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arxiv: 2605.07776 · v1 · submitted 2026-05-08 · 💻 cs.LG · cs.AI· cs.CL

Recognition: 2 theorem links

· Lean Theorem

Tracing Uncertainty in Language Model "Reasoning"

Nils Gr\"unefeld , Bertram H{\o}jer , Philipp Mondorf , Barbara Plank , Anna Rogers , Christian Hardmeier , Stefan Heinrich , Jes Frellsen
Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:16 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL
keywords uncertainty quantificationchain-of-thoughtlanguage model reasoningerror detectionGSM8Ktrace analysispredictive modeling
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The pith

Uncertainty profiles from language model reasoning traces predict whether the final answer is correct.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that reasoning traces can be treated as sequences of evolving model states whose uncertainty signals can be summarized into compact profiles. These profiles, built from simple shape descriptors such as slope and linearity of uncertainty over the trace, reliably forecast whether the trace produces a correct final answer. The approach improves on earlier methods and works even when only the first few hundred tokens are observed, pointing to the possibility of catching errors before generation finishes. Correct traces show a steeper and less steadily linear drop in uncertainty than incorrect ones, suggesting the profiles capture distinct generative dynamics.

Core claim

Across five language models on GSM8K and ProntoQA, uncertainty trace profiles predict whether a reasoning trace yields a correct final answer with AUROC up to 0.807, and reach AUROC 0.801 from only the initial segment of the trace.

What carries the argument

Uncertainty trace profile: a compact set of features that describe the shape of the uncertainty signal across the tokens of a generated reasoning trace, including its slope and linearity.

If this is right

  • Correct and incorrect traces exhibit qualitatively different uncertainty dynamics, with correct ones showing steeper and less linear decline.
  • Predictive accuracy remains high when profiles are computed from only the first few hundred tokens, enabling early detection of likely errors.
  • The method supplies a decision-making-under-uncertainty view of the generative process that underlies chain-of-thought reasoning.
  • The same profile features distinguish success across multiple models and both arithmetic and logical reasoning datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Early profile-based detection could support generation-time interventions that stop or redirect a trace once its uncertainty shape signals probable failure.
  • The approach may extend to tasks outside math and logic if the same uncertainty-shape features continue to separate successful from unsuccessful generations.
  • Training objectives that encourage steeper uncertainty decline might increase the fraction of traces that reach correct answers.

Load-bearing premise

The uncertainty values read from token probabilities during generation meaningfully track the quality of the underlying reasoning rather than just surface patterns in token production.

What would settle it

A controlled test in which the uncertainty signal is replaced by random values or by statistics unrelated to model confidence, after which the AUROC for predicting trace correctness falls to chance level.

Figures

Figures reproduced from arXiv: 2605.07776 by Anna Rogers, Barbara Plank, Bertram H{\o}jer, Christian Hardmeier, Jes Frellsen, Nils Gr\"unefeld, Philipp Mondorf, Stefan Heinrich.

Figure 1
Figure 1. Figure 1: The average uncertainty trace for Qwen 2.5 on GSM8K. Left illustrates the average [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: AUROC scores on models trained on features extracted based on increasing shares of the full traces (left: GSM8K, right: ProntoQA). Early correctness detection [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Change in coefficient share over the course of generation. Feature importance. We measure feature im￾portance via the coefficient share of the logistic regression, which is computed as the absolute coefficient of each feature as a fraction of the sum of all absolute coefficients. We aggregate static (µearly, µmid, µlate) and dynamic (slope, r 2 ) features to assess the group-level importance, which is comp… view at source ↗
Figure 4
Figure 4. Figure 4: Heatmap of uncertainty features across models and datasets. The heatmap is organized into [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sample from GSM-Symbolic. Numbers indicate sentence indices. µearly, µmid, and µlate are shown as horizontal lines and slope as a dashed linear-fit line, with the corresponding r 2 reflected in the spread of the data around that line. Each plot shows the uncertainty type with the token index on the x-axis, and the location of the first error in the incorrect trace is highlighted in yellow. 8 [PITH_FULL_IM… view at source ↗
read the original abstract

Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes summarizing LM reasoning traces (e.g., Chain-of-Thought) via uncertainty trace profiles—compact features such as slope and linearity of the per-token uncertainty signal—and shows that these profiles predict final-answer correctness on GSM8K and ProntoQA across five models, reaching AUROC 0.807 (and 0.801 from the first few hundred tokens). It further reports qualitative differences, with correct traces exhibiting steeper and less linear uncertainty decline, and frames the approach as a principled lens from decision-making under uncertainty.

Significance. If the uncertainty profiles are shown to capture reasoning dynamics rather than surface token statistics, the work would provide a concrete, early-detection method for analyzing and potentially intervening in LM reasoning processes, improving on recent related work with falsifiable AUROC metrics on standard benchmarks. The early-token result and qualitative profile distinctions are potentially actionable for test-time scaling.

major comments (3)
  1. [Method] The method section does not provide explicit equations or pseudocode for per-token uncertainty computation (e.g., whether it is negative log-probability, entropy, or another measure) or for extracting slope/linearity features from the trace; without these, it is impossible to determine whether the reported AUROC reflects reasoning quality or merely correlates with token rarity, length, or local predictability.
  2. [Experiments] No ablations or statistical controls are presented for surface statistics (sequence length, average token probability, or n-gram rarity) that could drive the uncertainty profiles; this is load-bearing for the central claim because the skeptic concern—that profiles proxy generation surface properties rather than reasoning dynamics—is consistent with the reported early-detection AUROC of 0.801 and the qualitative differences.
  3. [Results] The qualitative comparison of correct vs. incorrect traces (steeper, less linear decline) lacks quantitative effect sizes, confidence intervals, or hypothesis tests; without these, the claim that the profiles are “qualitatively distinct” cannot be assessed for robustness against the same surface-statistic confound.
minor comments (2)
  1. [Introduction] The abstract and introduction use “reasoning” in quotes but do not define the term operationally (e.g., whether it includes only GSM8K-style arithmetic or also ProntoQA); a brief operational definition would improve clarity.
  2. [Results] Table or figure captions for the AUROC results should explicitly state the number of traces per model/benchmark and any multiple-testing correction applied.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify areas where greater explicitness and controls would strengthen the manuscript. We address each major comment below and will incorporate revisions to improve methodological clarity, add necessary controls, and provide quantitative support for the claims.

read point-by-point responses

  1. Referee: [Method] The method section does not provide explicit equations or pseudocode for per-token uncertainty computation (e.g., whether it is negative log-probability, entropy, or another measure) or for extracting slope/linearity features from the trace; without these, it is impossible to determine whether the reported AUROC reflects reasoning quality or merely correlates with token rarity, length, or local predictability.

    Authors: We agree that the current description lacks the precision needed for full reproducibility and to evaluate potential confounds. Per-token uncertainty is defined as the negative log-probability of the generated token. Slope is the coefficient from ordinary least-squares regression of uncertainty against token position within the trace; linearity is the corresponding R-squared value. In the revised manuscript we will insert the explicit equations, a short derivation of the profile features, and pseudocode for the end-to-end extraction pipeline. These additions will make clear that the features emphasize the temporal shape of the uncertainty signal rather than its absolute level. revision: yes

  2. Referee: [Experiments] No ablations or statistical controls are presented for surface statistics (sequence length, average token probability, or n-gram rarity) that could drive the uncertainty profiles; this is load-bearing for the central claim because the skeptic concern—that profiles proxy generation surface properties rather than reasoning dynamics—is consistent with the reported early-detection AUROC of 0.801 and the qualitative differences.

    Authors: We recognize that the absence of such controls leaves open the possibility that the reported AUROCs partly reflect surface statistics. In the revision we will add a dedicated ablation subsection that (i) reports partial correlations between profile features and correctness after regressing out length and mean token probability, (ii) evaluates AUROC on the residuals of a linear model that predicts correctness from length, average probability, and n-gram rarity alone, and (iii) compares the full profile-based classifier against a baseline using only those surface features. Results will be shown for both complete traces and the early-token regime. Should the profile features retain substantial predictive power after these controls, the reasoning-dynamics interpretation will be reinforced; otherwise the claims will be appropriately qualified. revision: yes

  3. Referee: [Results] The qualitative comparison of correct vs. incorrect traces (steeper, less linear decline) lacks quantitative effect sizes, confidence intervals, or hypothesis tests; without these, the claim that the profiles are “qualitatively distinct” cannot be assessed for robustness against the same surface-statistic confound.

    Authors: We concur that qualitative statements require quantitative backing. The revised results section will include a table reporting, for each model and dataset, the mean slope and mean linearity (with standard deviations) separately for correct and incorrect traces. We will also provide 95 % confidence intervals around the differences and the results of two-sample t-tests (or non-parametric equivalents if normality assumptions are violated). These statistics will be presented together with the existing qualitative description so that readers can judge the magnitude and reliability of the observed distinctions while remaining mindful of possible surface-statistic confounds. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical feature-based prediction of correctness

full rationale

The paper computes per-token uncertainty from model probabilities, derives summary features (slope, linearity) of the resulting trace, and trains a classifier to predict an independent binary label (final answer correct/incorrect) on GSM8K and ProntoQA. This is a standard supervised evaluation whose reported AUROC values are obtained from held-out data rather than by algebraic reduction or self-referential definition. No load-bearing self-citations, uniqueness theorems, or ansatzes are invoked to force the central result; the method remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available so the ledger is necessarily incomplete. The central claim rests on treating token-level uncertainty as a proxy for reasoning state quality and on the informativeness of simple summary statistics such as slope and linearity.

axioms (1)
  • domain assumption Token-level uncertainty (entropy or similar) reflects the model's evolving internal state during reasoning
    Core premise for summarizing traces as evolving model states

pith-pipeline@v0.9.0 · 5531 in / 1346 out tokens · 55430 ms · 2026-05-11T02:16:20.731647+00:00 · methodology

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Works this paper leans on

52 extracted references · 52 canonical work pages · 1 internal anchor

  1. [1]

    Arcuschin, J

    I. Arcuschin, J. Janiak, R. Krzyzanowski, S. Rajamanoharan, N. Nanda, and A. Conmy. Chain- of-Thought Reasoning In The Wild Is Not Always Faithful, Mar. 2025

    work page 2025

  2. [2]

    Blundell, J

    C. Blundell, J. Cornebise, K. Kavukcuoglu, and D. Wierstra. Weight Uncertainty in Neural Net- works. In Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning Research, pages 1613–1622. PMLR, June 2015

    work page 2015

  3. [3]

    X. Chen, R. Aksitov, U. Alon, J. Ren, K. Xiao, P. Yin, S. Prakash, C. Sutton, X. Wang, and D. Zhou. Universal Self-Consistency for Large Language Model Generation, Nov. 2023

    work page 2023

  4. [4]

    Y . Chen, J. Benton, A. Radhakrishnan, J. Uesato, C. Denison, J. Schulman, A. Somani, P. Hase, M. Wagner, F. Roger, V . Mikulik, S. Bowman, J. Leike, J. Kaplan, and E. Perez. Reasoning Models Don’t Always Say What They Think, May 2025

    work page 2025

  5. [5]

    Cobbe, V

    K. Cobbe, V . Kosaraju, M. Bavarian, M. Chen, H. Jun, L. Kaiser, M. Plappert, J. Tworek, J. Hilton, R. Nakano, C. Hesse, and J. Schulman. Training Verifiers to Solve Math Word Problems, Nov. 2021

    work page 2021

  6. [6]

    doi: https://doi.org/10.1016/j.strusafe.2008.06.020

    A. Der Kiureghian and O. Ditlevsen. Aleatory or epistemic? Does it matter? Structural Safety, 31(2):105–112, 2009. ISSN 0167-4730. doi: 10.1016/j.strusafe.2008.06.020. Risk Acceptance and Risk Communication

    work page doi:10.1016/j.strusafe.2008.06.020 2009

  7. [7]

    S. M. Downes, P. Forber, and A. Grzankowski. LLMs are not just next token predictors.Inquiry: An Interdisciplinary Journal of Philosophy, Jan. 2025. doi: 10.1080/0020174X.2024.2446240. Published online 12 January 2025

    work page doi:10.1080/0020174x.2024.2446240 2025

  8. [8]

    Y . Fu, X. Wang, Y . Tian, and J. Zhao. Deep Think with Confidence, Aug. 2025

    work page 2025

  9. [9]

    Grattafiori, A

    A. Grattafiori, A. Dubey, A. Jauhri, A. Pandey, A. Kadian, A. Al-Dahle, A. Letman, A. Mathur, A. Schelten, A. Vaughan, et al. The Llama 3 Herd of Models, Nov. 2024. Author list truncated; full author list available at the arXiv page

    work page 2024

  10. [10]

    Grünefeld, J

    N. Grünefeld, J. Frellsen, and C. Hardmeier. An Isotropic Approach to Efficient Uncertainty Quantification with Gradient Norms, Mar. 2026

    work page 2026

  11. [11]

    D. Guo, D. Yang, H. Zhang, J. Song, P. Wang, Q. Zhu, R. Xu, R. Zhang, S. Ma, X. Bi, et al. DeepSeek-R1 incentivizes reasoning in LLMs through reinforcement learning. Nature, 645 (8081):633–638, Sept. 2025. ISSN 1476-4687. doi: 10.1038/s41586-025-09422-z. Author list truncated for brevity; see Nature publication for full list

    work page doi:10.1038/s41586-025-09422-z 2025

  12. [12]

    B. Højer. On the Notion that Language Models Reason. In 1st Workshop on Epistemic Intelligence in Machine Learning (EIML), EurIPS 2025, 2025. doi: 10.48550/arXiv.2511.11810

    work page doi:10.48550/arxiv.2511.11810 2025

  13. [13]

    Højer, O

    B. Højer, O. Jarvis, and S. Heinrich. Improving Reasoning Performance in Large Language Mod- els via Representation Engineering. In The Thirteenth International Conference on Learning Representations. OpenReview, 2025. doi: 10.48550/arXiv.2504.19483

    work page doi:10.48550/arxiv.2504.19483 2025

  14. [14]

    S. C. Hora. Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management. Reliability Engineering & System Safety, 54(2):217–223, 1996. ISSN 0951-8320. doi: 10.1016/S0951-8320(96)00077-4. Treatment of Aleatory and Epistemic Uncertainty

    work page doi:10.1016/s0951-8320(96)00077-4 1996

  15. [15]

    Towards reasoning in large language models: A survey

    J. Huang and K. C.-C. Chang. Towards Reasoning in Large Language Models: A Survey. In A. Rogers, J. Boyd-Graber, and N. Okazaki, editors, Findings of the Association for Computa- tional Linguistics: ACL 2023, pages 1049–1065, Toronto, Canada, July 2023. Association for Computational Linguistics. doi: 10.18653/v1/2023.findings-acl.67. 10

    work page doi:10.18653/v1/2023.findings-acl.67 2023

  16. [16]

    Hüllermeier, W

    E. Hüllermeier and W. Waegeman. Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods. Machine Learning, 110(3):457–506, Mar. 2021. ISSN 1573-0565. doi: 10.1007/s10994-021-05946-3

    work page doi:10.1007/s10994-021-05946-3 2021

  17. [17]

    Kambhampati, K

    S. Kambhampati, K. Valmeekam, S. Bhambri, V . Palod, L. Saldyt, K. Stechly, S. R. Sami- neni, D. Kalwar, and U. Biswas. Position: Stop Anthropomorphizing Intermediate Tokens as Reasoning/Thinking Traces!, Apr. 2025

    work page 2025

  18. [18]

    Z. Kang, X. Zhao, and D. Song. Scalable Best-of-N Selection for Large Language Models via Self-Certainty. In The Thirty-Ninth Annual Conference on Neural Information Processing Systems, 2025. doi: 10.48550/arXiv.2502.18581

    work page doi:10.48550/arxiv.2502.18581 2025

  19. [19]

    Kojima, S

    T. Kojima, S. S. Gu, M. Reid, Y . Matsuo, and Y . Iwasawa. Large Language Models are Zero- Shot Reasoners. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 22199–22213. Curran Associates, Inc., 2022

    work page 2022

  20. [20]

    Lanham, A

    T. Lanham, A. Chen, A. Radhakrishnan, B. Steiner, C. Denison, D. Hernandez, D. Li, E. Durmus, E. Hubinger, J. Kernion, K. Lukoši¯ut˙e, K. Nguyen, N. Cheng, N. Joseph, N. Schiefer, O. Rausch, R. Larson, S. McCandlish, S. Kundu, S. Kadavath, S. Yang, T. Henighan, T. Maxwell, T. Telleen- Lawton, T. Hume, Z. Hatfield-Dodds, J. Kaplan, J. Brauner, S. R. Bowman...

    work page 2023

  21. [21]

    Z. Ling, Y . Fang, X. Li, Z. Huang, M. Lee, R. Memisevic, and H. Su. Deductive Verification of Chain-of-Thought Reasoning. In Advances in Neural Information Processing Systems , volume 36. Curran Associates, Inc., 2023. doi: 10.48550/arXiv.2306.03872

    work page doi:10.48550/arxiv.2306.03872 2023

  22. [22]

    Z. Liu, C. Chen, W. Li, P. Qi, T. Pang, C. Du, W. S. Lee, and M. Lin. Understanding R1-Zero- Like Training: A Critical Perspective. In Conference on Language Modeling (COLM), 2025. doi: 10.48550/arXiv.2503.20783

    work page Pith review doi:10.48550/arxiv.2503.20783 2025

  23. [23]

    D. J. C. MacKay. A Practical Bayesian Framework for Backpropagation Networks. Neural Computation, 4(3):448–472, May 1992. ISSN 0899-7667. doi: 10.1162/neco.1992.4.3.448

    work page doi:10.1162/neco.1992.4.3.448 1992

  24. [24]

    GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

    I. Mirzadeh, K. Alizadeh, H. Shahrokhi, O. Tuzel, S. Bengio, and M. Farajtabar. GSM- Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models. In The Thirteenth International Conference on Learning Representations, 2025. doi: 10.48550/arXiv.2410.05229

    work page Pith review doi:10.48550/arxiv.2410.05229 2025

  25. [25]

    Mondorf and B

    P. Mondorf and B. Plank. Comparing Inferential Strategies of Humans and Large Language Models in Deductive Reasoning. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 9370–9402, Bangkok, Thailand,

    work page

  26. [26]

    doi: 10.18653/v1/2024.acl-long.508

    Association for Computational Linguistics. doi: 10.18653/v1/2024.acl-long.508

    work page doi:10.18653/v1/2024.acl-long.508 2024

  27. [27]

    Muennighoff, Z

    N. Muennighoff, Z. Yang, W. Shi, X. L. Li, L. Fei-Fei, H. Hajishirzi, L. Zettlemoyer, P. Liang, E. Candès, and T. Hashimoto. S1: Simple test-time scaling. In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pages 20275–20321, Suzhou, China, 2025. Association for Computational Linguistics

    work page 2025

  28. [28]

    R. M. Neal. Bayesian Learning for Neural Networks, volume 118. Springer Science & Business Media, 2012

    work page 2012

  29. [29]

    M. Nye, A. J. Andreassen, G. Gur-Ari, H. Michalewski, J. Austin, D. Bieber, D. Dohan, A. Lewkowycz, M. Bosma, D. Luan, C. Sutton, and A. Odena. Show Your Work: Scratchpads for Intermediate Computation with Language Models, Nov. 2021

    work page 2021

  30. [30]

    Y . Sale, P. Hofman, L. Wimmer, E. Hüllermeier, and T. Nagler. Second-Order Uncertainty Quantification: Variance-Based Measures, Dec. 2023

    work page 2023

  31. [31]

    Y . Sale, P. Hofman, T. Löhr, L. Wimmer, T. Nagler, and E. Hüllermeier. Label-wise Aleatoric and Epistemic Uncertainty Quantification. In Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, volume 244 of Proceedings of Machine Learning Research, pages 3159–3179. PMLR, July 2024. 11

    work page 2024

  32. [32]

    S. R. Samineni, D. Kalwar, K. Valmeekam, K. Stechly, and S. Kambhampati. RL in Name Only? Analyzing the Structural Assumptions in RL post-training for LLMs. In NeurIPS 2025 Workshop on Bridging Language, Agent, and World Models for Reasoning and Planning (LAW), 2025. doi: 10.48550/arXiv.2505.13697. Also accepted at NeurIPS 2025 Workshop on Foundations of ...

    work page doi:10.48550/arxiv.2505.13697 2025

  33. [33]

    Language models are greedy reasoners: A systematic formal analysis of chain-of-thought.arXiv:2210.01240,

    A. Saparov and H. He. Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought, 2023. URL https://arxiv.org/abs/2210.01240. Published at ICLR 2023

    work page arXiv 2023

  34. [34]

    Shanahan

    M. Shanahan. Talking About Large Language Models, Feb. 2023

    work page 2023

  35. [35]

    Smith and Y

    L. Smith and Y . Gal. Understanding Measures of Uncertainty for Adversarial Example Detec- tion. In A. Globerson and R. Silva, editors, Proceedings of the Thirty-Fourth Conference on Uncertainty in Artificial Intelligence, UAI 2018, Monterey, California, USA, August 6-10, 2018, pages 560–569. AUAI Press, 2018

    work page 2018

  36. [36]

    Chain of Thoughtlessness? An Analysis of CoT in Planning

    K. Stechly, K. Valmeekam, and S. Kambhampati. Chain of Thoughtlessness? An Analysis of CoT in Planning. In Advances in Neural Information Processing Systems, volume 37. Curran Associates, Inc., 2024. doi: 10.48550/arXiv.2405.04776

    work page doi:10.48550/arxiv.2405.04776 2024

  37. [37]

    CoRR , volume =

    K. Stechly, K. Valmeekam, A. Gundawar, V . Palod, and S. Kambhampati. Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens. InThe Thirty-Ninth Annual Conference on Neural Information Processing Systems, 2025. doi: 10.48550/arXiv.2505.13775

    work page doi:10.48550/arxiv.2505.13775 2025

  38. [38]

    Tomov, D

    T. Tomov, D. Fuchsgruber, T. Wollschläger, and S. Günnemann. Entropy Is Not Enough: Uncertainty Quantification for LLMs fails under Aleatoric Uncertainty. In NeurIPS 2025 Workshop on Structured Probabilistic Inference & Generative Modeling, 2025

    work page 2025

  39. [39]

    Turpin, J

    M. Turpin, J. Michael, E. Perez, and S. R. Bowman. Language Models Don’t Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting. In Advances in Neural Information Processing Systems, volume 36. Curran Associates, Inc., 2023

    work page 2023

  40. [40]

    URL https://www.science.org/doi/10

    A. Tversky and D. Kahneman. Judgment under Uncertainty: Heuristics and Biases: Biases in judgments reveal some heuristics of thinking under uncertainty. Science, 185(4157):1124–1131, Sept. 1974. ISSN 0036-8075, 1095-9203. doi: 10.1126/science.185.4157.1124

    work page doi:10.1126/science.185.4157.1124 1974

  41. [41]

    Tversky and D

    A. Tversky and D. Kahneman. The Framing of Decisions and the Psychology of Choice. Science, 211(4481):453–458, 1981. doi: 10.1126/science.7455683

    work page doi:10.1126/science.7455683 1981

  42. [42]

    Tversky and D

    A. Tversky and D. Kahneman. Rational Choice and the Framing of Decisions. The Journal of Business, 59(4):S251–S278, 1986. ISSN 0021-9398

    work page 1986

  43. [43]

    X. Wang, J. Wei, D. Schuurmans, Q. V . Le, E. H. Chi, S. Narang, A. Chowdhery, and D. Zhou. Self-Consistency Improves Chain of Thought Reasoning in Language Models. In The Eleventh International Conference on Learning Representations, 2023. doi: 10.48550/arXiv.2203.11171

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2203.11171 2023

  44. [44]

    J. Wei, X. Wang, D. Schuurmans, M. Bosma, B. Ichter, F. Xia, E. Chi, Q. Le, and D. Zhou. Chain-of-Thought Prompting Elicits Reasoning in Large Language Models. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 24824–24837. Curran Associates, Inc., 2022

    work page 2022

  45. [45]

    Wimmer, Y

    L. Wimmer, Y . Sale, P. Hofman, B. Bischl, and E. Hüllermeier. Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures? In R. J. Evans and I. Shpitser, editors, Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, volume 216 of Proceedings of ...

    work page doi:10.48550/arxiv.2209.03302 2023

  46. [46]

    A. Yang, B. Yang, B. Hui, B. Zheng, B. Yu, C. Zhou, C. Li, C. Li, D. Liu, F. Huang, et al. Qwen2 Technical Report, Sept. 2024. Author list truncated; full author list available at the arXiv page. 12

    work page 2024

  47. [47]

    A. Yang, A. Li, B. Yang, B. Zhang, B. Hui, B. Zheng, B. Yu, C. Gao, C. Huang, C. Lv, et al. Qwen3 Technical Report, May 2025. Author list truncated; full author list available at the arXiv page

    work page 2025

  48. [48]

    Zhang, Y

    A. Zhang, Y . Chen, J. Pan, C. Zhao, A. Panda, J. Li, and H. He. Reasoning Models Know When They’re Right: Probing Hidden States for Self-Verification, Apr. 2025

    work page 2025

  49. [49]

    Z. Zhao, Y . Koishekenov, X. Yang, N. Murray, and N. Cancedda. Verifying Chain-of-Thought Reasoning via Its Computational Graph. In The Fourteenth International Conference on Learning Representations, 2026. doi: 10.48550/arXiv.2510.09312. Accepted as Oral. 13 A Intuitions for the Uncertainty Types The three uncertainty types defined in subsection 2.2 can ...

    work page doi:10.48550/arxiv.2510.09312 2026

  50. [50]

    Final Answer

    and a near-tied two-way contest (Case 3) both produce high committal uncertainty, but only Case 14 2 also produces high entropy. The same low-entropy reading can therefore correspond to confident commitment (Case 1) or to a near-tied two-way contest (Case 3), and only committal uncertainty distinguishes them. B Extracting the Final Answer, ˆy Computing an...

    work page

  51. [51]

    A regex-based extractor attempts to pull a final answer from the answer portion of each generation

    contains_answer check. A regex-based extractor attempts to pull a final answer from the answer portion of each generation. Generations for which extraction fails are dropped

    work page

  52. [52]

    LLM correctness re-evaluation. For samples whose extracted answer differs from the reference under the regex matcher, we query an LLM auditor (gpt-5-2025-08-07) to re- evaluate correctness under a more lenient semantic match (e.g., 0.5 vs 1/2, mathematically equivalent expressions). When the auditor confirms correctness, we flip is_correct to True; otherw...

    work page 2025