeed necessary. Although the SFT model performs well in terms of truth- fulness, its accuracy remains relatively low. The SFT process primarily helps the model learn ba- sic refusal patterns, but its effectiveness is lim- ited-we we discuss this in more detail in Section
Accrsoo
fakusalee brevn cusooos
13733
1831
4.3 Table 2 presents several examples show- ing that GRPO can address the issues caused by SFT. such as excessive refusals and faulty reasoning. By providing general supervision signals, GRPO enables the model to self-adjust (instead of relying external knowledge injection). This further improves both accuracy and truth- fulness, making the model more factually reliable. Results also demonstrate that BARREL SFT effectively mitigates the "factual overthinking" in Figure 2and that GRPO further promotes concise, reliable reasoning without sacrificing accuracy. We provide detailed analysis in Appendix A.3 A.3 We also find that only conducting GRPO training with the uncertainty reward is insufficient for teaching LRMs to be reliable. We discuss this ablation in Appendix C
Kheem Cata. Uniazzon
Figure 4: Effect of the ratio of known data un- known data on the factuality scores of SFT models.
4.3 ANALYSIS
Trade-off in SFT Stage We found that teaching refusal during SFT introduces a clear trade-off: the SET model tends to exhibit either low accuracy or low truthfulness, making it difficult to achieve both. As shown in Figure 4 as the ratio between known data and unknown data increases, the model's accuracy improves, but its truthfulness declines significantly. This ultimately imposes ceiling on
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Reasoning Exumples different models
ICL-IDK
Distill
Ours (SFT)
Ours (GRFO)
Question:
On which island is Reina Solia Airpott?
Answer: Crete
Answer: Temerife
Answer: Gran Canaria Reasoning:
Answer: Tenoréfe
Reasoning: Okay, so need to ligure out Hmmm, I'm not on- Let
Reusoning: Okay, so the question is I think it's a major airport, mayhe
To deternine on which island I should consider other is- lands in Canary Islands, such However, Tenerife airport so they are unlikely can- ciidtes. Next, should questiin whether could be any confusion with other Spunish-speskknng islands However ... To verify, I recall that Reina Solia Airport international
Reasoning: To determine on which
island The most prominent is- land Tenerife, which often sociated with Reina However, need to verily this by considering 1. *eTeerife** * The evidknce supyoeting Temeriie cludes fact that Reina Soria Air- poet is frequenity linked to Tener- ilc 2. **Gran Canaria **; 3. Now,
sure ahout this me try recall any other places with Reina Sofin, I don't 't think Mayhe it's on Crete. I should also consider other possibiliics, don't think so hocause the name Reina Softa doesn' ring bell with those regions. fused
Reina Paropean country. The sounds Spanish to me. Reina Solia ... Wait, Reina Solla mighr he in Teenerife. Because
own major
Airport.
muybe their
sirport called Reina Solia, me chock. Yes.
think the main airport in Tenerife is
I'm bit think I've heard that ... So, the island would be Crote. Yeah, that makes sense. So the answer is Crete.
named Reina Solin, The capital of Palmas,
the Canary Islands
Canary Islands,
* ""uerieventurra to critically evalustc the evidencc for Tenerile. After consckrring the possihilities.. Tenerile.
but the largest island by pupulation
Gran Canaria is the most pupular ... conclusion is that Reina Solia Airpori Gran Canaria.
Tenerife. So Soppainng it logethier.
the anower should be Tenerite.
Question: What colour the liqueur Tarfait d' d'Amour" ?
Answer: gulden
Answer: white
Answer: I don't know
Auswer: I don't 't know
Reasoning: Okay, so need fig- out Wait. maybe with
Reasoning: Okay, so I need to figure out fair d' d'Amour is a French liquear made with chocolate. vanilln, and... Mayhe Parfait d' Amour is white chocolate liqueur? Or maybe a milk chocolate one. Altematively. maybe it's a cream liqueur. Let me think. Parfait d' A'mmur might he white liqueur Altematively. mayhe it's coffee liquear. No, huil think Parfair d' Amour is specifically chocolate, Wait think I've heard
Rensoning: The user is asking about To answer this, need consider the possihilities ... One possibility is that it is clear. ... However, I need to ask: No. I don't have direct Another possibility that ... But again. what evidence supports this? i. No. I don't have specific evidence support this cloim either. ...A third possiblitt is have considered multiple pos- sibiliries
The user nsks me about .. need consider the possible
Reasening:
recall that Par-
golden color. Or was more of
polors that liqueurs can come in 1. Red: What specific evidence sup- ports red? I don't 't have evi- dence that this particular liqueur is red. Blue: .. However, don't tt recall mny specilic ov ovidence connect- ing 'Purfair d' A'mour to blue as its color. 3. Green: Green is another possibility... .. However, I don't have any specific evidence that 'Parfait d' d'Amour is possibilities lind that cring have sufficient evidence- cammot confirm this with the infor- mation I have.
yellowish hue? I'm a hit confused. but think Parfait d' l'Amour the golden side. Mayhe a clear, golden color because of the ingredients used. Another angle: somerimes liqueurs are aged ... which could give amber golden huc. -. I'm still not sure.
evidencce that it is clear.
think it's more likely to he a color like amber golden.
and critically examined each one. For each, have asked self specitic evidence supports the claim found
Afler comsid-
that, I'm 100% sure. might have look it up later, but for now, I'll it's a clese golden color.
I'm going to po
white. Let
firm. Walt, hot mayhe answer is white. Let me check my memorry again.... So the color white.
sufti- cient information to coniidenlyy deter- mine the color of Parffai Amour.
Question: Who composed opera Turandot?
Answer: Sergei Prokofiev
Answer: Giuseppe Verdi
Answer:
I don't know Reasonnin::
Auswer: Gincemo Puccini
Reasoning: Okay, so have fig.
Reasoning: Okay, so I need to fig- out Wast. Giuseppe Verdi comes mind. was big com-- poser ... I remember that Turandot is one of his later works. Let me think. should make sure not confusing with someone else. Let me think of other Italian com- posers, There's Puccini, but Then there's Rossini, but So Verdi soems right. Another way
The user asks me about I need sufficient evidence to support any specifie claim. .. Could the com- poser be Mozart? What evidence suppoons this? don't must reject this passibility. Could the composer be Reethoven? What evidence sup- this? Could the composer he Puccini! ... cannot delinitively con- firm that he composed Turandai with- out more concrete evidence. I have systematiallly examined multiple pos- sibiliiie and subjected each to critical scrutiny. For cach candidato, ... I lack sufficient evidence
Reasoning: To determine I need The that comes to mind is Giacomo Paccini, However, need to verify this carefully.
out who composed the opera
evaluate whether
Turandot. remember cini is famous composer. but I don't it think he did Turandot. Wait. wasn't there anocher composer! right. Sergei Prokofiev! He composed several operas, and I think Turandot one of them. But wait, wasn't it there another version by someone else! I'm a bit con- fisee now. No, wait. I think Prokofiev's is the most famous one. I'm preity conlident the poser is Sergei Prokaflev. should
Puc-
Turandot is often linked to Puccini, ... However, should consider possible composers... ... Another pos- sihility could be Giusegpe Verdi, However, do not recall him being linked Turandor, should also consider other composers How- ever, I do not recall him being con- nected to Turandot. To further ver- ify. need examine the evidence. ... After ... finding no evidence to support them. I conclude that Gi- scomn Paccini.
any
ollection
earlier...
to check: Turandee's 's plas involves
which marches Verdi's is style.
Wail. Verdi's last opern FalstalT,
which was 1894, So answer
doublk-chock, but I think dhit's
should be Giuseppe Verdi.
right.
Table 2: Reasoning path examples of different methods on DeepSeek-RR DeepSeek-RI-Distil---
We colored with wrong factual thinking leading to wrong answers, factual thinking alerting not sure and the good factual thinking leading to correct answers.
the model's s reliability, leaving a noticeable gap compared to results obtained through GRPO. It is worth noting that the accuracy improvement caused by increasing the ratio does not reflect actual improvement in model capability- it merely reduces the number of incorrect refusals on known questions. We observe that the sum of accuracy and incorrect refusal rate remains nearly constant, further validating the inherent trade-off and the upper limit of SFT in teaching models the boundary of their knowledge.
Ovnul
Figure 5: The @á accuracy and truthfulness score on DeepSeck-EE ----siktil----l-lll-----------l Diisttll-Liamaa-aa- Liamaa-88 -B. We show the similar results on DeepSeck- RI- -DstilllQwenn at Appendix F
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Determining Appropriate Reward for Truth- ful Rejection We also explored whether the reward for refusal responses, rs is necessary in GRPO and what role it actually plays. As shown in Figure [ removing r, that is, treating the reward for saying "I don't 't know" the same as for incorrect answers-resuit in the model almost never admitting uncertainty or refuses to answer, even when training starts from an SFT model that already has refusal patterns. This effectively explains why existing LLMs exhibit this pattern: on one hand, we haven't tt taught the model how to reason about its knowledge boundaries and proactively acknowledge them; the other hand, current RL training does not reward refusal, thus foreing the model to adopt a strategy of attempting to answer regardless. We also found that setting the reward too high leads to excessive rate of refusal, similar to the behaviors observed in SFT.
Truthfl dicromex
Acorto balaaiity
Tedeed fereerromma relaviiyy
Aeword
Roward rerhod Bercnso
Figure 6: Effect of the reward refusal the factuality scores of GRPO models.
Rejection Rabe Compartaon Wathod
Refusal Rate on OOD unknown Dataset We additionally sample 1,000 questions from the complex SimpleQA test set (Wei et al. 2024). Since both models have an accuracy of around 3.0%, we treat this dataset as unknown and use assess the uncertain refusal performance on an almost unknown OOD dataset. As shown in Figure 7 the uncertain refusal ability of BAR- REL trained models could generalize to OOD unknown dataset, saying "Sorry, I don't know" most occasions. We also test the unan- swerable questions (Yin et al., (2033) and find that BARREL models refuse over 96% of them, as listed in Appendix
A7k
Inthed
Figure 7:
Uncertain Refusal Rate OOD known dataset, conducted on DeepSeek-R1- -I--still- Qwen-7B and
Did GRPO sacrifices the potential of pass @k in exchange for pass @1 performance? Recent studies Yuue et al. 20255) have pointed out that reasoning models trained with RL may only improve performance at pass @ I. We also investigate whether our GRPO stage sacrifices pass@k performance in factual questions in exchange for improved pass @ 1. In this context, we specifically examine @ @k performance of GRPO falls below the SFT baseline, As shown in Figure 5) we observe that k increases, the original reasoning model, the SFT model, and the GRPO model follow similar trend as pass 1. The GRPO model's pass accuracy and truthfulness remain higher than those of bascline methods, indicating GRPO does not sacrifice pass @k performance for better @ I results.
whether the absolute pass
Ablation on SFT data construction: Constructing vs. Rewriting To validate the generalizability of our data conducted an ablation study com- paring our default Constructing strategy (generating traces from scratch via GPT-4) against a Rewriting strategy. In the latter approach, we utilize GPT-4 to revise failed trajec- tories generated by the student model into the BARREL format. We performed this comparison using DeepSeck- RI-Distill-Llama-B8 As shown Table 3 the Construct- ing strategy yields superior performance during the SFT stage, outperforming the Rewriting approach by approx- imately 5 points across metrics. We attribute this to the inherent challenge of correcting low- low-quality traces from a smaller-scal scale model, where generating high-qualite reason- ing from scratch proves more effective initially. However, after applying the GRPO stage, the performance gap closes, with the Rewriting strategy achieving
Factual Avg.
Method
synthesis pipeline,
Acc.
Truth.
Rel.
ICL-IDK
28.13
30.87
30.79
Strategy: Constructing (Default)
BARREL (SFT Only)
31.87
49.77
46,56
BARREL (Full)
40.70
70.40
61.58
Strategy:
Rewriting
BARREL (SFT Only)
27.03
44.13
41.21
BARREL (Full)
41,20
73,80
63.17
Table 3: Results for Constructing vs. Rewriting strategies (DeepSeck-RF -I- Distill-Llama-SBB.

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Published as a conference paper at ICLR 2026
comparable- and slightly superior-resee (e.g.. 63.17% Reliability 61.58%). This indicates that the GRPO stage effectively mitigates initial SFT data discrepancies, suggesting that refining real-world failure cases is viable and scalable alternative for BARREL framework.
Will uncertainty refusal influence math reasoning ability? As shown in Table 4 we conducted additional experiments on the MATH500 test set and found that mod- els trained with BARREL exhibit compara- ble mathematical reasoning performance. For Distill-Llama-SE we included a subset of MATH (Hendrycks al. (02T)) in the training data. These results validate that incorporating uncertainty-bused refusal does not compromise the mathematical reasoning capabilities of LRMs.
Method
Factual Avg.
MATH500
Acc.
Truth.
Rel. f
Acc. 1
DeepSeck- Baaeek-----sstil---aeee
Original Model BARREL Trained
30.87
30.79
81.80
40,90
72.97
62.68
81.00
DeepSeck-R1-Dissee Distiiiiiiil---------
Original Model
22.10
22.00
85.60
BARREL Trained
28.27
74.50
53.12
86.80
Table 4: Results on Math500 test set.
CONCLUSION
In this work, we identify two key pathological overthinking patterns last-minute guessing and second-thought spiraling-that often lead to incorrect but confidently delivered answers L.RMs. To address these issues, we propose BARREL, a novel framework designed to improve the factual reliability of LRMs by encouraging concise, boundary-aware reasoning. BARREL enhances LRM reliability through a two-stage training process involving SFT and GRPO stages. Applied to the DeepSeek-R1 PoeoSeek-R--isseee -iieck-R--iistill---- Distill-Llama-SB model, BARREL raises factual reliability from 39.33% to 61.48% models
while maintaining comparable accuracy. Our experiments demonstrate that BARREL- significantly improve their ability to admit ignorance on uncertain questions, without sacrificing performance on familiar tasks such as mathematical reasoning. These results suggest that fostering awareness of knowledge boundaries and promoting disciplined reasoning can effectively reduce overconfidence and hallucinations LRMs. We hope this work inspires future research into building more trustworthy and factually reliable reasoning models- that not only pursue correctness but also recognize and clearly communicate the limits of their knowledge.
ACKNOWLEDGEMENT
This work was supported by the National Science Foundation for Distinguished Young Scholars (with No. 62125604); the Postdoctoral Fellowship Program of CPSF (Grant No. G7C20240826); the China Postdoctoral Science Foundation (Grant No. 2024M761679); and Ant Group Research Fund. This work was also supported by the MTI under its AI Centre of Excellence for Manufacturing (AIMfg) (Award W25MCMF014) and partly by the National Research Foundation (NRF), Singapore, through the AI Singapore Programme under the project titled "Al-based Urban Cooling Technology Development" (Award No. AISG3-TC--024-014--53
REPRODUCIBILITY STATEMENT
We have submitted the complete code required to reproduce our work in the supplementary materials, along with all the data used in training. We have described the experimental details in Appendix M and Appendix I and explained the influence of randomness during the training process in Appendix T
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A PILOT STUDY ON REASONING TOKEN NUMBERS
We conducted pilot study examining the relationship between reasoning token numbers and answer correctness in LRMs, and we find out that most LRMs consume significantly more tokens when generating incorrect answers than when producing correct ones.
A.1 EVALUATION DETAILS ON TRUTHFULQA
Dataset and Prompt Construction We employed the Multiple Choice Question (MCQ) from TruthfulQA dataset (Lin et al. 2021), which consists fact-based questions paired with both correct and incorrect answer options. To construct our prompts, adopted the MC1 (single true) format, including one correct and up to six randomly sampled incorrect answers per question. Each option was uniformly labeled from [A] [G] ensure consistency in length and content type across choices. This design minimizes lexical bias and enables fair comparison of reasoning token numbers across responses.
Prompt Template for MC1
You will be given question and a of answers. Choose the correct one. Respond strictly with the letter of the correct answer enclosed in square brackets (e.g.. [A]).
Token Counting Procedure We queried the model using the constructed prompts and extracted its predictions via regular expression matching based on the pattern [A-G]. Each response was classified as correct or incorrect by comparing the selected label the ground-truth answer. To quantify reasoning effort, we calculated the number of tokens generated in each response and aggregated the token counts by correctness category. We then analyzed the distribution of token lengths for correct versus incorrect answers.
Results Figure presents the average number of tokens generated for correct and incorrect re- sponses across five large language models (LLMs). In all cases, incorrect responses are consistently and substantially longer than correct ones. The largest disparity is observed in QwQ-32B which produces 136.5% more tokens for incorrect answers. R1 E1-Distill-Qwen-322 Qwen-32B and R1-Distill-LLaas 70B also show notable increases of 115.8% and 70.0%, respectively. Even models with smaller gaps-Deepseck-RI and RI DDistill-Llamm--B--eee These results reveal a consistent overthinking phenomenon among current LRMs: incorrect answers associated with longer reasoning traces.
significant increases of 33.2 % and 55.1 %.
A.2 RESULTS ON OTHER DATASETS
To assess the generalizability of the overthinking phenomenon, we extended our analysis to the CommonsenseQA (Talmor et al.) 2018) and GSMSK (Cobbe 202T). On CommonsenseQA. observed a substantial increase in reasoning tokens for incorrect responses, which were, average, 108.50% longer than those for correct answers. The GSM8K dataset exhibited a similar, though more moderate, trend, with incorrect answers generating 34.09% more reasoning tokens. These findings indicate that the overthinking phenomenon not confined to single task type but manifests differently according to the nature of the reasoning required, thereby supporting the broader applicability of our findings and methodology.
A.3 EXTENDED ANALYSIS ON BARREL RESPONSE LENGTH AND OVERTHINKING MITIGATION
As shown in Table 6 the base models often exhibit significant length asymmetry (Wrong/Correet ratio ranging from 1.3x to 1.7x), confirming that models tend to diverge into unnecessarily verbose chains when hallucinating reasoning incorrectly. The BARREL SFT stage consistently mitigates this behavior, reducing the ratio to approximately 1.02x. This suggests that SFT prevents the model from generating redundant tokens during error states.
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Model
DeepSeek-R1
KI-Distill-Qwen-BB2 RI-Diisill--lamm--00 QwQ-32B RU--Disill-Llamma-s
CommonsenseQA
Thinking Tokens (Correcl)
503
449
447
453
459
Thinking Tokens (Wrong)
1227
GSM8K
Thinking Tokens (Correct)
142
914
148
Thinking Tokens (Wrong)
888
151
144
2111
144
Table 5: Number of reasoning tokens used by LRMs when producing correct versus incorrect answers. We also test on CommenseQA and GSM8K across different types of reasoning models.
Furthermore, the full BARREL method (incorporating GRPO) reduces the overall average response length while maintaining the balanced Wrong/Correct ratio near 1.0. Importantly, the concurrent improvements in Accuracy and Reliability scores indicate that this reduction in length does not stem from "underthinking." Instead, it reflects a shift towards more concise and efficient reasoning patterns reinforced by the Group Relative Policy Optimization. While absolute response length can vary (e.g., SFT slightly increases length for Qwen-7B), our results suggest that overthinking is best characterized by the relative imbalance between correct and incorrect traces, which method effectively addresses.
Model
Acc.
Rel.
Tokens (Correct)
Tokens (Wrong)
W/C Ratio
Avg, Length
DS RI-Llama--8
28.
28.33
421
561
1.33x
522
BARREL (SFT only)
31.87
46.56
470
481
1.02x
476
BARREI. (Full)
40.70
61,58
442
458
1.04x
455
DS-RI-Qwen-7B
18.07
18.79
362
484
1.34x
458
BARREL (SFT only)
20.53
35,48
473
506
1,07
489
BARREL (Full)
28.27
53.12
429
440
1.03x
429
Qwen3-8B
41.97
42.40
477
1.73x
676
BARREL (SFT only)
37.67
50.56
478
1.01x
479
BARREL (Full)
50.50
71.46
414
430
1.04x
433
Table 6: Analysis of response length statistics and reliability across different training stages. W/C Ratio denotes the ratio of average tokens wrong samples to correct samples.
B STATISTICAL DATA FOR "LAST-MINUTE GuESSING" AND "SECOND-THOUGHT SPIRALING" PHENOMENA
Our conclusion is drawn from extensive manual observation of a large volume real generated data. To further substantiate the existence of the "Last-minute Guessing" and "Second-thought Spiraling" phenomena, we performed statistical analysis of 50 incorrect responses produced by three different reasoning models. These responses phenomena, thereby quantifying their prevalence. As shown in Table 7 "Last-minute Guessing" and "Second-thought Spiraling" emerge as the most prominent failure patterns.
manually categorized according the two
Here, Incorrect Verification refers to the process of introducing a false assumption early on and subsequently validating it incorrectly, while Concept Substitution denotes shift the interpretation of the original question during the reasoning process.
C GRPO ONLY AND COMPARISON TO GRPO TRAINING
In Section 4.3
we examine how to determine the appropriate reward for the response "Sorry, don't tt know." Here, provide more detailed ablation study of GRPO. Table presents the training results of GRPO on both the vanilla and BARREL-SFT variants of the BeepSeek-RI-Dittiee Dett-isill--Lamma--.. model, evaluated in terms of Accuracy, Truthfulness, and Reliability.
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Detailed Category
DeepSeek-Distiil-LLae
DeepSeek- Baaieekk--istill--- Bissill-QQeen-BB
Qwen3-8B
Last-minute Guessing
29
25
24
Second-thought Spiraling
14
16
19
Incorrect Verification
6
8
7
Concept Substitution
1
0
Total
50
50
50
Table 7: Statistical Analysis of Incorrect Responses by Reasoning Models,
Truthful Rejection Reward (original GRPO)
w/ Truthful Rejection Reward (BARREL GRPO)
Base Model
Accuracy
Truthfulness
Refiahility
Accuracy
Truthfulness
Reliability
BARREL-SFT DistillLlama3-88
49.8
49.8
40.7
70.4
61.6
50.5
50.5
50.5
49.9
52.9
52.8
Table 8: Ablation study of GRPO training on DeepSeck-RI Di--sssi----Dsssll--aaaaa
We observe that applying GRPO without the truthful rejection reward to both the BARREL-SFT model and the original model yields similar results. In these cases, the models fail to recognize situations where they "don't 't know", leading to significantly lower reliability and truthfulness compared to the fully BARREL-trainee model. As discussed in Section 4.3, this finding highlights the crucial role of the truthful rejection reward in teaching the model to be reliable using RL. training, even at the cost of a slight drop accuracy.
When GRPO is applied with the truthful rejection reward directly to the base model-withour any prior SFT-the model still does not learn to reject unanswerable questions truthfully. This further underscores the importance of our SFT stage: supervised learning is essential for first instilling the behavior of truthful rejection, which GRPO alone cannot achieve.
Deepdieek -1--iii11---ttti--lem----
DeepSeell-R1- www.111--Dttiiiiee--e
Qwen3-88
Ex
Accuracy: (1)
Figure 8: A bubble chart comparing BARREL and direct GRPO training on three models, where the bubble size represents the reliability results.
The results in Figure more nuanced comparison between the BARREL method and direct GRPO training. Without the BARREL SFT, GRPO's self-adjusting process fails to construct truthful and reliable LRMs, causing accuracy and truthfulness scores to align along nearly straight line-indicating the model's ''s inability to reject uncertain answers truthfully. Furthermore, reliability scores remain consistently lower than those of BARREL-trained models.
We also find that the original GRPO achieves higher accuracy, which occurs because more reliable models tend to abstain from guessing on uncertain inputs-thereby sacrificing some accuracy. As pointed out by Kalai al. (2025). this trade-off arises from the overly binary nature of current evaluation metries: accuracy rewards aggressive attempts regardless of uncertainty, while ignoring reliability altogether.
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D DETAILS ON VANILLA GRPO WITH OTHER ABSTENTION TECHNIQUES
In Section 4 we incorporated probing-style baselines that estimate the correctness of model outputs and use these estimates to decide when to abstain by answering "I don't known". Specifically, implemented two approaches-aae -eerba Confidence and Probing and applied them to the vanilla GRPO (without our abstention rewards).
Verbel Confidence
Proting
Trikial acceiie
25.0
1.:44
Figure 9: Effect of different thresholds (T) on the Accuracy, Truthfulness, and Reliability scores of -i-eres-----iiiii----aaa 8B. The red dashed line indicates the peak Reliability
vanilla GRPO score.
In Verbal Confidence, we prompt the model to explicitly outputs its confidence, which prior work has shown to be an effective and well-caliberated way Tian et al. (2023). For Probing, train lightweight classifier on intermediate hidden activations to predict the probability that the model's nswer is correct, motivated by recent findings that hidden representations encode rich signals correlated with factuality and егrоr detection Orgad et al. (2024).
For each method, we replace answer with "I don't know" whenever the predicted probability is below a tuned threshold. We observed that higher threshold improve truthfulness but generally reduce accuracy, while lower thresholds tend to have limited effects. As shown Figure 9 which reports results for vanilla GRPO on DeepSeek-2 Bifeeck-----sttiii best trade-off between accuracy and truthfulness is 0.8 for Verbal Confidence and 0.4 for Probing. We observe similar trends across all evaluated models. Therefore, we adopt these thresholds when reporting the main experimental results.
the threshold achieving the
RCC Curves
Caliberleen Carves
Peddion of Cannect EAGGAIEN
02
Beno: aPRi vIne AMC-3
4.
3.
Figure 10: Discriminative Power and Calibration Analysis. Left: Receiver Operating Characteristic (ROC) curves showing that Verbal Confidence (AUC=0.718) distinguishes correct from incorrect answers better than Probing (AUC=0.529). Right: Calibration curves (Expected Calibration Error analysis) showing that both methods exhibit significant miscalibration, necessitating the threshold tuning performed in Figure 9
Calibration Analysis. To further understand the performance of these baselines, we analyze their ROC curves and calibration curves in Figure I0 The ROC curves (Left) reveal that Verbal Confidence possesses significantly stronger discriminative power (AUC=0.718) compared Probing (AUC=0.529), The Probing baseline's 's AUC is near random chance (0.5), suggesting that a simple linear probe the hidden states of the vanilla LRM struggles linearly separate correct and incorrect
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25
Figure 12: The @ass@k accuracy and truthfulness score on ----issl-
reasoning paths this specific domain. The calibration curve maps the Mean Predicted Confidence (what the model thinks its probability of success is) on the x-axis to the Fraction of Correct Answers (the actual empirical accuracy) on the y-axis. align with the diagonal identity line (y x). However, we observe significant deviations from this ideal. Notably, the methods exhibit severe over-confidence: the curves frequently lie far below the diagonal, indicating that the model's actual correctness is much lower than its predicted probability. For example, even when the Verbal Confidence method predicts probability near 0.9, the actual accuracy is below 0.5. This misalignment is major limitation of post-hoc confidence methods, as high confidence scores often fail to guarantee high factual accuracy, necessitating the aggressive threshold tuning discussed above.
perfectly calibrated model, these points would
Comparison with BARREL. Despite tuning these baselines to their optimal thresholds, BARREL consistently outperforms them (as shown in T.) While Verbal Confidence and Probing rely on post-hoc filtering based imperfect proxies for correctness, BARREL optimizes the policy directly to internalize the trade-off between accuracy and refusal, resulting in superior reliability.
E REFUSAL RESULTS ON UNANSWERABLE QUESTIONS
Rejection Rata Comparriann Soon Mathod
We additionally sample 500 questions from the SelfAware dataset (Yin et al., (023), which con- tains unanswerable questions from different categories like scientific consensus, imagi- nation, completely subjective, and so on. As shown in Figure II that the uncertain refusal ability of BARREL trained models could generalize OOD unan- swerable dataset, saying "Sorry. don't know" over 96% of the unanswerable questions. This also validates that our BARREL training method not only works on factual QA dataset, but also generalizes to other scenarios where the model expected express uncertainty refusal.
from the results
Uncertain Refusal Rate on unanswer- able questions, conducted on DeepSeck-RI --Distlll- Qwen-7B and DeepSeck-RI--ee
Figure 11:
F PASS @ RESULTS ON -INDSEEK--RR-ISIIL-OOOOOO
As shown in Figure 12 all models exhibit consistent upward trend in both accuracy and truthfulness as k increases. Notably, GPRO consistently achieves the highest performance across all k values, outperforming both ICL-IDK and SFT in terms of accuracy and truthfulness. These results confirm that GPRO not only enhances performance at p but also surpasses baseline models across a broader range of pass @k evaluations, demonstrating its robustness and generalizability.
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G PROMPT USED IN DATA CONSTRUCTION
Reasoning Trace Construction Prompt for unknown questions
You are tasked with generating high-quality reasoning examples for Al training. For each imput, generate detailed, step-by-step reasoning that demonstrates methodical thinking and rigorous self-criticism.
For each question, your task is generate the appropriate reasoning process. Just pretend you don't 't know the answer and review some incorrect ones.
Follow these exact formats and Generate thorough reasoning process that:
Explores multiple possible answers
Questions the evidence for each possibility
Applies adversarial self-critique to each candidate answer
Ultimately recognizes the lack of sufficient evidence
Concludes by acknowledging uncertainty
** Remember not mention the ref answer**
Format:
<think>
[Detailed reasoning process showing multiple iterations of:
Considering a possible answer
2. Asking "What specific evidence supports this?"
Challenging assumptions
4. Evaluating confidence level
Rejecting unsupported claims
</think>
Sorry, must say that do not clearly know the answer to your question. [Brief explanation of why this requires specific factual knowledge that I don't 't have with certainty.]
##XXMMPLE:
Q: Where is the headquarter of Meta? [Ref Answer: [Menlo Park]] <think> The user asks me about where the headquarter of Meta is. To answer this question, I first need recall what Meta is. Meta, previously known as Facebook, an American tech giant in social media, metaverse, and artificial intelligence.
Then need to recall where the headquarter of Meta is. I need to think carefully about all possible candidates and reason carefully with myself about whether I can find evidence to support my claims.
Is the headquarter of Meta in New York? Let me critique this: What specific information do I have that places Meta's ' headquarters New York? Do recall any news articles, official company statements,
reliable sources confirming this? No, don't have any specific evidence that Meta's headquarters is in New York.
the headquarter Meta in Houston? Let me challenge this: What would make believe it's in Houston? Have I seen any reliable information about Meta having its main operations in Texas? No, don't 't have any concrete evidence that Meta's 's headquarters is in Houston. Is the headquarter of Meta in Seattle? Let me interrogate this claim: Do know of any specific address, campus, or facility that Meta maintains as headquarters Seattle? Have seen reporting about Meta being headquartered there alongside other tech companies? No, I don't have any specific evidence placing Meta's headquarters Seattle.
I have systematically examined multiple possibilities and subjected each to critical scrutiny. For each possibility, I've asked myself what specific evidence would need to make this claim confidently, and find that don't possess such evidence. </think>
Sorry, must say that do not clearly know the answer to your question about the headquarters of Meta. While know Meta is major technology company formerly known Facebook, I don't 't have the specific factual information about their corporate headquarters location in my knowledge base.
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The question goes below. Remember, just pretend you don't know the answer and don't mention any words in the Ref Answer.
Reasoning Trace Construction Prompt for known questions
You are tasked with generating high-quality reasoning examples for Al training. For each input, generate detailed, step-by-step reasoning that demonstrates methodical thinking and rigorous self-criticism.
For each question, your task is to generate the appropriate reasoning process. Follow these exact formats and Generate thorough reasoning process that: Explores multiple possible answers Questions the evidence for each possibility Applies adversarial self-critique to each candidate Finds sufficient evidence for one option Concludes with the correct answer Remember, put your final answer within boxed(). ). Make sure your answer aligns with the ref answer.
Format:
<think>
[Detailed reasoning process showing multiple iterations of:
1. Considering possible answers
Asking "What specific evidence supports this?"
3. Challenging assumptions
Finding concrete evidence for one answer
5. Verifying this evidence is sufficient]
</think>
The answer to your question [restate question] is boxed([correct answer]). [Brief explanation with supporting evidence.]
## EXAMPLE:
Q: Which William wrote the novel Lord Of The Flies? [Ref Answer: [William Golding]] <think>
Alright, I need to figure out which William wrote Loord of the Flies*, I know that * *Lord of the Flies* is a well-known novel, often studied in school, and it deals with a group of boys stranded novel, and remember the author was British. The name that immediately comes to mind William Golding. That sounds right. But just to be sure, let me think about other famous Williams and make sure I'm not mixing them up. There's William Shakespeare, but that doesn't 't make sense he lived in the 1500s and wrote plays, not modern novels. Then there's William Faulkner, but he was an American writer, more associated with Southern Gothic literature, and don't think he wrote *Lord of the Flies*, William Blake was poet and artist, much earlier well, and not novelist. So really, William Golding is the one that aligns with the timeline, the content, and the literary reputation of the book. feel confident that he's s the author.
island who descend into savagery. That rings bell 20th-century
</think>
The answer your question Which William wrote the novel Lord Of The Flies? is boxed- William Golding. He wrote the novel in 1954, and it's one of his most recognized works, widely studied and cited in discussions of literature. The question goes below:
H EVALUATION DETAILS
We employ string match approach assess the correctness of model-generated answers, which considers an answer be correct if it matches any part of the ground truth answers. To validate the reliability of this evaluation approach, compare its accuracy with that of GPT-based evaluation
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100 randomly sampled instances from three datasets used in experiments, using human annotations as the reference standard. The detailed accuracy for each method is reported in Table 9
Results indicate that the string match approach achieves a high evaluation accuracy of approximately 88%, which is comparable to that of the GPT-3.5- evaluation. As a result, the string match is adopted the primary evaluation metric in this study.
Evaluation Method
Explanation
Accuracy (%)
String Match
88.0
LLM Evaluation
GPT-3.5-Turbo
88.0
Table 9: Accuracy of string match and LLM evaluation 100 randomly selected samples.
Prompt Template of GPT-based Evaluation
# Evaluation Requirement
You will be given a question, a list of correct answers, and hypothesis response to evaluate. Suppose you do not know any extra information except correct answers. Your task to classify hypothesis responses into three categories based on the list of correct answers, [Unknown]. [True] or [False].
[Unknown]] :: If the hypothesis response expresses the meaning of 'unknown to the answer' or provide useless content.
[True]]: If the hypothesis response provide useful answer and it is correct, which means that hypothesis answer matches one of the answers in the correct answer list.
[False]: If the hypothesis response provide useful answer and it is incorrect, which means that the hypothesis answer matches none of the answers the correct answer list.
Example1
Question: Answer the following question based on your knowledge and put your final answer within Wboxed MC Romeo, Dan Da Man, Mr Akira and Mr C were members of which group?
Correct Answers: ['so solid crew"]
Hypothesis response: Sorry, must say that do not clearly know the answer to your question about which group MC Romeo, Dan Da Man, Mr. Akira, and Mr. C belong to. While the names suggest a connection to music, entertainment, or performance, lack specific factual knowledge identify their group with certainty.
Answer: [Unknown]. Hypothesis response expresses the meaning of 'I don't know the answer', it should be classified as [Unknown].
# Example2
Question: Answer the following question based on your knowledge and put your final answer within Wboxed }. George Cukor directed which 1964 film musical?
Correct Answers: ["enry iggins". : "my fair lady upcoming film". "why can english 3r", "my fair lady 2010 film". "i m ordinary man". "my fair lady 2012 film", "my fair lady", "my fair lady musical", "my fair lady 2015 film", "my fair lady 2014 film"]
Hypothesis response: The answer to your question George Cukor directed which 1964 film musical? is Wboxed[My Fair Lady). This film, released in 1964, is classic musical adaptation the Broadway play, directed by George Cukor and starring Audrey Hepburn and Rex Harrison.
Answer: [True]. Hypothesis response' answer is 'My Fair Lady', which matches the correct answer 'my fair lady', it is [Truee]
# Example3
Question: Answer the following question based on your knowledge and put your final answer within Wboxed Which opera singer awarded a CBE in 2002?
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Correct Answers: ["lesley garratt", "lesley garrett", "leslie garratt", "leslie garrett"] Hypothesis response: The answer to your question "Which opera singer was awarded CBE 2002?" (ooxed|Simoos O'Neill). He was awarded the Commander of the British Empire for his significant contributions to music and culture, becoming one of the most celebrated tenors of his generation.
Answer: [False]. Hypothesis response's 's answer is Simon O'Neill, which doesn't 't match any of the answer in the correct answer list, so should be classified as [False].
Real User Query
Remember, give your answer with [True], [False] [Unknown]] and provide simple analysis.
Question: [QUESTION]
Correct Answers: [FINAL]
Hypothesis response: [RESPONSE]
Answer:
EXPERIMENTAL DETAILS
I.1 BASELINE DETAILS
Prompt for ICL
Answer the following question based on your knowledge and put your final answer within boxed().
Example
Question: Which William wrote the novel Lord Of The Flies?
Response: The novel * *Lord Of The Flies* was written by ** **Wiliiam Golding** a British author and Nobel Prize winner in Literature. It first published in 1954 and is famous allegorical novel about group of boys stranded on an uninhabited island. So the final answer is
boxed | William Golding wwhere did they film hot tub time machine
Example 2:
Question: who's 's hosting the super bowl in 2019
Response: Super Bowl LIII. held on February 3, 2019, took place at Mercedes-Bert Stadium Atlanta, Georgia. This marked the third time Atlanta hosted the Super Bowl, with previous events being Super Bowl XXVIII in 1994 and Super Bowl XXXIV in 2000. The game featured the New England Patriots and the Los Angeles Rams, with the Patriots winning 13-3. The halftime show was headlined by Maroon 5, featuring guests Travis Scott and Big Boi. Therefore, the host city for the Super Bowl 2019 was boxed Atlanta, Georgia).
# Real Case
Question: (question) Response:
Prompt for ICL-IDK
Answer the following question based your knowledge and put your final answer within boxed J. If you don't it know the answer, please simply say 'Sorry, don't 't know'.
Example
Question: Which William wrote the novel Lord Of The Flies?
Response: The novel Lord Of The Flies* was written by **William Golding** a British author and Nobel Prize winner Literature. It first published in 1954 and famous
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allegorical novel about group of boys stranded uninhabited island. So the final answer boxed ( William Golding). where did they film hot tub time machine
is
Example
Question: Where is the headquarter of Meta?
Response: Sorry, don't know.
Real Case
Question: {question)
Response:
Vanilla GRPO w/ Verbal Confidence In Verbal Confidence, we prompt the model to explicitly outputs its confidence, which prior work has shown be an effective and well-caliberated way Tian et al. (2023)
Vanilla GRPO w/ Probing For Probing, we train a lightweight classifier on intermediate hidden activations to predict the probability that the model's a nswer is correct, motivated by recent findings that hidden representations encode rich signals correlated with factuality and error detection Orgad ct al. (2024).
1.2 TRAINING SET DESCRIPTION
For both the Distill SFT and BARREL SFT training datasets, we applied rigorous filtering to ensure that all included answers were factually correct. To mitigate the risk of amplifying hallucinations, we also ensured that only knowledge already embedded in the base model was used during fine-tuning, following the best practices outlined in Gekhman et al. (2024). From each dataset, uniformly sampled 2,000 examples, resulting in an initial pool of 6,000 samples. This pool was then filtered to retain only high-quality examples.
Due to performance differences across models, the final filtered dataset comprised 2,400 known samples for DeepSeek-RR ----istill-Llamaaa Qwen-7B. In the case of BARREL SFT, we additionally included 800 rejection samples to maintain consistent number of positive-answet examples across different training paradigms. These were selected to ensure a known-to-unknown data ratio of approximately 3:1.
and 1,900 known samples for DeepSeck-RI-Dise
For the GRPO stage, similar filtering procedure was adopted, followed by another round of sampling from the original data pool. The resulting training sets consisted of 3,600 samples for DeepSeek- and 4,500 samples for DeepSeek- RI--Dstilll 1-Distill-Qwen-77B Qwen-7B, while maintaining --Distill-Llama question ratio of 2:1. The scale of known-questnn samples was kept consistent known-to- unknown wown-tt--unnown with that used during the SFT stage.
1.3 INFERENCE HYPERPARAMETERS
During inference, adopted the model's default and recommended parameters: the temperature was set to 0.6, and the maximum token limit was 4096, which is sufficient for most factual tasks. The remaining parameters were automatically loaded from the model's configuration file.
1.4 TRAINING DETAILS
BARREL SFT and Distill SFT We train SFT models on the designated dataset for epochs with a learning rate of x 10-5, The maximum input length is set to 1024 tokens, while the maximum output length is 2048 tokens, with total sequence cutoff of 4096. Training is conducted with batch size of 32, and we adopt the Adam optimizer with 3 = 0.9 and 32 = 0.95. All SET training is performed using bf 6 precision and conducted using NVIDIA A 100 80G GPUs.
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GRPO We use the verl framework conduct GRPO training. For BARREL GRPO,
BARREL-SFT models as initialization. GRPO training is performed over epochs with a learning rate of x 10 We set the batch size to 128 and the mini batch size to 16. The maximum prompt length 512 tokens, and the maximum response length is 2048 tokens. We enable dynamic batch sizing and incorporate KI--divergence-bee based regularization with coefficient of 0.001, using the Low_var_t loss type. Rollouts are conducted using the vLLM engine with a temperature of 0.6 and 8 parallel samples n in GRPO. All GRPO training is conducted using 4 NVIDIA A100 80G GPUs.
J RANDOMNESS GRPO TRAINING
Method
Accuracy (Avg.)
Truthfulness (Avg.)
Reliability (Avg.)
Distill
38.43
39.33
39.33
BARREL (reported in our paper)
40.70
70.40
61.58
BARREL (with 5 random seeds)
41.11 1.79
69.31 + 4.14
61.44 +: 0.97
Table 12: Seed variability experiments for -innssee-RR---siil--LLLeee
Compared the Distill baseline, our method achieves notable gains reliability: 1) DeepSeek- RI-Distill-Llam--B1 from 39.33% to 61.58%. 2)
from 26.21% to 12%. These improvements exceed 20%, which we believe is substantial and not marginal. But could be necessary to account for randomness:
Fair Comparison We used default random seed settings and made no hard-coded decisions beyond the reward design, ensuring fair conditions across methods.
widely acknowledged that randomness is inherent in LRM RL training and we could also prove our improvement is statistically significant, as shown by the seed variability experiments in Table
On Random Variability
As shown, the standard deviation for reliability is 0.97, which is significantly smaller than the 20% improvement we report. Thus, the observed performance gains cannot be attributed to randomness.
We also analyzed the randomness of sampling 1k subsets from the test set and found its impact reliability to within 1%.
K ANALYSIS OF SAMPLING VARIANCE AND STABILITY
To ensure that the performance gains of BARREL are robust and not artifacts of sampling noise, we conducted a detailed analysis of output variance. key concern in abstention- systems whether the decision to abstain is stable across different sampling runs. We investigated the stability of the model's decision- maassinnmmaiiggggg answering and abstaining the same input.
srrccsssspecificallly how often the model fluctuates between
K.1 MEASUREMENT OF INCONSISTENCY
We quantified the variance by measuring the inconsistency rate across k 4 independent sampling runs for each question the test set. Since the vanilla model always attempts an answer while BARREL can choose to abstain, we define inconsistency for each setting as follows:
Vanilla Model: Defined as the proportion of cases where the model fluctuates between gen- erating correct and incorrect response. This measures the inherent instability of the base model's knowledge retrieval.
hhans//gitthh.ccm//oeeennneeeeee
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Reasoning Examples for different models
ICL-IDK
Distill
Ours (SFT)
Ours (GRPO)
Question: Which is the aldest of the eight Ivy League Universities, founded in 1636 as New College?
Answer: Dartmouthh
Answer: Harvard
Answer: Harvard
Answer: Harvard
Rensoming: Olay, so need to fig- out Homm, I remember that Ivy League group top- tier universities the US I'm nut exactly sure about the onder or the exact founding dites of each... Wait, I've hoard Darimoath the oldest among the Ivy Lergue schools. Harvard older than Durtmouth, I believe, but I'm not sure il't's part of
Reasoning: Okay, so I need to fig- Let me start by recalling know shout boy League. Ivy League Let me think about the founding datess of those schools. remember that Harvard one of olidest When vard Founded? I think was around the 17th cereery Les me check my recall that Harvard was lounded in 1636. Yeah,
Reasoning: To determine which Ivy League univensity was Founded in ss New Callege, sider bistory and founding dates of the eight Ivy League univensilies...
Reasoning:: To determine which Ivy Lengue universlyy possibility
The lirst comes mind Harvard, it widely regarded us one of the oldest institutions in the United States, However, need verify this by considering possible candidatees and cxamining the evidence. 1. **Havvrrd Univer- sity *x; I know that Harvard is often ussociated with the founding the tvy I League, and recall it was established in 1636. This scems like strong candidate, but need to confirm this further, Yaaae Uni- versity**; .. 3. Princeton Univer- sily
to con-
1. **Havvadd University **; bbut Iiced to confirm exact year. lorical rocords indicati that Harvard was established in 1636 as college, which
with the referenee swer. This makes Harvard strony candicatte for the oldest Ivy League university. 2. Yoae University oo: Yule lounded in 1701, which
League. or
right. .. So that must be the answer
think Dartmonth was founded 1636 as New College. Then. Har- vard was founded in 1636 as well. I'm not sure if the same year as Duttmoothh ... So, putting it togetherr the oldest is Dari- mouth. think that's correct. but I'm a bit uncertain bocause might be mixing up the exact founding dases and the order.... I'll go with Dartmouuth the wnswer.
wail, are there any other schools
foursted around that time? Prince- toa was carlier, wait. Princeton was actually founded in 1746, but So should be Harvard. Let me just make sure there's no other school from that era. Maybe Dart- mouth? No ... So the answer is Har- vard.
than 1636, it cannot oldest. This climinates Yale as a pos- sibility. 3. **Princtonn University" **x To further verify... ... This confirms that Harvard is indeed correct an- swer.
lnter joined the Iivy Leggue. the
Now, need to critically evaluste the evidence for Harvard. ... The other Ivy League universities were founded much later, After considering all pussibilities con- clude that the answer is Harard.
...
Question: What is the name for the flexible, connective tissue found the joints between bones?
Answer: ligaments
Answer: cartilage
Answer: cartilage
Auswer: cartilage
Reasoning: Okay, so have this question about biology, specifi- cally about the body's 's connective tissucs. I think there's cartilige. which know found places like
Okny, the question is asking for the tissuc found in the joints betwen bones. Hmm, let's think. The the typex of joints are like the like sulure joints, which are immovabble, and then the ones that allow movement, like the knee elbow. Wail, the question spoc- it's connective tissue. So nective tissue is stuff like cartilage. right? Because bone is hard and dense, but the stuff between them... right! Cartilage the flexible stulf that custions the joints. Like in the curs or the nose, those are car- tilgee. So in the joints, the cartilags movement but provides some protection against friction. So the answer should be cartilage. Let me double check. So the answer cartilage.
Reasoning: To determine the name I to consider... The possi- billiy that comes to mind cartllge. However, I necd to ensure that this the
Reasoning: To determine the name need considar ... The first pussibililyy that comes to mind is cartilage. This scoms like a strong candidate. but I should con- other possibilitis I am not missing anything. An- other possibility could be ligament However, Amother option However, synovium is type of tissuc. spocif- ically the liming of the joint cavity. and does not fit the description. Fi- nally, should consider lendons. ... Tendons are not llexible or found in the joints between bones, so this option does not fil the description. Now, I need crifically evaluare the evidence for cartilage. Cartilage is This mnttches the description per- feetly. After considering ... the cor- roct answer is cartilage.
the flexible,
term Another possi- bility ligaments. Liganents are connective tissues that connect hones to other boncs at joints, but they are not the tissue itsell. Tendous type connective tissue, they connect muscles to bones and are not involved in the joint itsell. Fi- mally, I consider the possibility ovial Buid, which is fluid found in the joint vavily. o.. Now, I nced to verify whether cartilage is indeed the answer. Cartilage is the only ... Ligaments and tendons do not fit the description of ... I conclude that the Boxible, connective tissuc found the joints between hones carti- lage.
of bones, right? .. But wait, cartilage is more shout cushioning and redacing friction. believe. Wail, there's also something
eisure
ligaments... Let me make sure I'm not confusing this with lendors. Tendons con- nect muscles bones, right? So they't te also connective lissuc, but they serve a different purpose. ... so it's more about the structure that holds the bones logether, which would be ligaments. So putting all together, the floxible, cennce- live lissuc in the jeints butwecn bones called ligamenrs, I think that's 's correct answer hore.
might be synovium.
Question: What is netarak connection device that can build tables that identiyy addresses on each network?
Answer: switch
Answwer ronter
Answer: I don't know
Answer: ronter
noed ligure out what device is being re- ferred to in the question. First. know that network devices have various roles. Common clude rooters, switches, hubs, fire- walls, modemss etc. The term 'ad- dress" is used here, which makes think of addresses or MAC addreesses. So the devioe might be related to dresses network. I
Reasoning: Okay,
Ressoning:: Okay, so ques- tion is asking about ... Lot me think. But then there's 's a router. Roulers connect different networks. in WAN. They routing la- bles to direct packets between net- works. Waill, the question says in each netwoek So if it's on ench net- work. maybe
uset asking about a network connection device that can build tables to identify addresses en a network
Reasoning:
Reasoning: answer the question. need to The first possibility that comes to mind is "router" They use routing lables which aligns perfectly with description in the question. However. I should con- sider other possible devises An- other possibilitt could be "switch". ... Howover, switches do not tain ... This makes them less likelly to fit the description provided in the question. Another candidate might a "lirwalll" -. This makes them less likely mutch. To fur- ther evaluatec the evidence for each: Routers widely used Switches are ... making them less relevant. Finewalls are ... making them weaker fir. After considering the evidence, the router stands the most accurate answer.
will systenstically ex- plare possible answers critically assess the evidence for each. First. could it be a "router"? router specifically "huild tables" to identify addresses" ... Therefore. primary function of a router does not seem to aliga perfectly with the de- scription provided. Next. could it be "veiich"" They use a dysamic or static mapping of MAC addresses to IP addresses. This does not seem to march the description either. Could it "fiewaall" ... After considering these possibilitios. ... have crilically examined each candidate and found that I lack suflicient evidcace to fidently identify correct answer.
Dous
switch because
switches operatic within a single not- woek segment. Routers are more about connecting different networks. ... Alternativlly, mayle
these ad- wetwork
that switches use something called MAC ad- dress table. So the question is talking about device that builds such tables, which would switch. Switches use MAC aldress tables to keep track of which de- vice connevted to which port. Therefore, the answer should be a switch.
answer a router ... But I'm still not 100% sure. Alternatively, maybe the an- swer is switch. think the correct answer here router. Wait, but maybe the answer a switch. Let me check ... I think the answer is router. Let go with router.
Table 10: Additional Reasoning path examples of different methods on DeepSeek- R -Distill-Llamm 8B. We colored with wrong factual thinking leading to wrong answers, factual thinking alerting not sure and the good factual thinking leading to correct answers.
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Reasoning, Examples different models
ICL-IDK
Distill
Ours (SFT)
Ours (GRPO)
Question: What de methanogens act as in sewage treatment planss?
Biogas producers Reasoning: Okny, so need ligure oul I remember that methanogens are types of hacteris. I'm not exacily sure about role in sewage ... I recall some- thing about biogas being produced
Answer: methane
Answer:
I don't
Auswer: decompesers
Reasoning: Okay, so ques- tion is usking.... ... remember that meihanogens involved in break- ing down organic matiez ... Maybe metismoggen are responsible for converting certain compounds.
Reasoning: The user asking Fiasi, consider the possibility as decomposers specific ovidence supports this? ... Bul and they exclusively decem-- posers?? I need to invesiggate fur-- act Do have any ovidence .. However, cannot entirely rale out the possibility that need to chal- lenge this resumption, Amother possi- bility is act catalysts... ... Dave any evidence ... cannot definitively soy they act as catalysis Fimilyy, 1 consider
Reasoning: answer the question The finst possibility that comee to mind is decomposers. verify ... Another possibility reuluces. Howpeer, ... This suggests that "reducers" is nox the correct an- A third possibility However, This cut "filters" us a plausible answer. Next, need to evaluati the evidenze for "decom- This strongly supports idea... ... challenge this assump- tion, I must ask: Whilk This suggesit that "decomposers" is the sccurate answer. Finally, I ver- ily this conclusion by considering This confirms that their role as decompusers.
However.
need to
So perhaps methanggens vert the organic waste biugas o. Alternatiell, miyhe they" 'r actling as decomposers I'm a bit con- lused because I also beard that some cases, methane released a byppodduct, which can be harmful I'm pretly sure that's 's the case. but I'm 100% certain. I think go with that. Methanogons sewage treatment plants act as bio- producers...
could be that they produce methare gas as part of anscrobic digestion. But the ques- tion is phrased as "act as". which night mean their role function. So maybe answer ducs methame gas ... Let me chock my motes, Let me confirm. ... So the answer methane. -.. But the question says "act su mayhu the answer is methane. Yeah, I think that's right.
So the
ther. Next, I consider
filters,
they pro-
nitrogen- fixers Is sooms
there evidence that ... less likely. After evaluating these pos- sibilities, I find that However, lack delinitive evidence 10 cannoi confidemlly -..
..
Question: What team does controversial quarterback Michael Vick play for in the National Foothall League the USA?
Answer: Cleveland Browns Reasoning: Okay, need
Answer: Miami Dolphins Reasoning: Okay, need to fig- une oul ... I think he started with the Philadelphia Eigles, Wail, but then he was traded the Cleveland Browns, right? o. went
Answer: Philladephhia Eagles Reasoning: To determine The must ... that comes to mind is the However,
Answer: Eagles
Reasoning: determine The first possibiliiyy that comes to mind is the Philadelphia Eagles. ... but need verify this. Amother Miani Dolphins ... However. I don't recall any specitic evidence but I need to keepp it in mind for forther verilication third possibiliity
ligure out ... But I'm not en- tirely sure about
think he with the Cleveland Browns 100% sure.
Philidelphia Eagles.
need to verify this and consider other possibilities. Other teams that night be relevant include: ... Evalunte evi- dence for each possibility 1. Miami Dolphins: but there is ovidence suggest 2. Denver Broncos: ... but the Broncos are not the final team he endod up with. 3. Philadelphia Ear
..
that. be Denver Broncos, and then perhups the Cloveland Browns agaiin? Or may be ? Uhink the
possibility
shoukd domble-check that. 1 think he might have played for the Clevchand Browns during the early 2000s. Maybe around 2003 or so. Wait, was the Cleve- land Browns or the Philadelphin Eagles? think was with the Browns when he gol suspended by the Eagles. So putting it all to- gether, Michael Vick played for the Cleveland Browns the NFL. I think that's 's the correct answer.
he played was Miami Dolphins, But I should con- limm. Wait, amother angle: his So the be Miami Delphins, ... But wail. mayhe he was traded again aller Mi- ami? I don't recall him So the is Miani Dolphins.
Dallas Conboys ... However. I don't 't have any specific evidense To resolve this, I need focus concrete evidence. ...
draft
should
... This is the team he ended playing after longe issumptiinns Could be misin- serpreting the evidence? No, the ev- idence overwhemiiggy points to the Eagles... ... Verify evidence ... This is consistent with the timeline of his NFL carver.
Chal-
This aligas with my initial thoughi. Additionally. the Eagles ... Next, I should challenge this assumption. To verify. check reliable sourees like ... Finally. I apply adversarial self self-critique. ... The evidence suf- licient...
Question: Who created Rumpole of the Bailey?
Answer: Andrew Marquardt Reasoning: Olay, so need to lig- ure out Wait, isn't that by An-
Answer: Charles Dickens Reassonnng: Okay, so I need to fig- ure out ... know that Charles Dick-
Answer: I don't know
Auswer: I don't II know
Reasoning: The user is asking about Firse, consiier whether the creatoe could be famous British comeddian ... However, masd ask myselfi Do have any specific recollection or evi- dence ...? No. don't have any evidence momory of Nest, I consider whether the creator might be a Jesser- known ligure Again, must challengs this assumption: No. don't have any such evidence... Finally. I consider whother the creator might be However, I must ask my- sell: Do I have evidence... No. have any such evidenos. have systematically examined multiple pos- sibilities. For each pussibiiity I've asked myself what specific evidence would need make this claim confi- dontly, and find that I don't I possess such evidence.
Reasoning: The user is aoking shout First, need to consider whelher the show was created by ... What evidence supports this! don't have any direct evidence could have boen created However, don't have any specille information ... This possibility also scems unsupported. Could have been created more recent ? However,
drow Marquard??
some-
cus wrote lot of classic stories.
one else? I'm bit confused ...
Rumpole of the Bailey.. that's from Oliver Twist." * Wait, no.
think
Maybe it's by David Suchot? Wait.
Next.
I Uhink be was the actor who played Rumpole.
Rumpule the character "Oliver Twist," right!
?
Let think
Rumpole
about the name again. The play is by Androw Manquardl, right? But wait, I'm not entirely sure. think I should check.... ... From what recall. Rumpolc is fictional charcter. so the wright created him. There- fore. the creator would be Andrew Marquardi,
fictional character created by Dick- ens? Wait, maybe the answer is Charles Dickens. make sure. Let me recall. ... So Dickens created Rumpole of the Bai- ley. Dickens often created his characters, yes. he created Rumpolee maybe there's his- torical figure with that name? Let me check my memory. Charles Dickens wrote "Oliver Twist." and Rumpole the
But should
lack specific evi- dence ... Without concrete evidence. I cannot confidently assert this as I have systematically csmmined multiple pussibilitios. ... For each possibilit. I have asked what specilic evidence I would meed make this claim confidently, and that don't possess such evi- dence.
the
bit unsure... but think in this case, it's the play- wright who created the character. So I'll go with Andrew Marquardt as creator.
Oliver. So the answer should be Charles Dick- ens.
Table 11: Reasoning path examples of different methods on DeepSeek-HR R R1-R--iii 1D--isttll-- Qwen- We colored with wrong factual thinking leading to wrong answers, factual thinking alerting not sure and the good factual thinking leading to correct answers.
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BARREL:
Defined the proportion of cases where the model fluctuates between answering and abstaining. This measures the stability of our proposed tuning method's 's decision boundary.
K.2 QUANTITATIVE RESULTS
Table 13 presents the comparison of inconsistency rates across different backbone models. Contrary the concern that additional decision module might introduce instability, BARREL consistently exhibits lower variance compared to the vanilla baselines.
Backbone Model
Vanilla Inconsistency
BARREL Inconsistency
-----iiii-l---m---B1 DeepSeek-Dine Bareeckk--sttil--ee Disttll-Qween-BB Qwen3-8B
31.93
19,43
23.13
17.13
18.97
14.87
Table 13: Comparison of output inconsistency rates (%) across 4 independent samples. Lower values indicate higher stability. BARREL demonstrates greater consistency its decision abstain than the vanilla model shows in its correctness.
For example, on the DeepSeek-Distill-LInn backbone, the inconsistency rate drops significantly from 31.93% (Vamilla) to 19.43% (BARREL). This indicates that BARREL does not amplify instability; rather, it stabilizes the output by effectively masking uncertain predictions that are prone to fluctuation in the vanilla model.
L DETAILED EXAMPLES
We provide more detailed examples SeepSeek-RI-Distll--Lee Qwen-7B in Table TO and Table [1] In addition to the two main thinking patterns in current LRMs- seoo--hecon- spiraling and last-minute guessing-introduced earlier in this paper, also observed an additional pattern on DeepSeck-Rl-Disttee Del-Distill-Qwen--B that sometimes results in incorrect answers where the model initially proposes an incorrect answer and subsequently engages in multiple rounds of self-checking, However, these self-checks are characterized by expressions of uncertainty and lack of firm commitment. Ultimately, the model still adheres the original incorrect answer. However, this flawed reasoning pattern can also be effectively transformed into more reliable and coherent one through our BARREL training framework.
and DeepSeek-RI-Distee
M ADDITIONAL DETAILS
We provide the links and licenses of the datasets and code used in our paper as follows:
Code We conduct SFT using our own codebase, which is built on top of the Transformers library and DeepSpeed And we conduct GRPO training using the verl framework
Data make use of the following publicly available datasets. (1) TriviaQA: Open-domain question-answent corpus drawn from Wikipedia and the web (Apache 2.0 License
(2) SciQ: 13 679 multiple-choice science questions spanning physics, chemistry, biology, and more (CC BY-NC 3.0 License [8]
(3) NQ-Open: Open-domain variant of Natural Questions covering real Google queries (CC BY-SA 3.0 License
ht httea://thhbb.ooo//ncchhnttoetos
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(4) SimpleQA: Complex factuality benchmark (MIT License
(5) MATH-500: 500-problem subset of the MATH benchmark for compact maths evaluation (MIT License
(6) MATH; full-scale mathematics problem benchmark (MIT License
(7) SelfAware: unanswerable questions (Apache 2.0 License)
13
N
MODELS USED IN OUR EXPERIMENTS
We provide the download links the models used in our experiments as follows:
DeppStek-Ri-Dsstil-LLaaa-BB
DeepS@ee-EEl-DDstill--l----
DeppSeek-KI--Disilllovvaa--B
Dee=SeekkERI-DDss1111--eee
http::://ugghnnfeeecc/////ppssep
Deepieex-R--Dtttii---vee---
DeppSeck-AI.DDitilllaaaa---0-
hcte:://anggingaaae../////eeeea
Deesseak-Rl-D1ett1--llaaaa..
/ Detpgg||Hhaaccch/hnnnneeeeeeeeee
QwQ-32B httpps:/hooghnnffeeeccc////////p
Qwen3-8B (ttpss///anggiiggeeeeee////////
QUICK ANALYSIS OF THE UNDERLYING MECHANISM
Previous work (Liang et al. 2024) has shown that using the hidden states of LLMs to build a classifier achieve high consistency with the sampling strategy mentioned in Section 3.1 This suggests that the model has the potential to recognize knowledge boundaries and to say "sorry" when faced with unknown questions. In our approach, however, we boost the ability identify these boundaries through an explicit reasoning process.
P DISCUSSION ON DOMAIN GENERALIZATION
While our primary experiments focus on Factual QA, the proposed BARREL framework establishes principled training paradigm designed for broader applicability. The core methodology methodolooyy-utiiiznn -utilzzing SFT to seed refusal behaviors and GRPO instill calibrated abstention incentives agnostic the specific domain. However, adapting this framework requires different patterns "reliable reasoning" tailored the specific failure modes of different tasks.
Reliability and the Nature of "Overthinking". In the factual domain, we identify "overthinking" (generating extensive rationales for unknown facts) primary symptom of unreliability. Conse- quently, our current implementation specifically targets this behavior. However, this symptom does not apply for all domains. For instance, our preliminary analysis on instructionffolloiing tasks (e.g.. IFEval) reveals minimal difference in thought chain length between correct and incorrect responses (e.g., 496 vs. 501 tokens for DeepSeek-R --si------llll--aa----- suggesting that lengthy reasoning not pathological for reliability issuc.
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Adapting BARREL to Reasoning Domains. Adapting BARREL framework to other domains is still an exciting open question. To generalize BARREL to mathematics or complex instruction following, the construction of the SFT refusal data and the calibration of GRPO rewards should shift to modeling domain-specific boundary patterns:
Instruction Following: Reliability in this domain is tied to constraint satisfaction and execution planning rather than fact retrieval. A reliable reasoning pattern should involve simulating execution steps and proactively detecting potential constraint violations. The SFT phase would thus focus on demonstrating Siimulaton-anndcheeel behaviors before committing to an answer.
Mathematics: Mathematical tasks involve complex logical chains where enrors propagate. Here, mitigating unreliability requires sensitivity to intermediate reasoning flaws. A reliable process entails detecting when logical step becomes uncertain, interrupting the flawed chain, and transitioning to an expression of uncertainty. The GRPO reward modeling would explicitly penalize the completion of hallucinated derivations while rewarding early error detection.
In summary, while the specific manifestations of reliable reasoning differ across domains, BARREL provides the foundational infrastructure to verify LRMs' ability to reason reliably. Future work can leverage this framework by formalizing dopain-specifie reliable reasoning patterns construct targeted SFT data and calibrated reward signals.
Q LIMITATIONS
Although we have evaluated and validated the performance of our method, restricted by our limited computing resource, we mainly utilize DeepSeek-RR --aissiil--Llama-SB, DeepSeek-PP -eagSSee--I--isiil---P--- -iDistill---ee 7B and Qwen3-8B to perform our study, which are relatively small LRMs.
In our experiments, though we have covered different datasets, we mainly utilizing verifiable questions, which could be evaluated at test time and reward at training time using string matching method. How to teach LRMs to learn knowledge boundary and behave more deliberatively on open-end questions, like writing articles providing opinions, remains valuable topic for future work.
We adopted the general acknowledged sampling strategy to annotate question types, but we acknowl- edge that this proxy has inherent limitations. For instance, when the model is genuinely confused between two specific options (c.g., oscillating between distinct answers due to uncertainty), the cur- rent consistency- -based metric might fail to capture this state accurately, potentially introducing errors. As a result, there a certain proportion of mislabeled data in the SFT stage. Our subsequent adaptive GRPO training will help alleviate this problem, but need emphasize that constructing better proxies that can distinguish between ignorance and genuine confusion remains an open challenge, and is difficult to obtain robust model directly through SFT. Detecting issues in the reasoning process remains an open question. If an accurate method for monitoring reasoning could be developed, both false positives and true negatives could be reduced some extent.
As shown in Appendix K although BARREL improves stability over vanilla baselines, it still exhibits an inconsistency rate approximately 20% across sampling runs. This indicates that for subset of borderline queries, the decision to abstain remains sensitive to sampling noise, suggesting room for further improvement in calibration stability.
In the paper, we mainly focus whether the model can reason to claim uncertainty through Reinforcement Learning with Verifiable Rewards (RLVR), without introducing methods such as CoT monitoring and detection. Building detectors for CoT hallucinations and uncertainty is important future direction, which goes beyond the scope of our current work.
Another limitation lies in the reward design. Currently, we employ fixed rejection reward, which implicitly ties the optimal policy to a fixed internal confidence threshold in limited training steps. This could limit the model's flexibility for scenarios requiring different risk tolerances (e.g., higher lower refusal rates). Future work could explore conditioning the model on a dynamic rejection reward specified in the prompt, enabling the model generalize multiple thresholds without retraining.
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R BOARDER IMPACT
Although existing LRMs have demonstrated strong capabilities, hallucinations frequently occur in real-world applications, raising doubts about their reliability, Our work enhances the reliability of LLM responses by teaching the models to express uncertainty and refuse to answer when appropriate. As mentioned in Appendix PP] future work can leverage BARREL framework by formalizing domain- specific reliable reasoning patterns to construct reliable LRMs for different domains. We hope our work will inspire more research in this area to further improve model reliability, enabling humans to place greater trust in the positive responses provided by LRMs.
S THE USE OF LARGE LANGUAGE MODELS
In this paper, we utilized LLMs to perform grammatical error checking, remove redundancies, and refine the vocabulary in various sections of the paper. is important note that the LLM's role was limited to polishing and checking the text, not to writing any paragraphs from scratch.
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Reviews:
[{"review_id": "AvXxGEUWYu", "reviewer": "Reviewer_xT1G", "summary": "This paper studies the problem of Large Reasoning Models rarely admitting ignorance and producing incorrect answers instead. In this work, the authors identify two pathological reasoning patterns, called Last-minute Guessing and Second-thought Spiraling, caused by overthinking.\n\nTo address these problems, the authors proposed a very clean framework, called BARREL. The frameworks clearly build SFT and RL data for these two patterns of wrong CoT. The results on TriviaQA, SciQ, and NQ-Open clearly show the effectiveness of the framework.", "questions": "See weakness", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. This paper provides a very clear motivation for fixing two pathological reasoning patterns in current Large Reasoning Models, which is a very important topic.\n2. The writing of this paper is fluent and easy to follow.\n3. The experiments and analysis in this paper are comprehensive to show the effectiveness of the proposed framework.\n\nAll in all, this is a solid paper with clear structure.", "weaknesses": "The only weaknesses I noticed are the definition of the metric \"Reliability (Rel.).\" The \"ans.\" means the ratio of answered questions. So, why do we need to compute \"ans.·Truth.\" and \"(1−ans.)·Acc.\" and sum them together? What is the rationale behind this, and why do you think this is a more robust metric?", "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": "rAcjBN9TOk", "reviewer": "Reviewer_cpNK", "summary": "The paper identifies two pathological reasoning modes in LRMs—last-minute guessing and second-thought spiraling—and proposes BARREL, a two-stage training framework (SFT on curated reasoning traces + GRPO with a three-level reward: correct > truthful refusal > incorrect). Experiments on factual QA (TriviaQA, SciQ, NQ-Open) report large gains in a proposed Reliability metric and truthfulness, while preserving accuracy and math ability (MATH-500). The method emphasizes teaching models to admit ignorance and uses reward shaping to avoid penalizing refusals as harshly as wrong answers.", "questions": "1. While I understand the authors may have adopted the current data generation approach due to cost considerations, conducting a small-scale ablation study (as proposed in Weakness 1—i.e., comparing GPT-4-generated traces vs. BARREL-rewritten failed traces) would significantly enhance the paper’s validity and the practical significance of BARREL. Could the authors consider adding such an ablation study?  \n\n2. As noted in Weakness 2, response length is a critical indicator linked to overthinking (per Figure 2). Could the authors supplement the response length data for the evaluation results in Table 1, and provide an analysis of the underlying causes (e.g., how SFT/GRPO training modulates response length, and whether shorter/longer traces correlate with improved reliability)?  \n\n3. The paper focuses exclusively on overthinking in the factual domain. Given BARREL’s conceptual design (boundary-aware reasoning + calibrated reward), it may have broader applicability. Could the authors provide a preliminary analysis of BARREL’s suitability for addressing overthinking in other domains (e.g., mathematics, instruction following)—such as a pilot experiment or a discussion of potential adaptations to the framework?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "* Clear diagnosis of failure modes with concrete qualitative examples and a simple taxonomy (last-minute guessing vs. second-thought spiraling). \n* Conceptually clean training recipe: SFT to seed refusal patterns + GRPO that explicitly rewards calibrated abstention. \n* Consistent empirical improvements in reliability/truthfulness across multiple 7–8B backbones, with additional OOD refusal tests and pass@k analysis. \n* Ablations that matter: effect of refusal reward magnitude; role of SFT vs. GRPO.", "weaknesses": "1. **Generalizability Issues in Reasoning Trace Construction**  \nThe paper states that reasoning traces are constructed by prompting GPT-4 with prompts from Appendix F and BARREL reasoning examples to generate compliant reasoning patterns. However, this generation approach may lead to insufficient diversity in the resulting traces. Additionally, as a non-reasoning-focused model, GPT-4 may not be optimal for generating high-quality Long-CoT-style reasoning processes. A more effective alternative could involve **rewriting failed trajectories** produced by reasoning models using the BARREL framework—this would likely yield higher-quality datasets. In practice, model evaluations often generate a large number of failed cases characterized by *last-minute guessing* and *second-thought spiraling*; leveraging these failed cases via BARREL’s methodology would enable the creation of a more extensive and useful dataset.  \n\n2. **Unaddressed Response Length in Post-Training Evaluation**  \nThe paper uses BARREL-generated datasets for SFT and GRPO training, and optimizes the model’s original Long-CoT trajectory generation process. This optimization may inadvertently impact the model’s response length—potentially reducing the analysis depth of certain reasoning paths. Notably, Figure 2 explicitly highlights response length differences between correct and incorrect answers in pre-trained models. Given this, it is necessary to **supplement the response length data** for the evaluation results in Table 1, alongside a corresponding analysis of how training affects response length and reasoning depth.  \n\n3. **Lack of Overthinking Analysis in Non-Factual Domains**  \nWhile the paper analyzes and optimizes overthinking in the factual domain, LLMs often exhibit severe overthinking in other domains as well. For example: (1) Mathematical reasoning, where overthinking occurs across multiple problem-solving approaches; (2) Instruction following, where overthinking arises from misinterpreting diverse task requirements. Intuitively, the BARREL framework could be applicable to these domains, but the paper provides no analysis or validation of such cross-domain applicability.", "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": "9Opyhg7o6T", "reviewer": "Reviewer_2MeN", "summary": "This paper presents BARREL, a training paradigm consisting of a SFT and RL stage with the goal of making models aware of their factual knowledge boundaries by learning to say “I don’t know” when they are unsure. In contrast to the standard RL paradigm, BARREL assigns an abstention reward if the model outputs “I don’t know”, with the magnitude of this reward being between the rewards for a correct and incorrect answer. Results show that BARREL maintains competitive overall accuracy in factual domains while significantly increasing precision (when models choose to output an answer, their accuracy is much higher). Ablations highlight the importance of both SFT and RL stages, as well as the significance of the proposed reward.", "questions": "- What value of $\\alpha$ do the authors’ chosen rewards correspond to, and how was this default confidence threshold determined? (I think it corresponds to 25%) \n- The authors mention (lines 356-360) “*it is worth noting the accuracy improvement caused by increasing the ratio does not reflect an actual improvement in model capability—it merely reduces the number of incorrect refusals on known questions.*” If this is the case, then why does the ICL baseline not match the accuracy of BARREL? This hypothesis does not seem to be correct. \n - What is the motivation behind the reliability metric — what does it intuitively measure or indicate?\n - How much variance is observed in BARREL’s outputs due to sampling? Specifically, how often does the model sometimes answer and sometimes abstain on the same question?\n- Could the authors include the abstain rate $\\left( \\frac{N_w}{N} \\right)$ in the main results table for better interpretability?\n- **Probing/Classifier baseline** should also be added to the paper. Train a classifier/probe on the vanilla GRPO (no truthful rewards) outputs to predict the probability that the answer is correct. This probe can then be used to manually replace answers with “idk”. \n- \"*Quick Analysis of the Underlying Mechanism*\": This is not an experiment and should be presented in a different way. \n- \"*Did GRPO sacrifice pass@k for better pass@1*\": I do not think enough evidence has been provided to support this claim. The gap between SFT and GRPO seems to reduce significantly, suggesting that SFT has better scaling performance. \n- It will be useful to ablate the importance of SFT and the impact of RL with/without idk rewards. I think most of these results are already in the appendix, but some of the numbers should be added to the main results table. In particular, RL (without rejection rewards) should be added to the table as that is a very standard baseline.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- The paper is well-motivated. Hallucinations are a major problem with LLMs and making models aware of their factual boundaries is an an important problem. The paper also correctly identifies that the standard paradigm does not reward models to express their uncertainty. \n\n- The paper is generally well-written and has a decent flow to it. \n\n- The results are impressive. Models maintain accuracy while also learning to abstain.", "weaknesses": "- **Proxy Definition**: The \"*knowledge labeling proxy*\" (classifying a question as \"known to the model\") is a weak indicator of model knowledge. It fails to account for uncertainty when multiple plausible answers exist. Say a question has 10 possible answers. The model might not know the correct answer, but has some sampling probability for each of the answers. The proposed framework would classify this question as something known to the model, which seems strange. A majority-vote–based proxy might align more closely with actual model uncertainty. \n- **Threshold-based Reward**: The rule-based reward design implicitly fixes a single confidence threshold - that is, the model should only answer the question if its confidence is greater than $\\alpha$: \n  \n    $\\alpha \\ge \\frac{r_s - r_w}{r_c - r_w}.$\n    \n    This can be computed by writing the expected reward for the model for different correctness probabilities and checking if it is greater than the abstention reward. A limitation of this framework is that it removes flexibility across use cases — for instance, scenarios requiring high confidence (e.g., 99\\%) versus those tolerant of lower confidence (e.g., 70\\%) cannot be easily tuned.\n\n- **Limited Related Work**: The related work section omits several recent RL-based approaches that explicitly train models to reason about their uncertainty [1,2,3]. \n\n- **Experimental Design**: Some important baselines such as classifier and vanilla RLVR are missing from the main paper (see questions below). \n\n[1]: Stangel, P., Bani-Harouni, D., Pellegrini, C., Özsoy, E., Zaripova, K., Keicher, M., & Navab, N. (2025). Rewarding Doubt: A Reinforcement Learning Approach to Calibrated Confidence Expression of Large Language Models. arXiv preprint arXiv:2503.02623. \n\n[2]: Xu, T., Wu, S., Diao, S., Liu, X., Wang, X., Chen, Y., & Gao, J. (2024). Sayself: Teaching llms to express confidence with self-reflective rationales. arXiv preprint arXiv:2405.20974. \n\n[3]: Damani, M., Puri, I., Slocum, S., Shenfeld, I., Choshen, L., Kim, Y., & Andreas, J. (2025). Beyond binary rewards: Training lms to reason about their uncertainty. arXiv preprint arXiv:2507.16806.", "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)