Mechanistic Detection and Mitigation of Hallucination in Large Reasoning Models
Authors: Zhongxiang Sun
Qipeng Wang
Haoyu Wang
Xiao Zhang
Jun Xu
Venue: ICLR 2026 Poster (2026)
Keywords: Reasoning
Hallucination
Mechanistic Interpretability
Primary area: alignment, fairness, safety, privacy, and societal considerations
TL;DR: We propose a Reasoning Score grounded in mechanistic interpretability to detect and mitigate reasoning hallucinations in LRMs, introducing RHD for detection and GRPO-R for mitigation via step-level rewards.

Abstract: Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model error has emerged—**Reasoning Hallucination**—where logically coherent but factually incorrect reasoning traces lead to persuasive yet faulty conclusions. Unlike traditional hallucinations, these errors are embedded within structured reasoning, making them more difficult to detect and potentially more harmful. In this work, we investigate reasoning hallucinations from a mechanistic perspective. We propose the **Reasoning Score**, which quantifies the depth of reasoning by measuring the divergence between logits obtained from projecting late layers of LRMs to the vocabulary space, effectively distinguishing shallow pattern-matching from genuine deep reasoning. Using this score, we conduct an in-depth analysis on the ReTruthQA dataset and identify two key reasoning hallucination patterns: early-stage fluctuation in reasoning depth and incorrect backtracking to flawed prior steps. These insights motivate our **R**easoning **H**allucination **D**etection (**RHD**) framework, which achieves state-of-the-art performance across multiple domains. To mitigate reasoning hallucinations, we further introduce **GRPO-R**, an enhanced reinforcement learning algorithm that incorporates step-level deep reasoning rewards via potential-based shaping. Our theoretical analysis establishes stronger generalization guarantees, and experiments demonstrate improved reasoning quality and reduced hallucination rates.

Published as a conference paper at ICLR 2026
MECHANISTIC DETECTION AND MITIGATION OF HAL- LUCINATION IN LARGE REASONING MODELS
Zhongxiang Sun Qipeng Wang', Haoyu Wang', Xiao Zhang' 1 Jun Xu
Gaolling School of Artificial Intelligence, Renmin University of China, Beijing, China Institute for the Future of Humanity, Renmin University of China Westlake University, China
sunzhongxi wwaphhongxinngeee ang@rucc.du.cm wqp @ ruc.edu.cn, wanghaoyu 924 @ruc.edu.cn. zhangx8 9 @uuc.edu.cn junxu ruw.euu.un.cnnn
ABSTRACT
Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model етrог has emerged--Rassoinng Hallucination-hherr logically coherent but factually incorrect reasoning traces lead to persuasive yet faulty conclusions. Unlike traditional hallucinations, these errors are embedded within structured rea- soning, making them more difficult to detect and potentially more harmful. In this work, we investigate reasoning hallucinations from mechanistic perspective. We propose the Reasoning Score, which quantifies the depth of reasoning by measuring the divergence between logits obtained from projecting late layers LRMs to the vocabulary space, effectively distinguishing shallow matthhing from genuine deep reasoning. Using this score, we conduct an in-depth analysis the Re ReTruthQA dataset and identify two key reasoning hallucination patterns: early-stage fluctuation in reasoning depth and incorrect backtracking to flawed prior steps. These insights motivate our Reasoning Hallucination Detection (RHD) framework, which achieves state-of-the-arr performance across multiple domains. To mitigate reasoning hallucinations, we further introduce GRPO-R, an enhanced reinforcement learning algorithm that incorporates step-level deep reasoning re- wards via potential- -based shaping. Our theoretical analysis establishes stronger generalization guarantees, and experiments demonstrate improved reasoning qual- ity and reduced hallucination rates. The source code and dataset are available at: /ttpss//ggiee com/ Jeryi Sun Reasoning Hal Lucination
INTRODUCTION
Hallucination has long been a critical safety challenge for Large Language Models (LLMs). this context, hallucination refers to outputs that appear fluent and coherent but are semantically inaccurate or lack factual grounding. With the advent of Large Reasoning Models (LRMs) as DeepSeek- RI (DeepSeek-Al 2025) and OpenAl's O-series (OpenAl 2025) Al systems have demonstrated unprecedented potential in solving complex real-world tasks. These models are typically trained with outcome-basee reinforcement learning (RL) and explicitly generate multi-step reasoning traces prior to final answers.
Recent studies have uncovered subtler form of hallucination emerging in LRMs (L al. 2025 Vectara Research 2025 OpenAl (2025), which is referred to as Reasoning Hallucination. Unlike traditional hallucinations, reasoming hallucinations are often embedded within logically coherent reasoning traces, making incorrect information more persuasive and harder to detect. This form of "plausible but incorrect" reasoning can elicit user trust, resembling the conjunction fallacy, where detailed yet misleading explanations are perceived as more credible than simpler ones (Tentori et al. 2004 Valmeekam et a..). Prior studies mainly assess the correctness of reasoning paths standard Chain-of- -hhuught (CoT) tasks over relatively simple problems (Xu et al.) 2024 Prasad al.) 2023 Li al. 2024b), with limited investigation into the mechanisms of hallucinations LRMs. Recent
"Corresponding author.

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Published as a conference paper at ICLR 2026
work has extended evaluation to long CoT generated by LRMs (He al. 2025 Lu et al. 2025 yet remains focused on error identification rather than uncovering underlying causes from mechanistic perspective. However, directly analyzing model-generated traces can be misleading due to the subtle nature of reasoning hallucinations. The emergence of Latent CO'T, where reasoning is embedded in hidden states rather than surface text, further obscures detection (Hao et al.. (024). These challenges call for probing the internal mechanisms behind reasoning hallucinations, enabling interpretable and robust hallucination detection.
Recent studies on the reasoning capabilities of LRMs (Mirzadeh et al. 2024 Yan et al. 2025) have shown that models often produce incorrect answers when their reasoning process relies on shallow pattern-matchan matching rather than genuine deep reasoning. This mirrors findings in cognitive science. where human thinking patterns are closely linked to the emergence of cognitive illusions (Kahneman) 2011: Weis & Kunde, 2024). Inspired by these observations, we investigate reasoning hallucinations LRMs through the lens of internal thinking patterns, where a central challenge is how to quantify whether a model is performing deep reasoning merely matching surface-level patterns from training data. Prior mechanistic interpretability studies highlight a functional division within language models: early layers primarily transmit information, while later layers perform more complex reasoning over aggregated context (Nikankin et al.) [2025] Chen et al., 2025a). Based on this insight, we introduce Reasoning Score, which measures the divergence between logits obtained from projecting late layers of LRMs to the vocabulary space. Through synthetic experiments, we validate the effectiveness of the Reasoning Score in measuring the depth of reasoning in LRMs, which reflects whether the model engages in shallow pattern- mendern-maten matching or deep reasoning ($ 3.1..
Building on the proposed reasoning score, we conduct extensive analyses on reasoning hallucinations using the ReTruthQA dataset. We identify three key patterns of reasoning hallucination: Pattern #1: large fluctuations in reasoning depth during the early steps, and Pattern #2: incorrect backtracking from later steps to earlier incorrect steps. We attribute these patterns to the presence of shallow pattern-maton
and overthinking steps, which undermine the LRM''s inherent abilities in self- verification and backtracking, ultimately leading to reasoning hallucinations ($ 3.2) Moreover, we observe that Pattern #3: overthinking steps exhibit a positive correlation between reasoning scores and perplexity, indicating spurious verification behaviors ($ 3.3). Based on these findings, we design the Reasoning Hallucination Detection (RHD) method, which significantly outperforms baselines across diverse domains in the reasoning hallucination detection dataset ($ 4.1..
We further investigate the underlying cause of shallow pattern pattern-matchine matching and overthinking steps in LRMs and attribute it the outcome-based RL paradigm commonly used during training. This paradigm incentivizes correct final answers but neglects whether intermediate reasoning steps reflect deep and meaningful thinking. To address this challenge, introduce a step-level deep reasoning reward based on the reasoning score and propose GRPO-R, a variant of Group Relative Policy Optimization (GRPO) (Shao et al. 2024 DeepSeek-AT 2025) that incorporates potential-based reward shaping. GRPO-R encourages deep but not excessive reasoning during RL fine-tuning Our theoretical analysis shows that GRPO-R leads to better generalization in outcome-basee RL, and empirical results confirm that it improves reasoning accuracy compared to standard GRPO ($ 4.2
RELATED WORKS
Hallucination of Language Models. Hallucination remains a fundamental safety concern for
LLMs, and outcome-supervised LRMs (DeepSeek-A[ 2025 OpenAl 2025) exacerbate this issue by
generating logically flawed but persuasive reasoning traces, a consequence of reward-seeking behavior
induced by outcome-basse RL without step-level supervision (Chen et al.
2025b] Valmeekam et al.)
Sun et al. (222cc). Detection approaches span uncertainty estimation ( (Kadavath et al. 2022 Ren et al. 2022). internal signal probing (Chen et al.] 2024] Li et al.. 2025b 2024a). process- critique models (He al. (025). and Process Reward Models (PRMs) (Zhang al. [2255] Sun et al., 2025b), though challenges remain due to the deceptive nature of hallucinated traces and the poor generalization of PRM signals (Zheng et al., 2024b). We address this by conducting mechanistic analysis of reasoning hallucinations and proposing a detection method grounded in internal model behavior.
Mechanistic Interpretability. Mechanistic interpretability (Ferrando et al., 2024 Elhage et al.
2021) explains model behavior by attributing predictions to internal components, e.g., attention heads
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Avgg
Racure
Recume
Score
Layer
Vocabulary Distribttion
Transfonmer-D D Layer
Rw()
LogitLans
Transformer-D D Layer
LogitLens
Transfomec Deodl
Hicklen State
9,03
Pattern Marching
Overtinkinn
Layer:
Appx
Lenf
Multi-sel--atien
Score
Attended Top-K Steps
Transfomme--D Layer
Layers
W
Embedding Matrix
( 22...
Figure 1: The illustration of the calculation processes for the Reasoning Score (Eq. 2}. CV Score (Eq. 3), and Attention Score (Eq. 4).
contextualize token representations (Ferrando & Voita 2024 Wu et al. 2024 Sun et al. 2026), while
FFNs serve as knowledge storage (Geva et al.] 2021 Intervention- based studies further reveal division of labor across layers, where early layers transmit contextual information and later layers conduct complex reasoning (Chen et al., 2025a Nikankin al. 2025 Li et al. 2024c). These insights motivate our Reasoning Score, which quantifies hidden state shifts in later layers capture thinking patterns and analyze reasoning hallucinations in LRMs.
EMPIRICAL STUDY OF REASONING HALLUCINATION
Our empirical study investigates the relationship between reasoning hallucinations and the thinking patterns LRMs,, where thinking patterns are quantified using reasoning score derived from mechanistic interpretability. This analysis reveals key reasoning hallucination patterns and guides the design of more effective detection and mitigation strategics.
3.1 REASONING SCORE: MEASURING REASONING DEPTH IN LARGE REASONING MODEL
To determine whether a reasoning step is generated via shallow pattern matching or genuine deep reasoning, we propose a Reasoning Score inspired by mechanistic interpretability. Prior studies analyzing the internal mechanisms of language models reveal a layered functional division: early layers primarily transmit information, while later layers perform more complex reasoning over aggregated context to produce correct outputs (Stolfo et al., 2023; Nikankin et al. 2025 Li et al.) 2024c; Sun al. (025a). Building on this insight, we define the reasoning score under the hypothesis that deeper reasoning is reflected by meaningful transformations in later-layer representations during generation.
Formally, a -RM-generated reasoning trace = [c1, C2...., ck] consists multiple reasoning steps, each associated with step-level reasoning score R that quantifies the depth of reasoning in step is composed of M tokens. The overall reasoning trace
Ck. Each reasoning step Cы (Lt.... ./, (/ score Rxcore is represented as sequence [R] R2 R& capturing the model's reasoning dynamies across steps. shown in Figure each score defined as the mean Jensen-Shannon divergence (JSD) between vocabulary distributions induced by hidden states from selected later layers and the anchor distribution from the final layer. To obtain the output distribution from each token hidden state ( of token th at layer j. we apply the LogitLens (nostalgebraist, 2020). which projects each layer-normalized hidden state into vocabulary space via the unembedding matrix Wo: LogitTens(( ()))) Layer Wy. This provides layer-wise interpretation of token
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Question
to buy some school supplies. buys crasers now cost 56.75 each, notcbooks now 511 poper that now costs $19, How much should Lian pay now, assuming that due to inflation, prices were 10% cheaper lost year??
bond
Ressoning Scume Trend uallaninated Supe.
Ressening Soore Trend of Truthfull Stops
Fluctuating
Stable
20
40
60
80
100
Stap
Step
Conrect Venfication:
(6)
Incorrect verfiicaion:
Inceerect Bucktraking Step (Mliguided Attenioon
Coneect Vattication::
Step 2 (Stallow Pateen Marching) Step
Step 44-9 Seep (Overtiikking)
Skep 2318ballow Putiern baachingg Step 24
Ulallucinated Steps Information
(b)
(c)
(d)
step the total
lutal
original
origital lotal the
amcunt
pay now, we
Step Suppose this your's 5 price ... year's prices
you''s prices wase 0.9P... find
should pay novi
Step querdinn zsking
should pay now, assuming due to prices were 10% citzape: lust your
step 73: Bu the queston asks how much he should pay now, witch is the new toall cost, So, the final answer 5251 High Attounion
Golden $291
Truthful Steps Information
Stap 23... So, partape qucetion din Be suauta le should jay ane consilaring the inflaiiion wlich would be you's mu hilliillllll by
Stap 24:... Soy has your's is $361, 90, and your's $201. So, queaion saking much much should pay now,
Figure 2: Case study from GSM-NoOp dataset Mirzadeh et al. (2024) on R1-7B. We sample both hallucinated reasoning trace (left) and a truthful reasoning trace (right) for the same question as preliminary analysis of reasoning hallucinations. Reasoning scores are scaled by 1e5.
prediction behavior and has been widely adopted for interpreting LLM internal representations (Hanaa et al. 2024 Zhou et al.] 2024 Yu et al. 2023).
The final step-level Reasoning Score R.ccure is computed as:
R R
Σ
JSD (aN (1h+t)) ,s (mm+1))
(1)
T
Enk
JEJ
Lj (mm-1) softmax
(LogitLens
(n)0))) j J.
where J denotes the of selected later layers and qN the anchor distribution from the final layer.
Intuitively, a larger score Ryvere indicates substantial transformation in output distributions within late layers, suggesting the model is actively engaging in deep reasoning by integrating earlier contextual information. In contrast, a smaller score implies distributional stability in late layers, indicating shallow pattern matching or heuristic-based processing without further reasoning, consistent with prior findings on the differential roles of early versus later layers.
Validating the Reasoning Score with GSM-NoOp. We validate whether the Reasoning Score faithfully reflects reasoning depth using GSM-NoOp (Mizzadeh et al.] (024)). a CSM8K-derived dataset where semantically irrelevant but plausible No No-Op phrases injected into problems. Al- though these phrases do not alter the correct reasoning path, prior work shows that LRMss are often misled by them, revealing their reliance shallow pattern matching (Mirzadeh al. 2024 This makes GSM-NoOp a suitable testbed: if the Reasoning Score captures reasoning depth, then steps misled by No-Op phrases should yield lower scores. We validate this using correct outputs from DeepSeek- Beeese---Disttt----eeeee
(R1-7B) to avoid confounds from hallucinated traces. Misled steps are labeled via GPT-4o. As GSM-NoOp is not publicly available, we re-implement compatible version following the original paper's methodology, with prompts and details provided in Appendix B
Results. Our empirical results in Figure 3 (a) show that reasoning steps misled by No-Op phrases consistently receive significantly lower Reasoning Scores compared non-misled steps. This supports our hypothesis that the Reasoning Score effectively captures shallow pattern- matching behavior and serves as indicator of whether model is engaging in deep reasoning.
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Reasoning Score Verification
CV Score Comparison (MATH)
Attention Scores Comparison (MATH)
Overall Moon
0.5
0.25
Mean
0.39
4.*
9,382
Mean Reasoning
2,671
Mean CV Score
0.20
0.150
Moon: Atfention
03
0.307
0.15
022
0.55
Midlending
Non-Mideewlngg
0.00
Truth
Hallucinaiion
0.0
Trush
Hallucinstion
(a)
(b)
(c)
Figure 3: (a) Reasoning Score validation on GSM-NoOp. (b) Evaluation of Pattern #1 (early fluctuations), and (c) Pattern #2 (misguidedly attention) on ReTruthQA, Asterisks indicate statistical significance based on t-test: * for p-value 0.05, and *** for p- 0.001.
3.2 REASONING HALLUCINATION ANALYSIS BASED ON REASONING SCORE
In this section, we leverage the mechanistically derived Reasoning Score as proxy for the thinking patterns of LRMs and investigate its relationship with the emergence of reasoning hallucinations. We begin with preliminary analysis to identify characteristic patterns associated with hallucinated rea- soning traces. We then analyze the generality of these patterns across domains using the Re ReTrruthQA dataset, and further examine the underlying mechanism that leads LRMs to exhibit such behaviors.
3.2. CASE ANALYSIS ON GSM-NoOPS
In this section, we conduct a preliminary analysis using the LRM R1-7B on a question from GSM- NoOp (Mirzadeh al. 2024), where "NoOp" statement is appended the end of math problem. To enable controlled comparison of reasoning hallucination patterns, we sample both a truthful and a hallucinated response from R1-7B the same question. Figure Suureeppreeee presents the question along with step-level reasoning scores Racore which quantify the depth of thinking at each step.
We observe that when the model generates reasoning steps that attend the added NoOp content, these steps typically receive lower Rycore, which in turn triggers the model's 's Self- Verification mechanism (Li al. 2025a). producing later steps with higher Racere that attempt to correct the earlier deviation (e.g.. (a) and (d) in Figure 2). However, in the hallucinated reasoning trace, we also observe overthinking phenomena steps with excessively high Ryorr that incorrectly revise the previous correct reasoning steps (c.g.. . (b) in Figure 2). These hallucinated traces contain more shallow pattern-matchin and overthinking steps, resulting in an overall unstable reasoning trajectory. From this case study, we identify the reasoning hallucination Pattern #1. hallucinated traces typically exhibit large fluctuations in reasoning score, especially during the early steps of the process.
Furthermore, observe that even when the model briefly arrives at correct intermediate steps, it often fails to maintain this correctness. In later steps, it performs Incorrect Backtracking, attending to earlier shallow overthinking steps, ultimately leading hallucination (e.g., (c) in Figure 2p. This motivates the reasoning hallucination Pattern #2: in the later stages of reasoning, the model tends to misguidedly attend to earlier hallucinated steps, either shallow or overthinking, making difficult to correct earlier errors and leading to hallucinated reasoning.
3.2.2
REASONING HALLUCINATION PATTERN ANALYSIS
In this section, we validate the two reasoning hallucination patterns identified in preliminary analy- sis($ 3.2. Pattern #1: large fluctuations in reasoning scores during early steps, and Pattern #2: incorrect backtracking to earlier hallucinated reasoning steps in later stages. We aim to assess whether these patterns generalize across broader domains and tasks. To this end, we conduct experiments on the ReTTruthQA dataset using the R1-7B model. ReTruthQA covers three reasoning domains: Math, Science, and Mult muultioog HopQA (Details in $ 5.II. For each domain, we construct two balanced subsets using gold hallucination labels: with hallucinated traces and one with truthful traces.
To evaluate Pattern #1, we measure the fluctuation of reasoning depth in the early phase of reasoning using the Coefficient of Variation (CV Score) (Everitt 1998), standard metric for quantifying
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Accuracy Amalysia for Ridnge
Remoning ing Score vs. Perplesity
Rising-2 Stable
Riing Consbiced
Stable Comsbicacy
6.8
3.0
Purplesity
2.5
Moun Perplestt
913%
644
2,.0
3.5
0.2
1.0
Cunissar
Dacosiiwax
Mtarg-2
Reasoning Score
(a)
(b)
(c)
(d)
Figure 4: Analysis of Pattern #1: (a) Consistency Analysis (QI); (b) Accuracy Comparison in Rising- 2 triples (Q2); (c) Reasoning score perplexity and (d) Perplexity of Rising-2 Stable (Q3).
sequence variability (shown in Figure lp. Specifically, focus on the first [K/r] steps of the
reasoning C (CI, C2, ................................ CR), and define: Reser
Reseree R Rooore-....
Rasie k/rl where
> 1 is constant controlling the size of the early-step window. The CV score over early reasoning steps is then given by:
o (Reerre)
CV(C) early
Je (R
where u(-) and o-) denote the mean and standard deviation, respectively.
To assess Pattern #2, we introduce a Attention Score that quantifies the extent to which later reasoning steps attend to earlier shallow-patter patteer matching overthinking steps (Figure T). Let the full reasoning trace be = (C1, c Ck) ) and define the later reasoning steps as Glater = {cx 1K For a step Cj E Cltter, we compute the mean attention from C₁ to each earlier step as:
[=
Hf
J.h
Ck Ggl
rECK REeg
LEC
h=1
where 1hb denotes the attention weight from token token head layer H is the number of heads per layer, L is the set of selected layers for aggregation, and the constant 7) defines late steps.
We then identify the top-K K most attended earlier steps based on Øк=クş Ta = Topp (( K), where Te is the of indices corresponding to the top-attended steps. The step-level attention score for cą is then defined as the proportion of these steps whose Reasoning Scores fall outside the normal range, either the lower quartile exceeding a high threshold T:
AttnScore(cs)
XEU JETE
Σ
1 (Rim QQunttiles///Ree (Raa))
K
Rdoo 2T)
where ((.) is the indicator function, Quantile, (oorr) denotes the first quartile of the reasoning scores (i.e., potentially shallow pattern-matching steps), and 7 is a threshold identifying potentially overthinking steps.
The trace-level attention score is computed by averaging over all later steps:
AttScore(C))
AttnScore(ce):
Crater
ECuerr
which reflects the extent which later reasoning steps attend earlier incorrect steps.
As shown in Figure 3(b and (c) and Appendix H across all three domains, hallucinated reasoning traces consistently yield significantly higher CV scores and Attention scores than truthful traces. This confirms that hallucinated traces more fluctuating in reasoning depth (Pattern #1) and more likely to attend prior incorrect steps (Pattern #2), demonstrating the generalizability of both patterns beyond the initial case study (Section 3.2.1p Detailed settings shown in Appendix H
Results.

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3.3 ANALYZING THE MECHANISMS BEHIND REASONING FLUCTUATION
We investigate the underlying mechanism behind Pattern #1, where hallucinated reasoning traces exhibit large fluctuations in reasoning depth. Building on our case study in Section 3.2.1 we hypothesize this stems from a built-in self-verification mechanism. Key questions still include: Q1: What triggers verification behavior in LRMs? Q2: Do excessively high reasoning scores reliably signal overthinking? Q3: If Q2 holds, what factors lead to the emergence of such overthinking steps?
To explore these, we construct step triples (c1, C22 C3) from reasoning traces: (1) Stable triples with minimal score variation from truthful traces; (2) Rising-1 triples from hallucinated traces with moderate score spike (Recore (Cs) T), potentially triggered by shallow pattern- matching in e2; and (3) R triples with extreme score spikes (Reenre > r), to probe overthinking behaviors.
Analysis. For Q1, we compare the logical consistency between e₁ and C2 Rising vs. Stable triples using GPT-4o judgmenss. As shown in Figurg 4aa, stable triples show significantly higher consistency, suggesting that verification is more likely to be triggered when earlier steps are inconsistent.
Regarding Q2, we assess the accuracy of 02 and in Rising-2 2 triples. FFigure 4(b) shows that while 22 is often correct, e3 introduces errors, confirming that excessively high reasoning scores reliably signal overthinking. Prompts of Q1 and Q2 are shown in Appendix
To investigate Q3, we firstly analyze the correlation between reasoning depth and perplexity. As shown in Figure 4fc), reasoning steps with higher Rscore generally exhibit lower perplexity, indicating more certainty outputs. However, Figure 4]d) reveals that Rising-2 triples, C3 steps, despite higher reasoning scores, have higher perplexity than those in stable triples, suggesting that overthinking may produce internally unstable generations. We term this phenomenon spurious verification, where the model performs misguided validation driven by autcome-based reward optimization. This insight leads us to identify a new hallucination pattern: Pattern #3: Overthinking steps exhibit a positive correlation between Recore and perplexity. More details analysis are provided in Appendix F
4 METHODS
4.1 REASONING HALLUCINATION DETECTION
Building upon the patterns uncovered our empirical study, we propose the Reasoning Hallucination Detection algorithm (RHD). Our approach leverages the step-level Reasoning Score Rycore to quan- tify thinking depth throughout the reasoning trace, and incorporates three identified indicators of hallucination: (1) Pattern #1: large fluctuations in reasoning scores during early steps, (2) Pattern #2: incorrect backtracking to earlier shallow or overthinking steps in later stages, and (3) Pattern #3: overthinking behavior where Rycore and perplexity exhibit a positive correlation.
Given a question Q and its reasoning trace with step-level scores Ranwer we define the overall Reasoning Hallucination Score as:
Hc ai Avg (ccore) + 02 CV(C) + AttnScoreeC + 04 PCC (PL(())) (5)
Overall Reasoning Dopch
Pattern #1
Parter #2
Partem #3
where @1, Q22 Or3, 044 are regression coefficients. Avg denotes the average reasoning score, CV
(Eq. (3) measures fluctuations during early-steps, AttnScore (Eq, 4 captures attention on earlier hallucinated steps, and PCC refers to the Pearson correlation coefficient between reasoning scores and step-level perplexity (CL(C), computed according to Eq.
4.2 MITIGATING HALLUCINATIONS VIA STEP-LEVEL REASONING SCORE SHAPING
Reasoning hallucinations often stem from two types of flawed steps: (1) shallow maatccin,, reflecting shortcut behaviors, and (2) overthinking, induced by excessive and misguided verification. A core factor is saccome-based RL, which only rewards the final answer and neglects intermediate
steps (Chen et al. [0226]] (02256/aalmeekam Valmeekam et al. Trrassuce Research] [024 Kalai et al. 2025). ) encouraging reward-hacking heuristies that may propagate through distillation (Wang et al. 2025)
To address this, we introduce an auxiliary process- reward based on the reasoning score Ryuore from Section 3.1 which measures the reasoning depth each step. This encourages meaningful
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reasoning while penalizing shallow overthinking steps. We model the reasoning process finite-horizon MDP A. where s E the reasoning state at step t, a E A denotes the next reasoning step, P is the transition probability and r, is the reward:
= = [0
t <TT,
rt 1 Rinal,
t= T.
Reward Shaping with Reasoning Score. We apply potential- based reward shaping (Ng ct al. 1999):
Ft = T2 + +*((5++1 - ((s)). with ( = 0,
which preserves the optimal policy while redistributing credit: V'(st) V(s+) - ((s)), where ((s.) E,
Ei= 'r
the value function of original reward and V*(es) is the shaped.
St
Potential Function Design.
To avoid encouraging overthinking, we clip the reasoning score:
a (scono Recore S. ((st) - Rscorr
Recore (8e)
00
otherwise,
where a > and T control the weighting strength and the threshold for overthinking, respectively.
To understand the generalization benefit of our proposed reasoning score-based shaping, we derive a uniform convergence bound under augmented rewards:
Theorem 1 (Generalization Gap with Augmented Rewards). Let the policy class II be such that ( is uniformly bounded in [0, Remax for any trajectory& & sampled from the environment. Each trajectory & = ($1, 01 Fi...., ST, QT FrT denotes a complete mulli-step reasoning trace. Suppose that IT has Rademacher complexity R., (II) based on independent training samples {E.)==1- Then, with probability at least 5, for any
for any II, the augmented return ((
E the following holds: Jres((T) Jraiin (T) S 2 Rr (TT)+ Rmax v
/log(1/5) where (ren(
2n
Egl [[[R(T, <)] is the expected test return and J J (T) EE R(T,, is the empirical training return.
The proof given in Appendix B Intuitively, our reasoning score acts as a regularizer that encourages logically consistent behaviors and effectively reduces the Rademacher complexity (II), thereby tightening the bound and improving generalization to unseen reasoning tasks.
Integrate into GRPO. To demonstrate compatibility with standard RL algorithms, integrate the reasoning score shaping framework into the Group Relative Policy Optimization (GRPO), a scalable and widely used RL algorithm for reasoning model training DeepSeek-A1] (2025): [Sha al. (2024):
Dai et al. (2026), yielding GRPO-R. All implementation and formulation details of GRPO-R are provided in Appendix C
EXPERIMENTS
5.1 REASONING HALLUCINATION DETECTION
Data and Evaluation. We evaluate our RHD method on the ReTruthQA dataset spanning three reasoning domains: Math, Science, and MultiHopOA (construction details in Appendix D) We adopt two evaluation settings: (1) Binary Detection, which assesses the model's ability to
detect hallucinations in individual (Q, () pairs using AUC and PCC: (2) Multi- Multi-Trace Ranking. which evaluates whether the model can rank truthful traces higher among multiple candidates (Q, [C,...,, CN )), following TruthfulQA-MC (Lin et al. 2021). We report MCI, MC2, and MC3 to measure hallucination ranking accuracy (Evaluation details are in Appendix
Models and Baselines. We conduct experiments on two openesource LRM: DeepSeek-R1-Dist13 1-wenn-7- (R1-7B) and
www.Diissiltieenn11 -1 (R1-14B) DeepSeek-AT (2025). We compare our method against six categories of hal-
lucination detection baselines: (1) Ensemble based self-evaluation (e.g.. ChainPoll (Friel &
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Table 1: Performance comparisons between RHD and baselines for Reasoning Hallucination Detec- tion. The boldface represents the best performance, and the underline represents the accodd-best. t means improvements are significant (paired t-test or DeLong test at p-value < 0.05).
LIXN
Caloporiis
Methods
BeYranhjA (MATED)
BuitratQAA (Sctrncc)
ReTnuigga (Mulillop())
Risary Dreccsos
Mate/Tluee Busking
Rivrry Detertion
Mali-Twcy Realing
Bisary Drssnos
Mall-Tare Rocking
AUC
PCC
MC1
MC2
MC3
ABC
PCC
MC1
MC3
MC3
ABCC
PCC
MCC
MC2
MC3
Chareell
0.3613
0.3030
0.3083
0.6468
0.2612
0.270
02293
0.6297
0,426
0.301
Erocatbic
LM+LM
0.372
0.3234
0.2004
0.3402
0.5345
0.1890
0.300
02103
03113
0.831
0.739
0.300)
Se/CWAGPP
0,727
0.491
0.4091
0.754
0.119
0/6819
0.2069
0.3793
0.303
0.686
0.1915
03118
P(Tra)
07216
0.2641
0.5455
0.5182
0/625
0,2512
0.5172
0.535
0.540
0.1684
0/426
0,3000
Qucortaiity
LN EN-Esogg
0.309
0.5553
0.125
0.144
PRC
07005
0.2856
0.9909
0.5434
0.650
0,4550
Length
Sorgth
0.5551
0.092
0,318
0,566
0.348
0,5510
00911
0,573
0,003
05335
0,5515
0.14%
05106
0,3567
0.474
PRM
Qves2 5-PRX--88
Owerd 5- PHNSBOCK
0.6001
0.5563
0.1354
0.246
0.473
04318
1.3000
02710
0.4572
0,3913
6.153
0,560
0.2208
0.1275
0,2200
0.4400
0.5655
0.1425
04444
0,2362
0.564
0.5422
0.1034
01066
0,535
0.226
B4167
BL3552
0340
LCM
GPT4-
W7513
0,692
0.7944
0,3022
0.491
01210
0.155
0.411
0.205
0.N45
0,555
0,2026
0,3655
0,3/0
0.200
0.265
63200
04455
0.7123
0.5424
022244
5.241
04400
013300
0.704
Seff-ware
UQAC
Ourx
KII
6,797%
0L4852
0.6991
6.745
0.56091
0.7194
0.906
IL5688
0.7060
BA255
0L7105
Ensenble
SecCasdGir
U1600
0.1441
0.2615
112314
0.653
0129K2
0.385
53141
Uncortaiity
LN
U1622
0.2244
0.3419
112990
0.4254
0.994
03125
012540
0,3675
PML
06525
0.2300
0.3546
02744
C/229
0/2255
0.1701
03355
0.2521
0.400
R1-14B
Length
Lez Scone
0.118
010110
0
C.5554
01:4KY
1LNSAS
0.3545
64211
0.1543
0/7/1
1L3454
0.4244
PRM
Quend2 --83--111
Quonn S-RAAS000K
065616
0.1248
0.1289
0.3518
0.3317
B.2097
113918
0.422
055153
0.055
0.544
015799
0.2555
02/51
2/475
2.045
011166
04483
033115
Saff-Nware
URAC
Figeefoom
06674
0.2901
015/4
0.7787
0.3111
0,3877
0.7636
ILSIM
0.3328
019675
0.125
0. 55500
81779
0.695
0.985
0.5117
111567
0.1520
0.799
Dars
RED
6.7392
0.367
3,302
0.7085
0 0.6654
0.708
0.063
866677
1.4714
0,5671
0.7355
0,3742
0.5785
0.4131
0.516
Table 2: Performance comparisons between GRPO-R and baselines. Bold indicates the best result.
Models
Qwea25-1.58 Enstruc
MATHIS00
ATME/2024)
GPQAdiammad) GPQAImuia GPOAirstende))
MATHE00
AIME/2024)
GPQArdimmed) GPQA(main) GPQAiestanedl
Banc
0.212
0.335
0.354
0.353
0.359
0.666
0.100
0.302
0.197
0.211
-GRPO
0.771
0,333
0.359
0,335
0,391
0.400
01155
6:47
0.214
0.266
-GRPO-R
0,758
0.367
0.414
0,31
0.357
0,490
0.335
0.347
0.243
0.275
Sanyal 2023); ) (2) Uncertainty based methods (e.g., P(True) Kadavath et al.
2022 )
(3)
Self-Awareness based approaches (e.g., UQAC Li et al. (2025b)); (4) LLM-as- CritiC (LCM)
models (e.g., GPT-4c); (5) Process Reward Models (PRMs) with step-level supervision (e.g..
Qwen2. 5 MM MRMM) (6) Length-based scoring, which uses trace length as proxy for
hallucination likelihood. Baselines and RHD implementation details are in Appendix[and J
Main Results As shown in Table [ RHD consistently outperforms most baselines across all ReTruthQA domains, model backbones, and evaluation settings, demonstrating strong robustness. Ensemble and LCM methods perform well in binary detection but struggle in multi-trace ranking, indicating difficulty in fine-gra aen-ggrined comparison. Uncertainty-bitt -bsed methods are sensitive to output length. while Process Reward Models often suffer from limited generalization. In contrast, RHD directly leverages reasoning mechanisms for more accurate detection. Self-awareness methods perform competitively but lack explicit reasoning analysis. The Length-based baseline performs well in multi-trace settings-uupooriing the intuition that overly long traces are more error-prowe prror-prone, but underperforms in binary detection, limiting its generality. These findings highlight the effectiveness of RHD modeling internal reasoning patterns for hallucination detection. Additional Qwen3-8B Yang et al. (2025) results, ablations and sensitivity studies are provided in Appendix
M N
and K
5.2 REASONING HALLUCINATION MITIGATION
Experimental Setting. To assess the effectiveness of GRPO-R in reducing reasoning hallucina-
tions, we fine-tune Qwen2. 5-1---1-----1111 5B Instruct and DeepSeek R1 R1-1. 121-1.3. 1155 on 2,000 examples
from OpenR1-Math 2 220K (Team 2024) using either GRPO or our proposed GRPO-R. We eval-
uate the accuracy (Hugging Face| 2025) two in-domain math
Light
man et al. (2023) and AIME 2024 4 AI-MO (2024a) -nd an out-of-distribution science bench-
MPQK (Rein et al. 2024). Implementation details are in Appendix O
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Main Results. As shown in Table GRPO-R outperforms GRPO across most of the tasks, indicating that shaping reasoning steps via the reasoning score enhances both factual accuracy and reasoning reliability. Gains GPCA further suggest improved generalization beyond training distribution. Additional sensitive and GRPO-variants analyses are Appendix Padd R Hallucination mitigation experiments in data distillation in Appendix SenndixxQuuna further validate the effectiveness of RHD model.
CONCLUSION
We study Reasoning Hallucination in LRMs from mechanistic perspective, probing internal model behaviors rather than surface text. We propose the Reasoning Score, a step-level metric grounded in mechanistic interpretability that quantifies reasoning depth. Using this lens, we uncover three characteristic hallucination patterns etaly-stage depth fluctuations, incorrect backtracking, and spurious ielficattioninduueen overthinking- and build RHD framework for their detection. Finally, we introduce GRPO-R, which integrates aesoning-score-basee shaping into reinforcement learning, improving accuracy and robustness across reasoning benchmarks. This establishes a unified pipeline from mechanistic analysis to practical mitigation of reasoning ballucinations.
ACKNOWLEDGMENTS
This work funded by the National Natural Science Foundation of China (62472426, 62376275), fund for building world-class universities (disciplines) of Renmin University of China. Supported by the School of Interdisciplinary Studies, Renmin University of China, and the Big Data and Responsible Artificial Intelligence for National Governance (BRAIN), Renmin University of China. constitutes phased research output of the Young Researcher Research Fund of the Renmin University of China-Westlakke University Joint Academy on Future Humanity. Supported by the Outstanding Innovative Talents Cultivation Funded Programs 2026 of Renmin University of China. Work partially done at Engineering Research Center of Next-Generation Intelligent Search and Recommendation, Ministry Education, and Beijing Key Laboratory of Research on Large Models and Intelligent Governance.
REFERENCES
Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774 2023.
AI-MO. Ai-mo/aimo--vaiidttonn-aiiii http:://heggingfeeecco//ttttsss MO/
aimo-valicon wttoo-aaaaaatiinnneam 2024a. Apache 2.0 License.
AI-MO. Ai-mo/aimo-vallidttonnnnmm
aimo-valicon vitoo-vaaiaaiinnn amc 2024b. Apache 2.0 License.
Chao Chen, Kai Liu, Ze Chen, Yi Gu, Yue Wu, Mingyuan Tao, Zhihang Fu, and Jieping Ye. Inside: Lims' internal states retain the power of hallucination detection. The Twelfth International Conference on Learning Representations, 2024.
Shiqi Chen, Jinghan Zhang, Tongyao Zhu, Wei Liu. Siyang Gao, Miao Xiong, Manling Li, and Junxian He. Bring reason to vision: Understanding perception and reasoning through model merging. arXiv preprint arXiv:2505.0544 2025a.
Yanda Chen, Joe Benton, Ansh Radhakrishnan, Jonathan Uesato, Carson Denison, John Schulman, Arushi Somani, Peter Hase, Misha Wagner, Fabien Roger, et al. Reasoning models don't 't always say what they think, arXiv preprint arXiv:2505.0541 2025b.
Roi Cohen, May Hamri, Mor Geva, and Amir Globerson. Lm Im: Detecting factual errors via cross examination. arXiv preprint arXiv:2305. 2023.
Roshan Cools and Mark Esposito. Inverted-u-shpped dopamine actions on human working memory and cognitive control. Biological psychiatry, 69(12)e e3-5 201
10

---

Published as a conference paper at ICLR 2026
Yanqi Dai, Yuxiang Ji, Xiao Zhang, Yong Wang, Xiangxiang Chu, and Zhiwu Lu. Harder is better: Boosting mathematical reasoning via difficult--warre grpo and multi multi-aspect question reformulation. arXiv preprint arXiv:2601.20611 106144, 2026.
DeepSeck-AL. Deepscek-rl: Incentivizing reasoning capability in llms via reinforccement learning. arXiv preprint arXiv:2501.12945 2025. URL https: wttp:/rrgabbb....s...././ 12948
Nelson Elhage, Neel Nanda, Catherine Olsson, Tom Henighan, Nicholas Joseph, Ben Mann, Amanda Askell, Yuntao Bai, Anna Chen, Tom Conerly, Nova DasSarma, Dawn Drain, Deep Ganguli, Zac Haffild-Doddss Danny Hernandez, Andy Jones, Jackson Kernion, Liane Lovitt, Kamal Ndousse, Dario Amodei, Tom Brown, Jack Clark, Jared Kaplan, Sam McCandlish, and Chris Olah. A mathematical framework for transformer circuits. Transformer Circuits Thread, 2021. URL https://transfoe wwt.ooormrrriicucutteeeeeeeeeeee pub/ muub/2021/ Erw.wwokkwiwie.........r.r html
Brian Everitt. The cambridge dictionary of statistics, In The Cambridge dictionary of statisties, pp. 360-360. 1998.
Javier Ferrando and Elena Voita. Information flow routes: Automatically interpreting language models at scale. arXiv preprint arXiv:2403.00824 2024.
Javier Ferrando, Gabriele Sarti, Arianna Bisazza, and Marta R Costa-jussà, A primer on the inner workings of transformer-based language models. arXiv preprint
00208, 2024.
Robert Friel and Atindriyo Sanyal. Chainpoll: A high efficacy method for Ilm hallucination detection. arXiv preprint arXiv:2310.1834 2023.
Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, and Tom Goldstein. Scaling up test-time compute with latent reasoning: A recurrent depth approach. arXiv preprint arXiv:2502.05171, 2025.
Mor Geva, Roei Schuster, Jonathan Berant, and Omer Levy. Transformer ner-ffr layers are key-value memories. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pp. 5484 5495, 2021.
Michael Hanna, Ollie Liu, and Alexandre Variengien. How does gpt-2 compute greater-than?: Inter- preting mathematical abilities pre-trained language model. Advances in Neural Information Processing Systems, 36, 2024.
Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason Weston, and Yuandong Tian. Training large language models to reason in continuous latent space. arXiv preprint arXiv:2412.06769, 2024.
Yancheng He, Shilong Li, Jiaheng Liu, Weixun Wang, Xingyuan Bu, Ge Zhang, Zhongyuan Peng, Zhaoxiang Zhang, Zhicheng Zheng, Wenbo Su, and Bo Zheng. Can large language models detect errors in long thain-of-though reasoning?, 2025. URL wtttt:::ss:siiiiii wttp:/iwwwrraab/aaa atgg/bb//220000
19361
Xanh Ho, Anh-Khoa Duong Nguyen, Saku Sugawara, and Akiko Aizawa. Constructing multi hop qu dataset for comprehensive evaluation reasoning steps. arXiv preprint 20t.:::21110000000 2020.
Hugging Face. Math-verify: A rule-based mathematical answer verification library, 2025. URL https:://github..co htt.:ttw...c...hh..eeete hww.aaaa/aaaaaaaa.....er MMtth-
Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, al. Language models (mostly) know what they know. arXiv preprint arXiv:2207.05221 2022.
Daniel Kahneman. Thinking, fast and slow. macmillan, 2011.
Adam Tauman Kalai, Ofir Nachum, Santosh S. Vempala, and Edwin Zhang. Why language models hal- lucinate. 2025. URL //api demanticsche ar. wwt./oorooaoaaooio : 94798

---

Published as a conference paper at ICLR 2026
Ann Langley. Between 'paralysis by analysis' and 'extinction by instinct'. Sloan Management Review, 36:63-76, 76, 1995.
Dacheng Li, Shiyi Cao, Tyler Griggs, Shu Liu, Xiangxi Mo, Eric Tang, Sumanth Hegde, Kourosh Hakhamaneshi, Shishir G Patil, Matei Zaharia, et al. Lims can easily learn to reason from demonstrations structure, not content, is what matters! arXiv preprint arXiv:2502.07374, 2025a.
Junyi and Hwee Tou Ng. The hallucination dilemma: Factuality- reinforcement learning for large reasoning models. arXiv preprint arXiv:2505. 246600 2025.
Kenneth Li, Oam Patel, Fernanda Viégas, Hanspeter Pfister, and Martin Wattenberg. Inference- time intervention: Eliciting truthful answers from language model. Advances in Neural Information Processing Systems, 36, 2024a.
Ruosen Li, Ziming Luo, and Xinya Du. Fg-prm: Fine-grained hallucination detection and mitigation in language model mathematical reasoning. arXiv preprint arXiv:2410.06304 2024b.
Yinghao Li, Rushi Qiang, Lama Moukheiber, and Chao Zhang. Language model uncertainty
quantification with attention chain, 2025b. UtLbttss::/ /ttp/aaiivvv..///.///ea/////aav. www.aaggg///ooooooooo......aaa.a 220./55533311 1115.111118.8..
Zhaoyi Li, Gangwei Jiang, Hong Xie, Linqi Song, Defu Lian, and Ying Wei. Understanding and patching compositional reasoning in 1lms. arXiv preprint arXiv:2402.14325 2024c.
Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards. Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. The Twelfth International Conference on Learning Representations, 2023.
Stephanie Lin, Jacob Hilton, and Owain Evans. Truthfulqa: Mcasuring how models mimic human falsehoods. arXiv preprint 1.Xiv:2109.07998 2021.
Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin. Understanding rl r1-zero-like training: A critical perspective. arXiv preprint arXiv:2503.20783, 2025.
Haolang Lu, Yilian Liu, Jingxin Xu, Guoshun Nan, Yuanlong Yu, Zhican Chen, and Kun Wang. Auditing meta-cognitive hallucinations in reasoning large language models. arXiv preprint arXiv:2505.13143, 2025.
Liangchen Luo, Yinxiao Liu, Rosanne Liu, Samrat Phatale, Meiqi Guo, Harsh Lara, Yunxuan Li, Lei Shu, Yun Zhu, Lei Meng, et al. Improve mathematical reasoning in language models by automated process supervision. arXiv preprint arXiv:2406.0659 2024.
Andrey Malinin and Mark Gales. Uncertainty estimation in autoregressive structured prediction.
arXiv preprint arXiv:2002.07650, 2020.
Potsawee Manakul, Adian Liusie, and Mark Gales. Selfcheckgpt: Zero-resource black-box hallucina- tion detection for generative large language models. In Proceedings of the 2023 Conference Empirical Methods in Natural Language Processing, pp. 9004-9017, 2023.
Iman Mirzadeh, Keivan Alizadeh, Hooman Shahrokhi, Oncel Tuzel, Samy Bengio, and Mehrdad Farajtabar. Gsm-symbolic: Understanding the limitations of mathematical reasoning large language models. arXiv preprint arXiv:2410.05529, 2024.
Andrew Y Ng, Daishi Harada, and Stuart Russell. Policy invariance under reward transformations: Theory and application reward shaping. In leml, volume 99, pp. 278 378-287. Citeseer, 1999.
Yaniv Nikankin, Anja Reusch, Aaron Mueller, and Yonatan Belinkov. Arithmetic without algo- rithms: Language models solve math with a bag of heuristics. In The Thirteenth International Conference on Learning Representations, 2025. URL Ral.https: htttp:://opeereee
wwt.:e///ffee formm?
id=09yTE26r22
Cheng NIu, Yuanhao Wu, Juno Zhu, Siliang Xu, Kashun Shum, Randy Zhong, Juntong Song, and Tong Zhang. Ragtruth: A hallucination corpus for developing trustworthy retrieval-augmente lan- guage models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguisties (Volume I: Long Papers), pp. 10862-10878. 2024.
12

---

Published as a conference paper at ICLR 2026
nostalgebraist.
Interpreting GPT: the logit lens. AI Alignment Forum, 2020. http:///ww....eaaaaaaaaa////aaaa
URL
OpenAl. Openai o3 and 04-mini system card, April 2025. UKL/ettpss//ppenaa.comm/ooeee
o3-o4 114-ming mini -ww.ii-ssttemcaae cardd/
Archiki Prasad, Swarnadeep Saha, Xiang Zhou, and Mohit Bansal. Receval: Evaluating reasoning chains via correctness and informativeness. arXiv preprint arXiv:2304. 10000,, 2023.
Ofir Press, Muru Zhang, Sewon Min, Ludwig Schmidt, Noah A Smith, and Mike Lewis. Measuring and narrowing the compositionality gap in language models. arXiv preprint arXiv:2210.03350, 2022.
David Rein, Betty Li Hou, Asa Cooper Stickland, Jackson Petty, Richard Yuanzhe Pang, Julien Dirani, Julian Michael, and Samuel R Bowman. Gpqa: A graduate-level google-proo q&a benchmark. In First Conference on Language Modeling, 2024.
Jie Ren, Jiaming Luo, Yao Zhao, Kundan Krishna, Mohammad Saleh, Balaji Lakshminarayanan, and Peter J Liu. Out-of-distribution detection and selective generation for conditional language models. In The Eleventh International Conference on Learning Representations, 2022.
Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024.
Alessandro Stolfo, Yonatan Belinkov, and Mrinmaya Sachan. mechanistic interpretation of arithmetic reasoning language models using causal mediation analysis. In The 2023 Conference on Empirical Methods in Natural Language Processing, 2023. URL htttps::/opeereeeee///
net/Eozum?id 33wwh4022Hhh
Zhongxiang Sun, Zihua Si, Xiaoxue Zang, Kai Zheng, Yang Song, Xiao Zhang, and Jun Xu. Largepig for hallucination-free query generation: Your large language model is secretly a pointer generator. In Proceedings of the ACM on Web Conference 2025, pp. 4766 4779, 2025a.
Zhongxiang Sun, Qipeng Wang, Weijie Yu, Xiaoxue Zang, Kai Zheng, Jun Xu, Xiao Zhang, Yang Song, and Han Li. Rearter: Retrieval- Retreetal-aummented reasoning with trustworthy process rewarding. In Proceedings of the 48th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 1251-1261, 2025b.
ZhongXiang Sun, Xiaoxue Zang. Kai Zheng. Jun Xu, Xiao Zhang, Weijie Yu, Yang Song. and Han Li. Redeep: Detecting hallucination in retrieval-augmente generation via mechanistic interpretability. In The Thirteenth International Conference Learning Representations, 2025c.
Zhongxiang Sun, Yi Zhan, Chenglei Shen, Weijie Yu, Xiao Zhang, Ming He, and Jun Xu. When personalization misleads: Understanding and mitigating hallucinations in personalized llms. arXiy preprint arXiv:2601. 2026.
Open-Ro Team. Openr1-math- //hgggingface..o//eeeeee// ctt.:eestccccaaatttseeeooae.s http://ppnnnrorrraee -Math 220k
dataset for mathematical reasoning, 2024. URL https:
Katya Tentori, Nicolao Bonini, and Daniel Osherson. The conjunction fallacy: A misunderstanding
about conjunction? Cognitive Science, 28(3)4667447, 2004.
Transluce Research. Investigating truthfulness in pre-release o3 model, 2024. URL https
Harsh Trivedi, Niranjan Balasubramanian, Tushar Khot, and Ashish Sabharwal. Musique Multihop
questions via single-hop question composition. Transactions of the Association for Computational Linguisties, 10:539-554, 2022.
Karthik Valmeekam, Kaya Stechly, and Subbarao Kambhampati. Lims still can't an'tt plan; can Irms? preliminary evaluation of openai's 's ol on planbench. In NeurlPS 2024 Workshop on Open- World Agents.
13

---

Published as a conference paper at ICLR 2026
Vectara Research. Deepseek-rl hallucinates more than deepseek 2025, URL bttps://wwi WwW betttaana.ccm//bbooo//eeeeeeeee http://ppppee----aaaaaaaaaeeeeer -aee--ttaeennee-----11
Xinyi Wang, Shawn Tan, Mingyu Jin, William Yang Wang, Rameswar Panda, and Yikang Shen. Do larger language models imply better reasoning? pretraining scaling law for reasoning. arXiv preprint arXiv:2504.0363: 2025.
Patrick P Weis and Wilfried Kunde. Switching between different cognitive strategies induces switch costs as evidenced by switches between manual and mental object rotation. Scientific Reports, 14 (1):6217, 2024.
Wenhao Wu, Yizhong Wang, Guangxuan Xiao, Hao Peng, and Yao Fu. Retrieval head mechanistically explains long-context factuality. arv preprint arXiv:2404.15574 2024.
Xin Xu, Shizhe Diao, Can Yang, and Yang Wang. Can we verify step by step for incorrect answer detection? arXiv preprint arXiv:2402. 10528, 2024.
Kai Yan, Yufei Xu, Zhengyin Du, Xuesong Yao, Zheyu Wang, Xiaowen Guo, and Jiecao Chen. Recitation over reasoning: How cutting-edge language models can fail on elementary school-level reasoning problems? arXiv preprint arXiv:2504.00500 00500, 2025.
An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, et al. Qwen2. 5 technical report. arXiv preprint arXiv:2412.15115. 2024.
An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report. arXiv preprint arXiv:2505.09388 2025.
Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William W Cohen, Ruslan Salakhutdinov, and Christopher D Manning. Hotpotqa: A dataset for diverse, explainable multi-hop question answering. Xix preprint arXiv: wwt.:.889.990000 2018.
Qinan Yu, Jack Merullo, and Ellie Pavlick. Characterizing mechanisms for factual recall in language models. In The 2023 Conference on Empirical Methods in Natural Language Processing, 2023.
Zhiyuan Zeng, Qinyuan Cheng, Zhangyue Yin, Yunhua Zhou, and Xipeng Qiu. Revisiting the test-time scaling of ol-like models: Do they truly possess test-time scaling capabilities? arXiv preprint arXiv:2502. 12215, 2025.
Zhenru Zhang, Chujic Zheng. Yangzhen Wu, Beichen Zhang, Runji Lin, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin. The lessons of developing process reward models in mathematical reasoning. arXiv preprint 2Xiv:2501.07300 2025.
Chujie Zheng, Zhenru Zhang, Beichen Zhang, Runji Lin, Keming Lu, Bowen Yu, Dayiheng Liu, Jin- gren Zhou, and Junyang Lin. Processbench: Identifying process errors in mathematical reasoning. arXiv preprint arXiv:2412.06559, 2024a.
Chujie Zheng, Zhenru Zhang, Beichen Zhang, Runji Lin, Keming Lu, Bowen Yu, Dayiheng Liu, Jin- gren Zhou, and Junyang Lin. Processbench: Identifying process errors in mathematical reasoning, 2024b. URL https:://// httlitttts//aaxtttt /ttp:///axxvvvvo absp://bb///222// 06559
Hanzhang Zhou, Zijian Feng, Zixiao Zhu, Junlang Qian, and Kezhi Mao. Unibias: Unveiling and mit- igating 11m bias through internal attention and fin manipulation. arXiv preprint arXiv:2405.20612 2024.
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CONTENTS
Introduction
Related Works
3
Empirical Study of Reasoning Hallucination
3.1
Reasoning Score: Measuring Reasoning Depth in Large Reasoning Model
3.2
Reasoning Hallucination Analysis Based on Reasoning Score
3,2.1
Case Analysis on GSM-NoOps
3.2.2
Reasoning Hallucination Pattern Analysis
3.3
Analyzing the Mechanisms Behind Reasoning Fluctuation
Methods
Reasoning Hallucination Detection
Mitigating Hallucinations via Step-Level Reasoning Score Shaping
Experiments
5.1
Reasoning Hallucination Detection
5.2
Reasoning Hallucination Mitigation
6
Conclusion
10
Appendix
15
Use Large Language Models
17
Proof of Generalization Gap with Augmented Rewards
17
Detailed Implementation of GRPO-R
19
D Re ReTruthQA Construction
20
D. Data Sources and Models
20
D.2 Reasoning Step Segmentation Strategy
21
D.3 Annotation Process
E
GSM-NoOp Construction Process
23
Details of Understanding the Mechanisms Behind Reasoning Hallucination Patterns
23
Prompt for Hallucination Patterns Analysis
25
More Results of Reasoning Hallucination Pattern Analysis
25
Evaluation and Baseline Details of Reasoning Hallucination Detection
26
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J
Implementation Details for Reasoning Hallucination Detection
26
RHD on Latent CooT Models
27
Additional Detection Results on Qwen3-8B
28
M Ablation Study of RHD
29
Sensitivity Analysis of RHD
30
Implementation Details for Reasoning Hallucination Mitigation
30
Sensitivity Analysis of Reasoning Score Weight in GRPO-R
31
RHD-Guided Reasoning Distillation
32
Extension GRPO-R Other GRPO Variants
32
S
Notation Summary
33
Complexity and Efficiency Analysis of RHD
33
Future Work
34
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A USE OF LARGE LANGUAGE MODELS
In accordance with the ICLR 2026 policy on the disclosure of language model usage, we confirm that Large Language Models (LLMs) utilized in the preparation of this paper. The usage limited to aiding with language fluency, grammar checking, and polishing of the writing. The research ideas, experimental design, theoretical analysis, and all scientific contributions were solely developed by the authors. No LLMS contributed at the level of contributing author.
Disclosure: Yes, aid polish writing. Details described in the paper.
B PROOF OF GENERALIZATION GAP WITH AUGMENTED REWARDS
Proof of Theorem 7
For any policy E II, define the augmented return
R( E)
(e().
Assume that Fx(E) E [0, Fmax] for each t, so that
R(T,E) E [0, Rmax].
Define the expected return:
(T) = BEND [R(T.E)),
and the empirical return:
1 Jirain (T)) = Σ (.). n
We aim bound the expected generalization gap between the test return and empirical return for policies in class II via Rademacher complexity. Let the function class be defined as
F = (S)(E) R( π E IT).
where R(x, {) is the total return trajectory & under policy x using the augmented reward F.. Our goal is to bound:
B[f(E) 1 Σ f(E)
sup (TS)((T) Jtrain (T)) sup TET
fEF
Let E be the training samples drawn i.id. from the environment distribution and ,,...,,; S. be another independent copy drawn from the same distribution. By using an independent ghost sample set and the triangle inequality, have:
)
Σ f(E) - f(E.) ] i=1
B(a.) fEF
sup
BEwD(f(E) - Σ f(E.)
EF(E) 1=1
= ((E)).EE
sup fEF
< BEJHE
sup SEF
(S(E) -(())
To simplify the expression, we now introduce independent Rademacher variables 01,..., On {-1,+1), where each a; takes value +1 or -1 with equal probability. Since f(E) - f(E)) is symmetric around zero due to & E, can write:
sup- Σ (U(E) - S(E))) feF
sup Σ of (S(E) - (I(E)- ((E)))
FEF n
We now apply the triangle inequality again:
sup
T: (+(E()) - f(()) < sup feF
ozf(E) + sup JEF i=1
-o))((E)
fEF
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Since -o; is still a Rademacher variable and &, and E have the same distribution, the expectations are equal. Thus, we obtain:
1 Σ (fi(Es)
sup
Σ (f(E))
- f(E)))
- (Es)
sup /EF n
SEF
= (F),(F),
where (J) the empirical Rademacher complexity of F.
Assume every return is bounded, 0 S [x) < Rmax. and that (x( is linear in the augmented per-step rewards (E):
T 2
(+(5)
Introduce the normalised return f+(5) == fx(E) Rumax [0, 1] and let F (fx π MJ. Because Rademacher complexity is positively homogeneous in its function class,
(emm))/mmxx
(F) RmnBamxx F) Rmax Rn (F).
We measure the complexity of the policy class precisely through these normalised returns and set R, (II) (F).
Justification. Even if the mapping ग + fr is not injective, Rademacher complexity monotone with respect to set inclusion: enlarging the function class can only increase R, Hence analysing the (possibly larger) class FF yields conservative upper bound the true policy complexity-exate what we need for a valid generalisation bound.
Combining the two displays yields
(F. S R.ma (II)
(the identity can be written as "<" because any alternative normalisation would only shrink the right-hand side).
Substituting the above bound into the symmetrisation result, we obtain
E sup
Jrest (T) Jirain (T) < 2 Rmax R2 (II),
ell
We now move from the expected generalization gap to a high-probability bound that holds uniformly over all policies II.
Let X; R(T,&E)) = ΣT trajectory. Then Juain (T) 1 ΣT= X, and (T) REgDD(X By assumption, X; E [0, Rmax).
1 Fr(()) be the augmented return of policy π the i-th training
Applying Hoeffding's inequality for bounded i.i.d. variables, we have for any fixed л E II:
Pr ([)ess(x)) - Jurann ( 2 =) S 2 eexp (- (-( (Rmax))
2ne2
Solving for yields that with probability at least 8,
log( log(1/5)
(rea(m)) Jirain (T) Rinax
(16)
2n
Define the worst-case generalization gap the policy class:
ASS) = sup (Jiea(TT) Jurain Jirai((T)) (T))
well
where S (Ei,..., En) is the training
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(i) Expected bound from above: Using symmetrization and Rademacher complexity arguments, already established:
Ess [s(A( 2 (TT).
(6)
(ii) priibbliobbiiitty deviation bound via McDiarmid's s inequality: Let us show that ((S) concentrates around its expectation. Consider replacing any single sample & in 8 by independent copy 4 Because each return X; = R(T, {,) is bounded in [0, Rmaxl and each contributes to the empirical mean, the influence of changing & is bounded by:
ASS) - A(S(0))
Rmax n
Hence, ((8) Rmax/n- Li-isschitz in each of its arguments.
Applying McDiarmid's inequality:
2x
(- 2n
(r E[A(S)] 2 Di=1 (Rmax/ /n/²
(
exp
(Rmax)²
Solving for again yields that with probability least 1 ò,
A(S) [[A(S)] + Rmax log(1/8)
2n
(iii) Final generalization gap: Combining Equation and 7 with probability at least over the random draw of the training set S, obtain:
log(1/5)
(Tee((T) Juain (TT) < Rmxx Rr (IT) + Rmax xEII
sup
2n
Equivalently, for all IT,
log(1 (gg(
(T))(T) Jurai((T)) S 22 (II Riax
(8)
2n
Conclusion. Equation 8 provides uniform generalization gap for any policy π E II, showing that the expected test-time performance is lower bounded by the training performance minus complexity-depenue regularization term. According to this theorem, (s) is well-aligned with genuine logical reasoning. it acts a regularizer that effectively reduces the Rademacher complexity R., (TT), thereby tightening the bound. This theoretical result highlights that our proposed process supervision framework not only improves credit assignment during training but also enhances generalization to unseen reasoning tasks.
the augmented reward
This theoretical result not only explains why our process supervision framework enhances generaliza- tion to unseen reasoning tasks, but also sheds light on the hallucination risk in outcome-based RL. Because outcome-only reward collapses trajectories with differing reasoning quality into a shared positive label, it greatly increases the functional hypothesis class and thereby the generalization gap. As result, models trained with such reward signals are more likely to memorize spurious patterns and produce hallucinated reasoning at test time.
C DETAILED IMPLEMENTATION OF GRPO-R
Our proposed process-level reasoning score supervision is compatible with any token-level RL algorithm. In this work, we instantiate it within Group Relative Policy Optimization (GRPO), yielding GRPO-R. GRPO is scalable and widely used RL framework for reasoning model training. which promotes the generation of high-quality reasoning trajectories by ranking G' candidate outputs based on their relative returns, without relying on explicit value estimation DeepSeck-Al 2005);
Shao et al. (2024).
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Table 3: Statistics of ReTruthQA dataset across domains.
Dataset
#Samples
#Traces
Avg Truthful Traces
Avg Hallucination Traces
MATH
57
417
3.35
3.96
Science
88
541
3.05
3.10
MultiHopQA 184
1186
2.74
3.70
Given a prompt q and G outputs foz 1 each output o, corresponds to a sequence of reasoning produced over K reasoning steps. In the original GRPO setup, only the final step receives a nonzero reward:
states
$; 1.
T final (TP = 0.
j= K. j K,
where nلساmal denotes the scalar reward assigned to the final outcome.
We replace this sparse signal with our shaped step-level reward using potential-based reward shaping:
petep( r. (j) Racore ($1g-1) (
where Racore (8) min (s), and we 7 1. These shaped rewards are collected into the set R', standardized as:
pstop step (j) (e)
std(R') R')
and used to compute token-level advantages:
gstep (j).
ji st
Finally, we optimize the policy using the enhanced GRPO objective, termed GRPO-R:
loi
To(ort
q. (i,e))))
JGRPO.R(()) = Eqp) [o (Olv)
min
Te (oi, g,0i,())
Tolos, q, 0i,ct)
clip(
1- 1, An..)
Tora 9. 0i,e)))
- - DKL (TO met
(9)
Relation to Factuality-Base RL. Factuality-orientedd RL methods improve a model's alignment with external world knowledge by assigning outcome-level factual rewards (Li & Ng 2025). These approaches address factual hallucinations and supervise only the final answer.
contrast, GRPO-R targets reasoning hallucinations eerors originating from the model's internal multi-step reasoning process. Our method introduces step-level reward derived from the Reasoning Score ($ 3.Jp. which regularizes the model's intermediate reasoning dynamics rather than factual correctness alone.
These two types of RL are complementary: factual RL enhances knowledge faithfulness, while GRPO-R R improves process faithfulness by promoting deep, coherent reasoning. Empirically (Table 2 reinforcing internal reasoning also brings secondary gains in factual reliability.
D RETRUTHQA CONSTRUCTION
D. DATA SOURCES AND MODELS
Due the absence of dedicated datasets for evaluating reasoning hallucination detection particularly for strong spen-source LRMs such as SeepSeek-R1-1 and R1-14B, we construct a new bench- mark specifically tailored to multi-step reasoning tasks following the previous annotation process of
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the hallucination detection dataset (Niu al. 2024). Unlike traditional hallucinations, reasoning hallucinations are often embedded within logically coherent reasoning traces, which makes the incorrect information more persuasive and substantially harder to identify. This intrinsic challenge necessitates careful and fine-grained human annotation in order to ensure reliable evaluation.
We select three major categories of reasoning tasks: Math, Science, and Mul t HopQA.
For Math, we construct the dataset using benchmark datasets commonly used for evaluating mathe- matical reasoning capabilities, including MATH500 (Lightman al. 2023 2024b), and AIME 2024 (AI-MO) 2024a).
AMC 2023 (AI-MO)
For Sci Science, adopt GPQA (Rein et al. 2024). PhD--evel science multiple-choice QA dataset with questions authored by domain experts in physics, chemistry, and biology.
For MultiHopQA, HotpotQA QA (Yang et al. 2018).
randomly sample 1000 questions from four multi-hop QA datasets:
(Ho et al. 2020), MuSiQue (Trivedi et al.
2022], and Bamboogle (Press et al. 2022).
For each question, we generate 20 responses using DeepSeek-Rl-Distt -i-ek--R1-issse 11-ween--e--- and PeepSee--Rl-iittee -wee---wee-e-ee 14B via random sampling. The prompting format is follows:
Math:
Please answer the following math question. You should provide your final answer in the format Separate your following steps using An In.
Question: An n
Science:
Please answer the following multiple-choice question. You should provide your final choice in the format \boxed YOUR_CHOICE), Separate your following steps using \nt \n. Question ion: An An
MultiHopQA:
Please answer following question. You should provide your final answer in the format (NSWEW Separate your following steps using \n. Question: An
D.2 REASONING STEP SEGMENTATION STRATEGY
We adopt a two-stage segmentation procedure. First, we split the reasoning trace based on cognitive behavior tokens such </think>, Wait, But, However, Hmm, Alternative which typically mark transitions in reasoning patterns. Then. we apply finer-grained split based on formatting: as specified in the prompt, the LRM is instructed separate reasoning steps using \n An. which we use as a delimiter. This hybrid approach ensures both rule-based and model-aligned step boundaries.
D.3 ANNOTATION PROCESS
Automatic hallucination trace identification. To ensure precision and avoid noise caused by random model errors, reasoning trace is labeled as hallucinated only if its rollout becomes incorrect with failure rate exceeding 90% from a specific reasoning step onward, measured over 16 rollouts. We adopt binary search-ste style trace slicing procedure inspired by OmegaProcess (Luo al. 2024 to efficiently identify hallucination points. This strategy ensures stability and causality in hallucination step detection, avoiding incidental errors due sampling randomness. For the Science domain,
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Figure 5: Interface Display of the Data Annotation Platform.
which mainly consists of multiple-choice questions and may contain correct guesses, we additionally perform multiple random rollouts for traces with correct answers to ensure success rate above 90% before labeling them as truthful.
2. Filtering non-hallucination failures. We use GPT-4o-Mini to exclude samples where the incorrect final answer is due to clearly flawed or illogical reasoning, which does not satisfy our definition of hallucination (i.e., coherent and persuasive chains with underlying logical or factual errors). The filtering prompt is:
Please evaluate if the following reasoning for the given question is logically sound and leads to correct solution.
Only respond with a score between and 1, where: O: completely incorrect or illogical reasoning
perfectly sound and correct reasoning
Question: (question)
Reasoning: (reasoning)
Score (0-1):
3. Human validation. We further perform human annotation to verify borderline cases. Two annotators with least undergraduate-level backgrounds in computer science independently assess whether the reasoning trace is valid. We developed a web-based annotation platform with a timer (Figure 5) to standardize reading time. Based on average reading speeds (200-300 wpm for academic text), and trace lengths (typically 2000-3000 words), we set the following maximum judgment times: (I) MultiHopQA: 3 minutes (2) Math: minutes (3) Science: minutes
Annotators must determine within the allotted time whether reasoning trace contains hallucinations. If they fail to identify an error in time, the trace is labeled as correct. Cases judged correct by humans but verified to be incorrect labeled as hallucinations, ensuring that the resulting dataset captures only traces that genuinely mislead users, which is aligned with the definition of reasoning hallucination.
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Final dataset statistics shown in Table 3 For the Multi-Trace Ranking Setting, directly the collected hallucinated and truthful responses. For the Binary Detection Setting, which focuses on single-response aceuracy, retain hallucinated and one truthful response per question to reflect more realistic ad-hoc usage scenarios.
E GSM-NoOP CONSTRUCTION PROCESS
Following the construction procedure proposed in Mirzadeh et al. (2024). randomly sample 300 examples from the GSM8K dataset. For each question, we use GPT 4o to generate a No-Op phrase using the following prompt:
Given the following math question, generate a seemingly relevant but ultimately inconsequen- tial statement (No-Op) that can be added to the question without affecting its solution. Question: [Question]
Generate No-Op statement that:
Is short and concise
2. Seems relevant the context
3. Does not affect the mathematical reasoning
Is natural and fits grammatically
No-Op statement:
We then use GPT-4o combine the generated No-Op phrase with the original question using the following prompt:
Please combine the following math question and No- No-Op phrase into single, natural-sounding question. The No-Op phrase should be integrated smoothly without changing the mathemati- cal meaning.
Math Question: [Question] No-Op Phrase: (NoOp Phrase]
Combined Question:
The merged questions form our constructed GSM-NoOp dataset.
To evaluate whether the generated reasoning steps misled by the inserted No-Op phrase, prompt GPT-4o with the following instruction:
Please evaluate if the following reasoning step is being misled by the given No-Op phrase. Provide a score between and 1, where:
O means the step is not misled by the No-Op phrase at all means the step is completely misled by the No-Op phrase Values in between indicate partial misleading
Note: Simply mentioning the No-Op phrase does not count being misled. If the step
mentions the No-Op phrase but explicitly rejects or explains why it is irrelevant to solving the problem, this should be scored O.
Reasoning step: [Reasoning Step) No-Op phrase: (NoOp Phrase]
Please provide only number between 0 and 1, with up decimal places, wrapped in \boxed[]. }. For example: \boxed(0.85]
F DETAILS OF UNDERSTANDING THE MECHANISMS BEHIND REASONING HALLUCINATION PATTERNS
In this section, we focus on analyzing the underlying cause of Pattern #1, as Pattern #2 has already been explained through the attention behavior of LRMs in the previous section. Pattern #1 highlights that hallucinated reasoning traces tend to exhibit larger fluctuations in reasoning depth, particularly in the early steps. Inspired by our preliminary analysis in 3.2.1 hypothesize that this may stem
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from the model's built-in verification capability. However, several key questions remain: Q1: What triggers verification behavior in LRMs? Q2: Do excessively high reasoning scores genuinely indicate overthinking? Q3: If Q2 holds, what factors lead to the emergence of such overthinking steps?
To answer these questions, we construct reasoning step triples (c), C2, C3) with different properties drawn from reasoning traces: Stable: The first type consists of triples from truthful traces where adjacent steps differ in Racore by less than 0.1, representing stable reasoning. Rising-1: The second type contains hallucinated triples where Recore Racone (c2) 1 and Rezore (c3) < 4, used to analyze verification triggered by shallow pattern-matching. Rising-2: The third type is similar to Rising-1 I but with Rscore > 4, aimed at understanding overthinking induced by verification. We construct Stable, Rising-1, 11 and Rising-2 triples to probe dynamics (early fluctuation, over-verification. Each set contains 600 step-triples per domain (Math, Science, MultiHopQA), totaling 1,800 triples, with balanced sizes for fair comparison.
Analysis. To investigate Q1, we analyze whether reasoning steps C1 and C2 in the stable and rising (Rising-1 1 + R2sing-2) triples are logically consistent, using GPT-4o as the judge (prompt details in Appendix G). As shown in Figure 4[a), the stable triples exhibit significantly higher consistency between and 22 than rising triples, indicating that LRMs are more likely to trigger verification when early steps are internally inconsistent.
To examine Q2, we evaluate the correctness of C2 and in Rising-2 triples. Using ground-truth answers and GPT-4o-based annotation (prompt details in Appendix G), we assess whether these steps are logically aligned with the ground-truth answers. As shown in Figure 4(b), 0o in Rising-2 triples is substantially more accurate than cg. confirming that verification in this case often modifies correct reasoning into incorrect steps. These findings support the hypothesis that excessively high Rscer values in hallucinated reasoning traces are symptomatic of overthinking steps that exhibit apparent reasoning depth but in fact reflect spurious detrimental reasoning.
To address Q3, we analyze the relationship between perplexity and Raewe- Specifically, we randomly sample 200 reasoning steps from ReTruthQA and compute their perplexities as follows:
PPL(ck)= = exp
(Teal
Σ
logp (1itta (mmmm)
(10)
|ckl
m++1
Eok
PPL(C)- = PPL()), (PL((e)))
(11)
where p(th ) denotes the model's predicted probability for token *t +1 given the prefix th Sm
within the reasoning trace.
As shown in Figure 4cc), perplexity and Rosure are strongly negatively correlated steps with higher reasoning depth tend to have lower perplexity, which is intuitive since deep reasoning often yields more predictable outputs. However, when comparing the final step C3 across stable and Rising-2 triples, we find interesting phenomenon in Fiiuue d() despite having higher Racore, C3 Rising-2 triples has higher perplexity than in stable triples. This suggests that overthinking steps induced by an incorrect verification result in an uncertain or internally unstable generation.
We hypothesize that such overthinking may reflect spurious verification- behavior where the model performs superficial or misguided validation in pursuit of higher reward during RL fine-tuning. This behavior can persist through distillation into smaller models, propagating reasoning hallucinations. Based on this analysis, we identify a third hallucination pattern: Pattern #3: Overthinking reasoning steps exhibit a positive correlation between Rscore and perplexity (PPL).
Experimental Validation. Building on this observation, to further validate whether excessively high reasoning scores reflect overthinking steps, we sampled reasoning steps with scores 2 2.5 (excluding shallow nattern-macching steps) from various data types on R1-7B and used GPT-4o to annotate the correctness of each step (using the same prompt as in Appendix G).. We then used the reasoning score to predict step correctness, searching for the optimal Fl threshold the range 2.5-5 (step size 0.1). Results show that across different datasets, the optimal threshold for Fl is always > 4, which matches the hyperparameter 7 set in Appendix H This demonstrates a strong correspondence between excessively high reasoning scores and overthinking steps. Interestingly, this phenomenon aligns with findings in cognitive neuroscience: both insufficient and excessive reasoning can lead to poor decisions (Langley 1995 Cools & D'Esposito
2011
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Table 4: Optimal threshold for Fl across datasets.
MATH
MultiHopQA
Science
Best 7
F1
Best r
F1
Best 7
F1
Value
4.0
0.7617
4.4
0.7495
4.5
0.7821
CV Score Comparison (MATH)
CV Score Comparison (Science)
CV Score Comparison (MultifloQA)
0.25
0.259
Overall
Overal Mean
0.20
9.93
0.20
Mran CV Seore
0.150
0.15
0.15
Mean CV
02-
0.30
0.1
Truth
Iullucinatio
Truth
Truth
Halltcination
Attention Comparison (MATH)
Attention Scores Comparison (Science)
Attention Scores Comparison (MultitopQA)
0.5-
Overall Mas
0.4
Uverall Mean
Overall Mean
Mean Atteatora Scure
0.399
Mean Aftention Score
0.321
0.3
11288
Mean Mean Attenton
0.3-
V.307
0.2
9.2-
Truh
Hollasinatinn
Truth
Hallacinsiam
Truhh
Hallucinuiin
Figure 6: Evaluation of Pattern #1 and Pattern #2 on ReTruthQA, Asterisks indicate statistical significance based I-test: * for p-value 0.05, and *** for p-value 0.001.
G PROMPT FOR HALLUCINATION PATTERNS ANALYSIS
Prompt for step consistency analysis of Q1:
Please evaluate whether the following reasoning step introduces a new solution approach compared to the preceding steps. Respond with score of ( or 1, where:
0: The step follows the same solution approach as the previous steps.
1: The step explores new solution approach direction. Reasoning step: (step content) Previous steps: (step content)
Score (0/1):
Prompt for step correctness analysis of Q2:
Please evaluate whether the following reasoning step aligns with the final answer. Respond with a score of 0 or 1, where:
O: The step is inconsistent with the final answer.
The step consistent with the final answer. Reasoning step: (step)
Final answer: (answer)
Score (0/1):
H MORE RESULTS OF REASONING HALLUCINATION PATTERN ANALYSIS
The hyperparameter settings involved in Section 3.2 follows. The constant r, which controls the size of the early-step window, is empirically set to r = 2. The constant 17, which defines the portion of late reasoning steps, is ') 0.75. The constant K, used in computing attention
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earlier steps, is set to K 5. The threshold for identifying potentially overthinking steps is set to
T = 4. These hyperparameters are derived from case analysis and are applied consistently throughout the subsequent reasoning hallucination detection and mitigation experiments.
The validity of Pattern #1 and Pattern #2 is verified across all domains of ReTruthQA, with exper- imental results shown in Figure [6] where across all three domains, hallucinated reasoning traces consistently exhibit significantly higher CV scores and Attention scores than truthful traces.
I EVALUATION AND BASELINE DETAILS OF REASONING HALLUCINATION DETECTION
Based on ReTruthQA, we design two evaluation settings for RHD model: (1) Binary Detection Setting: This setting assesses the model's ability detect hallucinations in individual question- reasoning pairs (Q.C), measuring detection performance using the Area Under the ROC Curve (AUC) and Pearson Correlation Coefficient (PCC); (2) Multi-Trae Ranking Setting: This setting evaluates the model's ' ability to identify the truthful answer among multiple reasoning traces for the same question (Q, {C1, C2. ..... Cs}). We follow the evaluation setup of TruthfulQA-MC (Lin et al., 2021], and report the following metrics: MCI: The percentage of instances where the hallucination score of the most hallucinated reasoning trace exceeds that of all truthful traces, MC2: The normalized total hallucination score assigned to the hallucinated reasoning traces; MC3: The percentage of hallucinated reasoning traces that receive a higher hallucination score than all truthful traces. These metrics collectively measure the ranking quality of hallucination detection in multi-sample generation settings.
For baselines, we consider the following categories: (1) Ensemble-based self-evaluation meth- ods, where hallucination scores are obtained through repeated generation, self verification, or peer voting among LLMs. This category includes ChainPoll (Friel & Sanyal, 2023), LMvLM (Co-
hen al. 2023), and SelfCheckGPT (Manakul et al., 2023). (2) Uncertainty-base
methods, which estimate hallucination likelihood based model uncertainty, including P(Truc) (Kada)
vath et al. 2022), LN-Entropy (Ren et al., 2022), and Perplexity (PPL) (Malinin & Gales 2020).
(3) Self-awareness- lucinations, such as UQAC (Li et al. 2025b) and EigenScore (Chen et al. 2024).
methods, which rely on internal model representations
detect hal-
(4) LLM-
as-Critic models, including GPT-4c (Achiam al., 2023) and Qwen2. 5-3225322 32B Yang al.)
2024). which act as external evaluators of reasoning traces, (5) Process reward models, such Qwen2 S-Math-7B-PRRe et al. 2025), trained with step-level supervision for reasoning evaluation. (6) Length-based scoring. motivated by recent findings that longer reasoning traces are more prone to hallucinations (Zeng et al. 2025), we include LengthhScoree, which directly uses the length of the reasoning trace as its hallucination score.
(Zheng et al.
2024a) and Qwen2. 5 MathhPPM-- 7B (Zhang
J IMPLEMENTATION DETAILS FOR REASONING HALLUCINATION DETECTION
We conduct all experiments on machines equipped with NVIDIA A6000 GPUs and 52-core Intel(R) Xeon(R) Gold 6230R CPUs running at 2.10GHz. We utilize the Huggingface Trans fo ormer and TRL libraries to implement and run our experiments. During response generation, we use random sampling with a temperature of 0.7 and a maximum decoding length of 15,000 tokens for Math tasks and 10,000 tokens for all other tasks. For Reasoning Hallucination Detection (RHD), we perform two-fold validation to select optimal hyperparameters, while baselines are tuned within the ranges specified in their original works. To ensure stability, all randomized experiments are repeated three times and the average results are reported.
We conduct grid search to identify the optimal reasoning score weights Specifically, we search 02. 03, and 044 over the interval [o, 1] with a step size 0. and a₁ over 1,,, 1] with the same step size. Two-fold cross-validation is used to select the final hyperparameters. For R1-7B, the best weights in the Math domain are Q1 = 0, Qz = 0.4, 03 = 0, and a4 = 0.3 for the Multi-Tran Ranking setting, and 01 0, a2 0.9, ag 0.8, and a4 0.4 for the Binary Detection setting. In the Science domain, the best weights are a = 0.1, 02 = 1.0, ag = 0, and a4 = for Multi-Trace Ranking, and
on -0.4, 02 0.9, 03 0.5, and 04 0.1 for Binary Detection. In the Mu l t HopQA domain,
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Table 5: Ablation study of the RHD model on three different domains of ReTruthQA, Each row removes one component of the hallucination score.
MATH
Science
MultiHopQA
Model
Variant
MC1
MC2
MC3
MC1
MC2
MC3
MC1
MC2
MC3
RHD
0.6591
0.4765
0.5699
0.6207
0.5448
0.6009
0.7660
0.6255
0.7103
RHD (w/ Avg(Rscore)
0.6591
0.4765
0.5699
0.6128
0.5307
0.5934
0.7383
0.6032
0,7082
R1-7B
RHD (w/o CV Score)
0.6364
0.4663
0.5330
0.4483
0.3862
0.4977
0.7447
0.6043
0.6996
RHD (w/o Attention Score)
0.6591
0.4765
0.5699
0.6207
0.5448
0.6009
0.6383
0.5372
0.6123
RHD (w/o PCC Score)
0.5909
0,3830
0.5210
0.6207
0,5448
0.6009
0.6809
0,5553
0.6323
RHD
0.3692
0.3005
0,4644
0.6667
0.4714
0.5671
0.5785
0.4421
0.5154
RID (w/o (
0.3538
0.2867
0.4847
0.7241
0.4609
0.5531
0.5589
0.4284
0.5290
RI-14B
RHD (w/o Score)
0.3692
0,2882
0.4725
0.6470
0.4484
0.5332
0,5455
0.4273
0,5403
RHD (w/o Attention Score)
0.3231
0,2692
0.4503
0.6724
0.4511
0,5190
0.5702
0,4322
0,5180
RHD (w/ PCC Scorc)
0.3692
0.2882
0.4725
0.6724
0.4601
0.5683
0.5785
0.4421 0.5154
the best weights are 01 = 0.4, 02 = 0.1, 03 = 0.6, and 04 = 0.4 for Multi-Trace Ranking, and 0n 02 03 0.3, and 04 0 for Binary Detection.
For R1-14B, the best weights in the Mat h domain are (1 = 0.3, 02 = 0.7, 03 = 0.1, and 04 = 0.1
for Multi-Trace Ranking, and on 0, 02 0.3, 03 1.0, and 04 0.2 for Binary Detection. In the Science domain, we obtain 0 = 0, Q2 = 0.5, 03 = 0.5, and a4 = 0.1 for Multi- Trati-Trace Ranking, and α₁ -0.2 02 0.2, 0g 0.9, and 04 0.1 for Binary Detection. In the Mult MoltiHopQA
domain, the optimal weights are 01 0.7, 02 = 0.9, = 0.1, and 04 = 0.0 for Multi-Trace Ranking, and a₁ 1.0, 02 0, a3 0.1, and 04 0.1 for Binary Detection.
Candidate reasoning score layers J are selected from {14, 16, 18, 20, 22, 24, 26} for R1-7B and from {32, 36, 40, 42, 44, 46) for R1-14B, while attention score layers are fixed across models as (1,3,5, 5, 7,9, 11, 13}. The models used in our experiments, DeepSeek-R1-D) and /Aaegc/nnfeeec///eeesssssa///ppp
-Qwen-7
are publicly available at https
R1 R1- http:://huggiggfccccco//eeeee ai/eeepSeeeeeeeeeeeeeeeee R1 iistiill Qwen 14B respectively.
7B
and
K RHD ON LATENT COT MODELS
To validate whether our proposed hallucination detection framework can be effectively extended to latent Chain-of- Thouuhh (Co'T) models, we conducted additional experiments on Huginn-0125, the most mature and open-sourced latent reasoning model currently available (Geiping et al. 2025).
Application to Huginn- The Huginn-0125 model is composed of a prelude block, core recurrent block (where latent reasoning primarily occurs), and a coda block. We treated each recurrent block as reasoning step and applied the Reasoning Score measure reasoning depth, focusing on Pattern #1 (CV score). Due to the model's 's architectural design, Pattern #2 (AttnScore) and Pattern #3 (PCC) could not be applied. We sampled 100 examples from GSM8K the dataset. Since the model itself does not possess self-reflection capability, hallucination labels were assigned based on ground-trus correctness: correct answers were treated non-hallucinated and incorrect answers as hallucinated. Results in Table ( show that our method achieved higher detection accuracy of latent reasoning hallucination compared the perplexity baseline (computed only on output tokens), demonstrating RHD's s applicability to latent CoT architectures.
Comparison with Text-only Detection Methods. We further examined whether text-only detection methods can serve as effective alternatives in the latent CoT setting. Specifically, we evaluated Process Reward Model Swwen2.5-PMM-775 and ChainPoll. Experimental results in Table 6 indicate that these methods, when applied directly to the final generated text without analyzing the latent reasoning process, underperform compared to our latent reasoning based approach.
To better understand this gap, we conducted a case study on Huginn-0125 outputs and identified several sources of failure for text-only methods:
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Format confusion and ambiguous expression. Consider the following GSM8K problem: Anthony and his friend Leonel read about the importance of keeping pets at home and decided to start adopting cats and dogs from the local rescue center. Anthony has 12 cats and dogs, 2/3 of which are cats. Leonel has half times as many cats as Anthony and seven dogs than Anthony. How many animals in total do the two have?
Huginn-0125 produced the following intermediate reasoning:
"0.67x10.67 cats. We'll round this to 11 cats for simplicity. Anthony has 12- 11=<12-11=1>/ dog. Leonel has half as many cats as Anthony, so he has 1=5.5555 cats. We'll round this to cats for simplicity."
Although the final answer was numerically correct, the text contained artifacts such as x<<12-11=>>> and "0_ 67>>1 0. 67 cats." These inconsistent notations suggest that certain reasoning was carried out in the latent space before being partially surfaced, leading to ambiguous expressions that mislead text-only detectors.
Non-linear and highly jumping narration. Consider the following arithmetic problem:
John hits 70% of his free throws. For every foul he gets 2 shots. He gets fouled times game. How many free throws does he get if he plays in 80% of the 20 games the team plays?
Huginn-0125 generated:
"John gets 5 x = 10 free throws per game. 80% of 20 = 16 games. Then says: 10 fouls per game 3 10 Thus, John gets 16 x 3 48 free throws."
The reasoning begins correctly but suddenly introduces nonsensical statements such "10 fouls per game = 3 x 10," which are mathematically incoherent. Such non-linear jumps likely originate in the latent CoT process and cannot be effectively diagnosed from surface text alone.
Incomplete sentences. In several cases, Huginn-0125 generated outputs that began with truncated phrases such "ends each delivered..." without subject introductory clause. These malformed sentences indicate leakage of incomplete latent reasoning into surface text, further reducing the reliability of text-only detection models.
These observations highlight that text-only methods are limited in detecting hallucinations when latent reasoning artifacts leak into surface text. By contrast, our approach explicitly analyzes the latent reasoning process, enabling more reliable detection. Importantly, combining the two perspectives proves complementary: empirical results show that integrating our method with ChainPoll achieves the best overall performance.
Table 6: Performance of different hallucination detection methods on Huginn-0125. Our RHD approach, when combined with ChainPoll, achieves the best results, indicating complementary benefits.
Method
AUC
PCC
LNE
0.6343
0.2312
Qwen2.5-PRM-77
0.6460
0.2640
ChainPoll
0.6732
0.3074
RHD
0.6914
0.3210
RHDD+ChainPoll
0.7225
0.3564
L ADDITIONAL DETECTION RESULTS ON QWEN3-88
To examine the generality of our detector beyond the RI-7B/14B backbones, we further evaluate RHD Qwen3- 83 over the RETRUTIQQ Math and Science domains. As shown in Figure 7 our method forms the outer envelope across all five metrics (AUC, PCC, MC1/2/3), indicating consistent improvements over diverse baselines. These results mirror the trends reported in the main paper (Ri-7B/14B), suggesting that (i) modeling early-stage depth fluctuations, (ii) penalizing misguided backtracking, and (iii) recognizing overthinking (positive RScore-PPL. correlation) remain effective
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[8366
[02-.]]
Emglo
Overl: PRMPIIK
Quee?
Owarl. PRM
Quee3 PRM
CPT4-
G7T4a
[U..LL3]
[KS-10]]
MC2 R145
NCC
[8.445
(a) RETRUTHQA (Math).
(b) RETRUTHQA (Science).
Figure 7: Performance comparison on Qwen3-8B. Radar plots summarize five metries: AUC, PCC, and MC1/2/3. Our method (red, dashed outline) consistently dominates the baselines on both domains.
cues different backbone and domains. Overall, RHD maintains strong binary detection ability (AUC/PCC) while also excelling in multi-trace ranking (MC1/2/3), reinforcing its robustness across architectures and tasks.
M ABLATION STUDY OF RHD
In this section, we analyze the contribution of each module within the RHD model reasoning hallucination detection. As shown in Table removing any single component leads to significant performance drop on most datasets in the Reasoning Hallucination Detection task. This validates the effectiveness of adopting a multivariate regression formulation, where all components jointly serve as covariates. Although some coefficients may appear less influential they demonstrate notable impact in others. This observation suggests that different domains exhibit distinct hallucination pattern preferences, further supporting the validity of the empirically discovered patterns, which can be effectively leveraged for reasoning hallucination detection.
certain domains,
Beyond component-level ablations, we also evaluate alternative step-level signals by replacing the Reasoning Score with entropy and variance, resulting in RHD(Entropy) and RHD Vaariance. As shown in Table both variants perform substantially worse than the original RHD across MATH, SCI- ENCE, and MULTIHOPQA. The main reason is that entropy and variance only characterize properties of single distributions, while our approach explicitly models distances between distributions across layers, which crucial for capturing mechanistic interpretability insights. Furthermore, leveraging the logit lens mitigates the superposition problem in hidden states, enabling more accurate reasoning hallucination detection.
Finally, we analyze the robustness of the shallow-step threshold used in the Attention Score com- ponent. In the main method, we adopt the 25% quantile of early reasoning steps as the cutoff for identifying shallow steps, which follows common statistical practice for lower-bound filtering and is consistent with our CV-based fluctuation analysis Appendix [F] To further examine its stability, we vary the threshold over [10%, 20%, 25%. 30%, 40%) and evaluate its impact on MATH-MC3 and MultiHopQA-Mor under the same setting as Figure g Table shows the results.
We observe that performance remains stable across a wide range of threshold values, with the most consistent and balanced results occurring around the 20-30% range. The 25% setting selected in the main paper lies near the empirical optimum and yields strong performance both benchmarks. These results further confirm that RHD is robust to the choice threshold and does not rely on fine-grained hyperparameter tuning.
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Table Impact of selecting candidate layers from different depth layers of LRMs.
Math
Science
MultiHopQA
Layers
MC1
MC2
MC3
MC1
MC2
MC3
MC1
MC2
MC3
High
0.6591
0.4765
0,5699
0.6207
0.5448
0.6009
0.7234
0.5957
0.6799
Middle
0.6591
0.4765
0.5699
0.6207
0.5448
0.6009
0.7021
0.5862
0.6678
Low
0.6591
0.4765
0.5699
0.6207
0.5448
0.6009
0.7660
0.6255
0.7103
Table 8: Sensitivity of the shallow-step threshold in the Attention Score.
Threshold MATH-MC3
MultiHopQAAMCC3
10%
0.5612
0.7035
20%
0.5683
0.7101
25%
0.5699
0,7103
30%
0.5707
0,7089
40%
0.5521
0.6974
N SENSITIVITY ANALYSIS OF RHD
In this section, we conduct sensitivity analysis experiments to investigate the impact of design choices in RHD. Inspired by the underlying reasoning mechanism, we fix the reasoning score to extracted from the later layers of LRMs. Our primary focus is on selecting the appropriate layers for computing the attention score. Specifically, we evaluate three different layer groups: shallow layers (1, 3, 5, 7, 11, 13), middle layers (8, 10. 12, 14, 16, 1 88, and deep layers (14, 16. 18, 20, 22, 24, 26) on R1-7B. The experimental results are shown in Table 7 We observe that, across the Math and Science domains, the choice of attention layers has limited influence final performance. In contrast, for the Multi Ho domain, shallow layers yield stronger results, aligning with the mechanistic interpretation that earlier layers are primarily responsible for information transmission. Based on these findings, we select the shallow layers as candidate layers for computing the attention score.
We further perform sensitivity analysis influential feature weights in RHD across domains. We vary the feature weights in (0.1, 0.3, 0.5, 0.7, 0.9), and present the results in Figure g We observe that most features exhibit initial increase in performance followed by either decline stabilization. The limited variance across settings indicates that the model is not overly sensitive to individual hyperparameter values, demonstrating the robustness and stability of the RHD framework.
For the threshold т, its selection is based on the analysis described in Appendix F we performed sensitivity experiments values [4.0, 4.4, 4.5), and found that the optimal result is achieved at 4.0. Setting the threshold too high improves precision but reduces recall. Encouraging an appropriate depth of reasoning helps the model generalize better, which demonstrates the effectiveness of our chosen hyperparameters.
O IMPLEMENTATION DETAILS FOR REASONING HALLUCINATION MITIGATION
We fine-tune the models for reasoning hallucination mitigation using a RL framework with the following hyperparameters: batch size of 8, learning rate of 1.0 x 10-6, and 1 training epoch. We enable gradient checkpointing to reduce memory usage. The model is configured with maximum prompt length of 512 and maximum completion length of 7680. For parameter- efficient tuning, we adopt LoRA with rank r = 16 and a = 16, applied to all linear layers During each training step, sample 16 genera-
(lora_tare hargge_moduulesall1111111 tions per query.
The reward function is weighted sum of three components: (1) accuracy reward that combines rule-based parser (Hugging Face 2025) and LLM--s-a-Judge (Lightman et al., (203) to determine correctness, addressing the issue where the final answer is correct but fails rul-bbased extraction
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Table 9: Ablation results on RI-7B when replacing reasoning score with entropy or variance.
Math
Science
MuhillopQA
Method
AJC
PCC
MC2
AUC
MCI
MC3
RHD
0.7978
0.4852
0.4765
0.3699
0.2062
0.5448
0.7361
0.7660
0.7105
(HD(/uu
0.5302
0.2380
0.6700
0.5637
Variance)
0.6459
0.5257
0.1031
0.4689
Math MC3
MultiHopQA MC3
0.53
0.70
0.50
MC3
0.65
Attention Score
0.45
CV Score
CV Score
Rzoore
Avg Rocore
0.40
PCC Score
PCC Score
0.2
0.4
0.6
0.8
Weight
Weight
ReTruuhQA (Math)
ReTruthQA (MultiHopQA)
Figure 8: We conduct sensitivity analysis of each module in RHD, using R1-7B on the Math and MultiHopQA subsets of Re Tr. We vary the weights assigned to different components and observe the resulting performance the MC3 metric.
(reward for correct, 0 for incorrect); (2) format reward that ensures adherence to the required reasoning format <thi nhhink>>n..
whi tkk <e>>nnaawwwrr \n.. An</ /naswer>> (reward 1 the format correct, otherwise);; and (3) a tag count reward that softly encourages the inclusion of each of the four required tags (sthink>, </think>, <answer>, </ //answer>) by assigning 0.25 for each tag present. The reward weights are set to 1.0, 0.1, and 0.1 for the accuracy, format, and tag count rewards, respectively.
For evaluation, we use the same accuracy-based metric as in training, and report re- sults by averaging over four sampled generations per input. The fine-tuned model, DeepSeek-R1-Disttae -i-iee--------iiii-eee------- 5B, is publicly available at lattps://huggingfet co /ttpdeppeeckaa/pppppeeeeeee -i-
Sensitivity Analysis
Sensitivity Analysis (DeepSoek-Rl-L..
0.8
MATH500
A1MB,2024)
0.7
MATH500
Score
GPQA(main)
0.6
AIME(2044
0.3
GPQAiestenddi
GPQA,dimond)
0.5
GPQA(mein)
0.2
GPQA(extendal))
0.05
0.10
0.20
0.30
0.05
0.10
0.20
0.30
Figure 9: We conduct sensitivity analysis on the weight of the reasoning score reward in GRPO-R, evaluating its impact on the accuracy metric. Experiments are carried out on both Qwen2.5-1.5B Instruct and DeepSeck-R1-1.5B by varying the weight parameter a.
P SENSITIVITY ANALYSIS OF REASONING SCORE WEIGHT IN GRPO-R
To investigate the sensitivity of the reasoning reward weight in the GRPO-R objective, conduct experiments on both DeepSeek-R1-2 5B and Qwen2. 5-1. -n-stnntuue We vary in the range [0.05, 0.1. 0.2, 0.3] and evaluate the models' performance accordingly.
Experimental results in Figure indicate that both models achieve the best average performance when = 0.1. As increases beyond this value, we observe gradual decline in performance.
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Table 10: Sensitivity analysis of threshold 7 across benchmarks.
Model
MATH500
AIME(2024)
GPQA(diamond) GPQA(main)
GPQA(extended)
GRPO-R - 4.0
0.788
0.367
0.414
0.371
0.357
GRPO-R 4.4
0.788
0.367
0.409
0.371
0.352
GRPO-R 4.5
0.784
0.333
0.389
0.355
0.348
Table 11: Accuracy of distilled models across benchmarks using different sampling strategies.
Distillation is performed on D2wen2.5-1.5B-Instrue using reasoning traces from R1-14B.
Method
MATH500
AIME (2024)
GPQA (diamond)
GPQA (main)
GPQA (extended)
Swen2.5-1.5B-mmm
0.466
0.100
0.202
0.197
0.211
Random 20%
0.504
0.100
0.247
0.230
0.242
RHD 20%
0,520
0.100
0.263
0.210
0.249
Random 50%
0.488
0.033
0.187
0.248
0.266
RHD 50%
0,516
0.200
0.247
0,250
0.242
100%
0.488
0.100
0.217
0.210
0.214
These results suggest that incorporating the reasoning score reward can effectively mitigate reasoning hallucinations without compromising accuracy, as long as remains a secondary signal. However, overemphasizing the reasoning model's ss ability to optimize for correctness, indicating that the reasoning signal should not dominate the outcome-based reward objective.
(i.e., assigning it large weight) can lead degradation in the
Q RHD-GUIDED REASONING DISTILLATION
Distilling long-chain-of of-thhughttth data from large reasoning models fine-tune smaller LLMs has be- come a widely adopted strategy for improving reasoning capabilities (DeepSeek-AI) (2025). However, directly fine-tuming small LLMs on raw LRM-generated data risks transferring undesirable reasoning behaviors such as shallow pattern matching or overthinking, potentially introducing reasoning hallu- cinations into the smaller models. To address this issue, we propose using the RHD score rank distillation data and select more truthful samples for training.
The distillation setup uses a learning rate of 5.0 x 10-5, 5, batch size of 8, and LoRA applied to all linear layers with parameters 1ora_r= 16 and lora__ aorr_alphaaaa = 16. We use the training data from the hallucination mitigation experiment where R1- 21-144 produces correct answers, along with their corresponding reasoning traces and final answers. We then score each reasoning trace using the RHD metric and sort the data in descending order. The top 20% and 50% of ranked samples are distilled into smaller model, R1-1.55 5B, and compared against randomly sampled subsets of 20%, 50%, and 100% of the same data.
Results, as shown in Table demonstrate that RHD-guided distillation consistently yields better performance across most evaluation benchmarks. In contrast, distillation using 100% of the raw data results degraded performance, likely due noise introduced by hallucinated or low-quality samples. These findings validate the effectiveness of RHD in selecting high-quality data and mitigating reasoning hallucinations in downstream small LLMs during the distillation process.
R EXTENSION GRPO-R TO OTHER GRPO VARIANTS
Our hallucination mitigation framework seamlessly integrated into diverse GRPO variants. By incorporating mechamistically-insiire step-level reasoning score via potential- based shaping. the framework is orthogonal to existing GRPO improvements and can be applied on top of them without modification.
designed as general mechanism that can be
To further validate this claim, we conducted experiments on Dr. GRPO (Liu et al. 2025 sentative variant that modifies the group relative optimization scheme. As shown Table [2] Dr. GRPO achieves stronger in-domain gains than vanilla GRPO but suffers from reduced robustness on out-of-domain evaluation. Importantly, Dr. GRPO-R (our framework applied Dr. GRPO) consis-
repre-
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tently improves over Dr. GRPO across both in-domain and out-of-domain settings. These results demonstrate that our framework is compatible with and complementary to existing GRPO variants, highlighting its effectiiveness
ceneral-purpont strategy for mitigating reasoning hallucinations.
Table 12: Performance of Dr. GRPO and Dr. GRPO-R across benchmarks.
MATH500
AIME(2024)
GPQA(diamond) GPQA(main) GPQA(extended)
Base
0.772
0.333
0.354
0.333
0.339
+Dr. GRPO
0.778
0.367
0.364
0.333
0.342
+Dr. GRPO-R
0.792
0.367
0.394
0.364
0.357
In addition to Dr. GRPO, we further validate our hallucination mitigation framework against widely used step-leve level reward baseline. Specifically, adopt a Process Reward Model (PRM) following Shao et al. (2024), where step-level scores are provided by Qwen2.5-PRMM-75 We replace the reasoning score in GRPO-R with PRM scores, denoted GRPO+PRM, for comparison.
Experimental results show that on in-domain MATH datasets, GRPO+PRM achieves results compa- rable to GRPO-R. However, nut-of-distribution SCIENCE datasets such GPQA, GRPO+PRM performs noticeably worse than GRPO-R, and in some cases even worse than the base model. This indicates that compared to 0wen2.5-PRM-77. using the reasoning score a process reward only enhances reasoning within the training domain but also generalizes better across domains, underscoring the robustness of GRPO-R. Moreover, incorporating PRM leads to significantly in- creased training cost. Since PRM itself is a large model, GRPO+PRM requires more training time compared GRPO-R, further highlighting the efficiency advantage of our approach. Finally, our framework is compatible with PRM. When combining PRM scores with reasoning scores as the final process reward (denoted as GRPO-R+PRM), the performance drop on out-of-distribution GPQA benchmarks is effectively alleviated, demonstrating the complementary benefits and generalizability of GRPO-R.
Table 13: Comparison between GRPO-R and step-level reward baselines.
Method
MATH500
AIME(2024)
GPQA(diamond)
GPQA(main)
GPOA(extended)
Base
0.772
0.333
0.354
0.333
0.339
+GRPO-R
0.788
0.367
0.414
0.371
0.357
+GRPO+PRM
0.780
0.367
0.343
0.330
0.333
-GRPO-R+PER
0.792
0.400
0.409
0.373
0.355
NOTATION SUMMARY
To improve clarity and reproducibility, we provide a comprehensive summary of the key notations used throughout the paper. These notations cover the main components of the Reasoning Score, the RHD detection metric, and the GRPO-R reinforcement learning formulation. The table below consolidates all symbols, their meanings, and where they introduced in the manuscript.
This notation summary aims to make the paper easier to follow and ensures consistency across the detection and mitigation components of our framework.
T COMPLEXITY AND EFFICIENCY ANALYSIS OF RHD
This section presents the theoretical complexity and empirical runtime of the proposed Reasoning Hallucination Detection (RHD) method.
Theoretical Complexity. For reasoning trace C = [C1 .c...... cxl containing M tokens, the Rea- soning Score is computed as the mean Saaennon Divergence (JSD) between the vocabulary distributions of small set of later layers ([Jl 4-6) and that of the final layer. Fach ISD operation
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Table 14: Summary of the major notations used in the paper.
Notation
Description
Racore
Step-level Reasoning Score measuring reasoning depth via later-layer logit divergence.
CV(C)
Coefficient of Variation of early-step reasoning scores, quantifying reasoning fluctuation.
AttnScore(C)
Attention based metric capturing incorrect backtracking and overthink ing behaviors.
PPL(C)
Step-level perplexity sequence used for detecting spurious verification. Pearson correlation between reasoning depth and perplexity (Pattern #3 indicator).
PCC PPL(C))
02, 04
Regression coefficients combining hallucination indicators into the final RHD score.
Riial
Terminal reward indicating correctness of the final reasoning answer in GRPO-R.
(st)
Potential function based the clipped reasoning score, used for potential-based reward shaping.
Discount factor controlling reward-shaping dynamics; set to 1 for stabil- ity and invariance.
r
Threshold separating normal vs. overthinking reasoning steps when computing clipped potentials.
Tt, Ft
Original and shaped step-level rewards in the GRPO-R formulation. Value function after reward shaping, ensuring policy-invariance of the optimal solution.
V'(s:)
scales linearly with the vocabulary size V, i.c., O(V), consisting of simple element-wise logarithm and multiplication. Therefore, the overall complexity
O(J) x M x V).
For comparison, the computational cost of single Transformer forward pass
O x M d²),
where L and denote the number of layers and hidden dimension. Since the dominant cost comes from quadratic attention and feedforward operations, the linear JSD computation introduces only negligible constant factor relative to model inference.
Moreover, the design of RHD follows mechanistic interpretability findings that early layers primarily transmit shallow lexical signals. Hence, we compute divergences only over the final 4-6 layers, reducing overall cost by roughly order of magnitude while preserving its strong correlation with reasoning depth.
Empirical Runtime. We further evaluate the practical overhead of RHD by measuring its detection time per query on R1-7B and R1-14B models. All measurements are conducted using HuggingFace Transformers with batch size on the ReTruthQQ (MATH) benchmark.
Summary. RHD achieves competitive detection performance while maintaining a sub-second runtime of approximately 0.3 seconds per query. Compared with ensemble-based reward-model- based detectors, RHD is 10-20x faster due to its lightweight design: it operates directly on cached hidden states and performs JSD computation only on few later layers. This efficiency makes RHD suitable for large-scale or real-time reasoning hallucination analysis.
U FUTURE WORK
Our current framework relies on internal model activations and is thus restricted to open-source LRMs with accessible activations. Extending this line of research to black-box models remains
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Table 15: methods.
Average detection time per query (seconds) for representative hallucination detection
Category
Method
R1-7B
R1-14B
Ensemble
ChainPoll
7.02
7.64
Ensemble
LM-v-LM
12.37
11,45
Uncertainty
P(True)
0.10
0.11
Uncertainty
LN-Entropy
0.05
0.09
Self-aware
EigenScore
0.11
0.13
Self-aware
UQAC
0.45
0.76
PRM-based
Qwen2.5-PRM-7B
10.89
10.35
LCM
Qwen2.5-32B
15.83
16.23
Mechanistic
RHD (ours)
0.30
0.33
important open challenge. Nevertheless, the discovered patterns and metrics may inspire proxy-based extensions that approximate internal reasoning signals without direct access.
Furthermore, our experiments are conducted on moderate-scale models and datasets due to compu- tational constraints. natural future direction is to scale the proposed framework larger model families and broader domains, which may provide deeper insights into the universality and robustness of reasoning hallucination mitigation.
35


Reviews:
[{"review_id": "59VyOqWit5", "reviewer": "Reviewer_umeb", "summary": "This paper studies reasoning hallucinations in large reasoning models, where models produce coherent but incorrect reasoning. It introduces a Reasoning Score based on internal layer divergences to measure reasoning depth and distinguish shallow pattern matching from real reasoning. Using this metric, the authors identify three hallucination patterns and propose the Reasoning Hallucination Detection framework and GRPO-R reinforcement learning method, which together improve reasoning accuracy and reduce hallucinations across multiple benchmarks.", "questions": "See weaknesses", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The work analyzes internal layer dynamics. It also bridges interpretability and reasoning reliability.\n2. The work combines analytical diagnosis (RHD) with actionable intervention (GRPO-R) into a full pipeline.", "weaknesses": "1. The work lacks a validation/ablation study of the later-layer divergence correlating with reasoning depth.\n2. Layer-wise JSD across all tokens is computation-intensive, which may be limited when scaling to larger models.\n3. The work only focuses on Qwen series models. There is no study on other model series, such as the Llama.", "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": "TqZDWAnvBF", "reviewer": "Reviewer_zVVx", "summary": "This paper presents Reasoning Score (RS) to tackle the problem of reasoning hallucinations in Large Reasoning Models (LRMs). RS can quantify reasoning depth by analyzing divergence in late-layer logits, then distinguish shallow pattern-matching from deeper reasoning. By applying RS to the ReTruthQA dataset, two hallucination patterns are identified, including early fluctuations in reasoning depth and incorrect backtracking to flawed prior steps. With these findings, the authors propose Reasoning Hallucination Detection (RHD) framework to achieve state-of-the-art performance, and a GRPO-R approach that can integrate step-level reasoning rewards for better generalization and reduced hallucination rates.", "questions": "1. How does RHD perform when applied to reasoning models other than R1?\n\n2. Many hallucinations can be made by the lack of factuality of language models, and there has been some previous work investigating this topic. Technically speaking, these approaches also adopt (supervised) fine-tuning plus GRPO-like algorithms to solve the problem. Compared with them, what are the advantages possessed by the proposed method?\n\n3. How does the hyperparameter, $\\gamma$, influence the performance of the proposed method?\n\n4. How do models refined by RHD perform in reasoning on OOD domains or datasets?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1. The problem tackled in this paper, i.e., reasoning hallucinations, is crucial in modern language models and corresponding downstream tasks.\n\n2. The patterns identified in this paper are important to address the hallucination issues.\n\n3. The presented results demonstrate the effectiveness of the proposed approach.", "weaknesses": "1. The experimental results are mainly collected from the DeepSeek series, which cannot well demonstrate the generalizability of the proposed method.\n\n2. Many hallucinations can be made by the lack of factuality of language models, and there has been some previous work investigating this topic. Technically speaking, these approaches also adopt (supervised) fine-tuning plus GRPO-like algorithms to solve the problem. Compared with them, what are the advantages possessed by the proposed method?\n\n3. Some notations, e.g., $R_{final}$, are not explained. I suggest the authors list all parameters and notations in a Table in the appendix.\n\n4. How does the hyperparameter, $\\gamma$, influence the performance of the proposed method?\n\n5. How do models refined by RHD perform in reasoning on OOD domains or datasets?", "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": "SoljfPyLCv", "reviewer": "Reviewer_Sw2r", "summary": "The authors propose a simple extension of information theorectic metrics to measure hallucination in reasoning outputs. Particularly these use the Jensen Shannon Divergence between the vocab distributions at intermediate and final layer. The authors show some validations on how this score correlates with accuracy, perplexity and shows how this score performs better than baselines based on Entropy/EigenScore or PRMs.", "questions": "See the weakness section", "limitations": "", "rating": 2, "confidence": 4, "soundness": 1, "presentation": 2, "contribution": 1, "strengths": "The motivation and general writing in the paper is clear & it is a relevant problem to solve", "weaknesses": "- The main hallucination score seems to be overtly simple. I feel this is more like the standard information theoretic measures Like entropy being rehashed for reasoning outputs (which typically have a sequence of steps). And like entropy, perplexity etc I feel these kinds of token level metrics would be noisy and would suffer from capacity bottleneck and robustness issues (I mean in many cases reasoning fallacy or logical inconsistency may not be associated with a high JS Divergence at the token level. This would probably only capture some of the simpler more obvious hallucinations. \n\n- Also, I feel computing such a token level score at each intermediate layer of the model can be even more noisy. The only analysis done on the reliability of these scores in Table 3 and 4 does not seem enough.\n    - Validation of GSM-Noop - Introducing Noops are one of the simplest kinds of injected hallucinations, \n    - Validation on Stable/Rising sets: Not clear what is the size of the sets. This shows overall there is some correlation between the score, the accuracy and the perplexity but that can be from the fact that it is capturing some of the lower hanging hallucinations. \n\n- The main hallucination scoring is also somewhat heuristical. There are multiple hyperparameters involved (one in Attention Score, 4 in the final hallucination score, \\tau etc). This makes it more tricky to be practically used. The authors need to explicitly show through their experiments whether it is sensitive to these hyperparameters or not.\n\n- How can we definitely say that GRPO-R “encourages deep—but not excessive—reasoning during RL fine-tuning”  — the R-score no matter what is a noisy proxy. I would assume this scoring would be way more noisy and also varying (not robust), sensitive to minor changes in token space. The experiment results in table 2 are also not convincing. Esp for Qwen. Doing this on the small model 1.5B may not be enough\n\n- Why are GRPO related experiments and R-Score based RHD experiments done on separate benchmarks (ReTruthQA and GPQA). This makes the conclusion a bit disjoint from each other. Why can’t the detection and mitigation be applied on the same benchmarks. \n\n- Overall the scoring seems like a slightly better strategy on avg than the baselines but whether it is really generalizable or robust, it’s not clear from the experimental results. Practically speaking too many hyperparameters would make usage of this too unstable and complex - so it is important for authors to show how sensitive it is to hyperparams.", "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": "sNE2TewQt9", "reviewer": "Reviewer_MJhw", "summary": "This paper tackles the challenge of detecting and preventing reasoning hallucinations, which can be described by factually wrong but logically coherent/convincing chain-of-thought traces typically produced by large reasoning models (LRMs). First, a reasoning score is proposed based on the assumption that hallucinations relate to shallow reasoning, which can be characterized by static activations (i.e., low entropy) in the late Transformer layers. Based on empirical analysis, we see that the reasoning score alone cannot predict hallucinating steps/traces. To this end, different patterns are characterized that aim to describe different hallucination effects, such as shallow pattern matching and consecutive verification (#1), incorrect backtracking to earlier hallucinated steps (#2), and overthinking steps with both high reasoning score and perplexity (#3). The final reasoning hallucination detection (RHD) algorithm combines all derived metrics. Finally, the reasoning score is included in GRPO to mitigate hallucinations (dubbed GRPO-R). Experimental results on a novel benchmark (ReTruthQA) show superior performance in detecting hallucinations using RHD. Moreover, applying RL with GRPO-R improves overall performance on reasoning benchmarks (MATH500, AIME, GPQA).", "questions": "I would appreciate if the rebuttal could address the individual weaknesses. Besides, Ref. (Valmeekam et al.) is missing the date.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "Overall, this paper aims to address a crucial and indeed difficult problem in LRMs. I see the main strengths in:\n\n1. The paper covers quite a large scope, starting from introducing a novel benchmark (ReTruthQA), over to an atomic reasoning score, a derived reasoning hallucination detection algorithm (RHD), and finally a method to mitigate reasoning hallucinations (GRPO-R). This is also reflected in the very comprehensive appendix. \n2. The approach seems to be effective in both detecting hallucinations and improving the reasoning performance. \n3. The paper is well written.", "weaknesses": "My main reservations are concerned with ambiguities in defining and quantifying hallucinations. \n\n1. Potentially ambiguous evaluation. As there are apparently no datasets available on reasoning hallucinations, this paper proposes a self-generated one (ReTruthQA). As described in appendix D, traces are labelled based on final reasoning outcomes, GPT-4o-Mini, and two human validators. No labeling accuracy is provided (e.g., based on a subset that has been even more thoroughly labelled with more models and human validators). This makes both the justification of the reasoning score and the comparison to other methods difficult. For example, GPT-4o as an LLM-as-Critic (LCM) has clearly non-perfect AUC in Table 1. However, it is used as a labeling method in section 3 (Figures 3 and 4). \n2. Heuristic detection mechanism. Clearly, the proposed reasoning score alone is not sufficient to detect hallucinations (is a high or low score desirable?). Hence, derivatives (statistical measures, relationships to attention and perplexity) had to be introduced, requiring many hyperparameters. While the reasoning score seems not to be effective, it is still included in the Reasoning Hallucination Detection (RHD). It is questionable how much the average reasoning score can help. Indeed, it is often not even activated by setting $\\alpha_1$=0. The questionable impact of the average reasoning score is also shown in Table 5 (sometimes better scores without it in R1-14B) and Figure 8 (the highest drop with increasing weight in the reasoning score). One could even question why we don’t use the inverse of the reasoning score as well. \n3. Task-, model-, and metric-specific hyperparameters. As described in Appendix J, the proposed RHD uses specific hyperparameters for every task, model, and even metric (AUC, MC1-3). Did a similar hyperparameter tuning go into the baselines? \n4. Unclear gain of GRPO-R. While GRPO-R seems to improve the accuracy on the standard task, an analysis of the actual reasoning hallucination reduction is missing. It is not clear where the gain in accuracy comes from.", "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)