REVIEW 2 major objections 4 minor 49 references
Correctness probes, tested on OC–SJ conflicts, follow the model's own judgement rather than objective correctness in every cross-domain condition.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
Transferable LLM 'truth' probes preserve a self-judgement-associated polarity rather than an objective-correctness polarity when the two conflict.
T0 review reviewed 2026-08-01 challenge →
load-bearing objection Conflict-based factorial design is a real contribution and the transfer asymmetry is robust enough to change validation practice; the component-level 'SJ polarity' claim leans on the linear model assumption, but the broader cautionary conclusion survives it. the 2 major comments →
Diagnosing Correctness Probes under Self-Judgement Confounding
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
Core claim
The paper's central claim is that when objective correctness (OC) and self-judgement (SJ) are separated, the component of a correctness probe that transfers across domains preserves SJ-associated polarity, not OC-associated polarity. On conflict cases, the conventional mixed contrast Wmix ranks wrong/self-endorsed responses above correct/self-rejected responses, and the OC-only mass-mean control does the same in all eight cross-domain conditions. The factorial contrast Wmeta (SJ-associated) predicts held-out SJ above chance within domain and across domains in all eight model-by-direction evaluations, whereas Wtruth (OC-associated) is at or below chance for OC ordering. This pattern develops
What carries the argument
The load-bearing object is a factorial decomposition of the conventional 'correct minus incorrect' contrast. With cell means mu_A (correct, endorsed), mu_B (correct, rejected), mu_C (wrong, endorsed), mu_D (wrong, rejected), the paper defines Wmix = mu_A - mu_D, Wmeta = [(mu_A - mu_B)+(mu_C - mu_D)]/2, and Wtruth = [(mu_A - mu_C)+(mu_B - mu_D)]/2, and interprets them under an additive linear model of the answer-token residual stream in which OC and SJ each contribute a direction and the interaction cancels. The conflict set B/C provides the test: an OC readout should rank B above C, an SJ readout should rank C above B. These directions are fitted on one domain and scored on held-out or cross
Load-bearing premise
The interpretation rests on the assumption that the answer-token residual stream is a linear additive mixture of separate OC and SJ directions, with the interaction cancelling in factorial contrasts; if the true encoding is nonlinear or confounded with other variables like answer style, the 'OC-associated' and 'SJ-associated' labels are fitted contrasts rather than true latent directions.
What would settle it
Find a model or domain where, on the same B/C conflict set, the OC-associated direction Wtruth transfers above chance while the SJ-associated direction Wmeta does not, with confidence intervals excluding the paper's asymmetry. Alternatively, show that controlling for a specific confound (e.g., response verbosity or topic) reverses the B/C ordering of Wmix, or that a causal intervention that changes self-judgement while leaving objective correctness fixed fails to move the probe's ranking.
If this is right
- If a correctness probe transfers across tasks, the transfer may reflect the model's confidence or endorsement rather than objective truth; transferability alone does not validate a truth readout.
- Conflict cases (correct-but-rejected vs wrong-but-endorsed) provide a practical diagnostic for deciding what a probe tracks.
- The SJ-associated direction is the robust transferable component across four models and two source domains, including zero-target-fitting transfer to MMLU and TruthfulQA.
- The distinction between OC and SJ is operationalized by a separate Yes/No judgement; the probe's answer-token signal predictably aligns with that later judgement.
- The observed asymmetry develops in middle-to-late transformer layers and persists under controls for answer likelihood, sequence length, token count, and null directions.
Where Pith is reading between the lines
- A natural extension is to test the same factorial conflict diagnostic on larger or non-instruction-tuned models; the paper only covers up to 14B instruction-tuned models, so it is an open question whether the asymmetry holds elsewhere.
- If the SJ signal is largely endorsement or commitment, then interventions that shift a model's self-judgement (e.g., prompt-induced confidence) might move the probe's ranking of B versus C without changing objective correctness — a testable prediction that would sharpen the causal reading.
- The results suggest re-examining published 'truth direction' findings: without conflict-based validation, those directions may have been tracking confidence all along.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes a diagnostic for correctness probes that separates objective correctness (OC) from the model's self-judgement (SJ) by constructing conflict cases in which the two variables predict opposite orderings. It extracts final-answer-token residual-stream activations, defines factorial contrasts Wmeta and Wtruth intended to isolate SJ- and OC-associated directions, and evaluates their within-domain and cross-domain transfer across four instruction-tuned models and two free-response domains, plus zero-target-fitting OOD evaluations on MMLU and binary TruthfulQA. The central empirical finding is that the SJ-associated direction transfers above chance in essentially every condition, while the OC-associated direction has below-chance or near-chance AUCs for the expected OC ordering, and the conventional mixed contrast often ranks wrong/self-endorsed responses above correct/self-rejected responses. The paper concludes that transferability alone does not establish objective-correctness semantics.
Significance. If the result holds, it is an important and timely caution for the interpretability literature: it provides a concrete, multi-model demonstration that a transferable correctness readout can preserve the polarity of the model's own judgement rather than external correctness. The paper's strengths are substantial: four models, two free-response domains and two OOD benchmarks, strict confidence-filtered conflict sets, cluster-bootstrap inference that resamples source and target questions, source-label-shuffle and random-direction nulls, token-count and answer-likelihood residualization, and a second strict-pair draw. The OC-only mass-mean control is particularly valuable because it shows that even a direction fitted without any SJ labels follows SJ on conflicts. The paper is also unusually candid about its scope and the conditional nature of its estimates.
major comments (2)
- [Abstract; §5.1/Eq. S1; Scope (S12)] The component-level labels Wmeta and Wtruth are derived from the additive linear model x = α o vOC + β s vSJ + η o s vINT + ε. If the true residual-stream encoding is nonlinear, or if OC and SJ directions are not separable in the way this model assumes, then these vectors are fitted contrasts rather than semantic directions. The paper acknowledges this in Scope, but the abstract and Discussion state the component-level conclusion ('SJ-associated polarity', 'the SJ-associated direction') without the caveat. Please either qualify the abstract explicitly (e.g., 'under a linear factorial decomposition of activation means') or provide a nonlinear-probe check to show the labels are not artifacts of the linear estimator. The broader cautionary conclusion is supported independently by the OC-only mass-mean control, but the component-level interpretation rests on Eq. S1.
- [Method (SJ elicitation); Exp2B; S12] Source and target SJ labels are generated by the identical yes/no self-judgement prompt, whereas OC labels come from dataset-specific parsers or answer keys. Cross-domain transfer of Wmeta could therefore partly reflect shared surface alignment of the elicitation procedure rather than a stable semantic self-judgement direction. The answer-likelihood residualization, the OC-only control, and the counterbalanced X/Y control reduce this concern materially, but the Discussion should state the asymmetry explicitly: the SJ transfer evidence is symmetric in task format in a way that the OC evidence is not. S12 mentions that SJ may contain variance from confidence, familiarity, or response policy, but does not connect this to the source-target sharing of the judgement prompt.
minor comments (4)
- [Eq. S1 and surrounding text] The terms 'latent directions vOC and vSJ' may suggest independent latent axes. Since Wmeta and Wtruth are defined as factorial contrasts and are not shown to be orthogonal or unique, please clarify in the main text that these are operational contrast directions, not necessarily independent semantic axes in activation space.
- [Sample flow and Scope] The attrition from the original pools to the strict paired sample is severe (e.g., OLMo-3-7B Math retains 362 strict pairs from 5,549 questions). The main text states the conditional nature of the estimand, but it would help readers if the approximate retention rates were stated in the main experimental protocol rather than only in the supplement.
- [Figures 2–4] The figures are information-dense and the colors (teal/amber, blue/orange) may be hard to distinguish in grayscale. Adding direct text labels at the curve level or using line styles would improve accessibility.
- [Results, OOD section] The all-layer counts such as 458/560 (81.8%) are described as descriptive in S6, but the main text could explicitly remind readers that adjacent layers are not independent observations so these proportions are summaries, not primary inference.
Circularity Check
No circularity: transfer results are held-out/OOD with zero target fitting; factorial labels are explicit constructions, not fitted-then-renamed predictions.
full rationale
The central empirical chain is not circular. Wmeta and Wtruth are constructed as factorial contrasts from source-domain cell means (S5.1, Eqs. S6–S7), explicitly labelled as 'operational labels for the SJ-associated and OC-associated factorial contrasts.' The transfer claims (Exp2B, Table 1) freeze these source directions and evaluate them on B/C conflicts in a different domain, including MMLU and TruthfulQA with no target-domain direction fitting (S10). This is a genuine out-of-sample generalization test, not a re-fit on the target labels. Exp1's Wmix = µA − µD is a conventional correctness-labelled contrast; the OC-only mass-mean control (S8.2) is fitted with OC labels only, yet ranks C above B on target conflicts, so the Exp1 reversal is not forced by using SJ labels in fitting. Held-out grouped folds (Exp2A), source-label-shuffle and random-direction nulls (S8.3), token-count matching, answer-likelihood residualization, and counterbalanced X/Y judgement labels further support the empirical asymmetry. The linear associative model in Eq. S1 is an interpretative assumption; the paper explicitly scope-limits the factorial contrasts to 'linear activation-mean directions' and notes they 'do not assess nonlinear or task-adapted correctness predictors' (Scope, S12). An assumption that is stated and testable is a correctness risk, not circularity. The only self-citation (Lu, Song, and Wang 2025) is contextual and not load-bearing for the derivation.
Axiom & Free-Parameter Ledger
free parameters (3)
- SJ confidence threshold tau =
0.7
- Fixed layer window =
normalized depth [0.40, 0.80]
- Pilot filtering thresholds =
ncorrect < 8; mean pilot output length < 380 tokens
axioms (3)
- domain assumption Final-answer-token residual streams are well approximated by x = alpha*o*vOC + beta*s*vSJ + eta*o*s*vINT + epsilon with additive, separable OC and SJ signals
- domain assumption A one-token Yes/No self-judgement after the answer is a valid operational measure of self-judgement
- domain assumption The high-confidence strict-pair selection and question-level filtering do not systematically bias the OC-SJ conflict set toward the observed asymmetry
invented entities (1)
-
Latent task directions vOC and vSJ
independent evidence
Cite this review
Pith. "Pith review of Diagnosing Correctness Probes under Self-Judgement Confounding." pith.science (2026). https://pith.science/paper/WKEE3SQD
@misc{pith2026260716799,
author = {Pith},
title = {Pith review of: Diagnosing Correctness Probes under Self-Judgement Confounding},
year = {2026},
howpublished = {\url{https://pith.science/paper/WKEE3SQD}},
note = {Machine review of arXiv:2607.16799}
}
read the original abstract
Hidden-state readouts can predict whether language-model outputs are correct, but objective correctness (OC) usually agrees with the model's own self-judgement (SJ), leaving the decoded signal semantically ambiguous. We construct conflict cases in which OC and SJ predict opposite readout orderings. On high-confidence disagreements, conventional correctness-labelled contrasts often rank incorrect/self-endorsed responses above correct/self-rejected responses, following SJ rather than OC. We estimate factorial SJ- and OC-associated directions and evaluate their polarity across mathematical reasoning and factual recall. Across four instruction-tuned models up to 14B parameters, the SJ-associated direction transfers above chance in both cross-domain directions for every model, whereas the OC-associated direction has a below-chance point estimate for the expected OC ordering in every corresponding condition. This transfer asymmetry develops across middle-to-late layers, persists under answer-likelihood, sequence-length, and null-direction controls, and extends to MMLU and binary TruthfulQA without target-domain direction fitting. Across the studied models and diagnostic subsets, the most reliably transferable component preserves SJ-associated polarity. Transferability alone therefore does not establish objective-correctness semantics.
Figures
Reference graph
Works this paper leans on
-
[1]
T ruthful QA : Measuring How Models Mimic Human Falsehoods
Lin, Stephanie and Hilton, Jacob and Evans, Owain. T ruthful QA : Measuring How Models Mimic Human Falsehoods. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022. doi:10.18653/v1/2022.acl-long.229
-
[2]
Lin, Stephanie and Hilton, Jacob and Evans, Owain , year =
-
[3]
International Conference on Learning Representations , year =
Measuring Massive Multitask Language Understanding , author =. International Conference on Learning Representations , year =
-
[4]
arXiv preprint arXiv:2110.14168 , year =
Training Verifiers to Solve Math Word Problems , author =. arXiv preprint arXiv:2110.14168 , year =
-
[5]
A Diverse Corpus for Evaluating and Developing E nglish Math Word Problem Solvers
Miao, Shen-yun and Liang, Chao-Chun and Su, Keh-Yih. A Diverse Corpus for Evaluating and Developing E nglish Math Word Problem Solvers. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 2020. doi:10.18653/v1/2020.acl-main.92
-
[6]
Are NLP Models really able to Solve Simple Math Word Problems?
Patel, Arkil and Bhattamishra, Satwik and Goyal, Navin. Are NLP Models really able to Solve Simple Math Word Problems?. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021. doi:10.18653/v1/2021.naacl-main.168
-
[7]
Measuring Mathematical Problem Solving With the MATH Dataset , url =
Hendrycks, Dan and Burns, Collin and Kadavath, Saurav and Arora, Akul and Basart, Steven and Tang, Eric and Song, Dawn and Steinhardt, Jacob , booktitle =. Measuring Mathematical Problem Solving With the MATH Dataset , url =
-
[8]
Solving General Arithmetic Word Problems
Roy, Subhro and Roth, Dan. Solving General Arithmetic Word Problems. Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing. 2015. doi:10.18653/v1/D15-1202
-
[9]
Lightman, Hunter and Kosaraju, Vineet and Burda, Yuri and Edwards, Harrison and Baker, Bowen and Lee, Teddy and Leike, Jan and Schulman, John and Sutskever, Ilya and Cobbe, Karl , booktitle =. Let. 2024 , url =
2024
-
[10]
International Conference on Learning Representations , year =
Discovering Latent Knowledge in Language Models Without Supervision , author =. International Conference on Learning Representations , year =
-
[11]
The Internal State of an LLM Knows When It ' s Lying
Azaria, Amos and Mitchell, Tom. The Internal State of an LLM Knows When It ' s Lying. Findings of the Association for Computational Linguistics: EMNLP 2023. 2023. doi:10.18653/v1/2023.findings-emnlp.68
-
[12]
Inference-Time Intervention: Eliciting Truthful Answers from a Language Model , url =
Li, Kenneth and Patel, Oam and Vi\'. Inference-Time Intervention: Eliciting Truthful Answers from a Language Model , url =. Advances in Neural Information Processing Systems , editor =
-
[13]
First Conference on Language Modeling , year=
The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets , author=. First Conference on Language Modeling , year=
-
[14]
Zou, Andy and Phan, Long and Chen, Sarah and Campbell, James and Guo, Phillip and Ren, Richard and Pan, Alexander and Yin, Xuwang and Mazeika, Mantas and Dombrowski, Ann-Kathrin and Goel, Shashwat and Li, Nathaniel and Byun, Michael J. and Wang, Zifan and Mallen, Alex and Basart, Steven and Koyejo, Sanmi and Song, Dawn and Fredrikson, Matt and Kolter, J. ...
-
[15]
2022 , eprint=
Language Models (Mostly) Know What They Know , author=. 2022 , eprint=
2022
-
[16]
Transactions on Machine Learning Research , issn=
Teaching Models to Express Their Uncertainty in Words , author=. Transactions on Machine Learning Research , issn=. 2022 , url=
2022
-
[17]
Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , pages =
Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback , author =. Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , pages =. 2023 , address =. doi:10.18653/v1/2023.emnlp-main.330 , url =
-
[18]
Xiong, Miao and Hu, Zhiyuan and Lu, Xinyang and Li, Yifei and Fu, Jie and He, Junxian and Hooi, Bryan , booktitle =. Can. 2024 , url =
2024
-
[19]
Designing and Interpreting Probes with Control Tasks , author =. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing , pages =. 2019 , publisher =. doi:10.18653/v1/D19-1275 , url =
-
[20]
Computational Linguistics , volume =
Probing Classifiers: Promises, Shortcomings, and Advances , author =. Computational Linguistics , volume =. 2022 , doi =
2022
-
[21]
2025 , eprint=
Qwen2.5 Technical Report , author=. 2025 , eprint=
2025
-
[22]
arXiv preprint arXiv:2407.21783 , year =
The Llama 3 Herd of Models , author =. arXiv preprint arXiv:2407.21783 , year =
-
[23]
ACM Transactions on Information Systems , volume =
A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions , author =. ACM Transactions on Information Systems , volume =. 2025 , publisher =. doi:10.1145/3703155 , url =
doi:10.1145/3703155 2025
-
[24]
A Unified Representation Underlying the Judgment of Large Language Models , author =. 2025 , eprint =. doi:10.48550/arXiv.2510.27328 , url =
-
[25]
Decoupling Metacognition from Cognition: A Framework for Quantifying Metacognitive Ability in
Wang, Guoqing and Wu, Wen and Ye, Guangze and Cheng, Zhenxiao and Chen, Xi and Zheng, Hong , booktitle =. Decoupling Metacognition from Cognition: A Framework for Quantifying Metacognitive Ability in. 2025 , doi =
2025
-
[26]
Do Large Language Models Know What They Don
Yin, Zhangyue and Sun, Qiushi and Guo, Qipeng and Wu, Jiawen and Qiu, Xipeng and Huang, Xuanjing , booktitle =. Do Large Language Models Know What They Don. 2023 , address =. doi:10.18653/v1/2023.findings-acl.551 , url =
-
[27]
Kumaran, Dharshan and Patraucean, Viorica and Osindero, Simon and Veli. How. 2026 , eprint =. doi:10.48550/arXiv.2604.22271 , url =
-
[28]
2026 , eprint=
How do LLMs Compute Verbal Confidence , author=. 2026 , eprint=
2026
-
[29]
Haller, Patrick and Ibrahim, Mark and Kirichenko, Polina and Sagun, Levent and Bell, Samuel J. , year =. doi:10.48550/arXiv.2510.11905 , url =. 2510.11905 , archivePrefix =
-
[30]
2025 , url =
Orgad, Hadas and Toker, Michael and Gekhman, Zorik and Reichart, Roi and Szpektor, Idan and Kotek, Hadas and Belinkov, Yonatan , booktitle =. 2025 , url =
2025
-
[31]
, booktitle =
Li, Ji-An and Xiong, Huadong and Wilson, Robert and Mattar, Marcelo G and Benna, Marcus K. , booktitle =. Language Models Are Capable of Metacognitive Monitoring and Control of Their Internal Activations , url =
-
[32]
Cheang, Chi Seng and Chan, Hou Pong and Zhang, Wenxuan and Deng, Yang , editor =. Do. Findings of the Association for Computational Linguistics: ACL 2026 , month = jul, year =. doi:10.18653/v1/2026.findings-acl.34 , pages =
-
[33]
Current Directions in Psychological Science , volume =
Metacognition and Uncertainty Communication in Humans and Large Language Models , author =. Current Directions in Psychological Science , volume =. 2026 , doi =
2026
-
[34]
2025 , url =
The Geometries of Truth Are Orthogonal Across Tasks , author =. 2025 , url =
2025
-
[35]
2026 , eprint=
Olmo 3 , author=. 2026 , eprint=
2026
-
[36]
Patel, Het and Chen, Tiejin and Wei, Hua and Papalexakis, Evangelos E. and Chen, Jia , year =. Are. doi:10.48550/arXiv.2604.19974 , url =. 2604.19974 , archivePrefix =
-
[37]
The Truthfulness Spectrum Hypothesis , author =. 2026 , eprint =. doi:10.48550/arXiv.2602.20273 , url =
-
[38]
Probing the Geometry of Truth: Consistency and Generalization of Truth Directions in
Bao, Yuntai and Zhang, Xuhong and Du, Tianyu and Zhao, Xinkui and Feng, Zhengwen and Peng, Hao and Yin, Jianwei , booktitle =. Probing the Geometry of Truth: Consistency and Generalization of Truth Directions in. 2025 , publisher =. doi:10.18653/v1/2025.findings-acl.38 , url =
-
[39]
Testing the Limits of Truth Directions in
Poulis, Angelos and Crovella, Mark and Terzi, Evimaria , year =. Testing the Limits of Truth Directions in. doi:10.48550/arXiv.2604.03754 , url =. 2604.03754 , archivePrefix =
-
[40]
Proceedings of the 2nd Conference on Language Modeling , year =
Language Models Fail to Introspect About Their Knowledge of Language , author =. Proceedings of the 2nd Conference on Language Modeling , year =
-
[41]
Singh, Shashwat and Linzen, Tal and Ravfogel, Shauli , year =. Can. doi:10.48550/arXiv.2605.26242 , url =. 2605.26242 , archivePrefix =
-
[42]
Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pages =
When Truthful Representations Flip Under Deceptive Instructions? , author =. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pages =. 2025 , publisher =. doi:10.18653/v1/2025.emnlp-main.826 , url =
-
[43]
Proceedings of the AAAI Conference on Artificial Intelligence , volume =
When Truth Is Overridden: Uncovering the Internal Origins of Sycophancy in Large Language Models , author =. Proceedings of the AAAI Conference on Artificial Intelligence , volume =. 2026 , doi =
2026
-
[44]
Enhancing Uncertainty Estimation in
Xiao, Zeguan and Dou, Diyang and Xiong, Boya and Chen, Yun and Chen, Guanhua , journal =. Enhancing Uncertainty Estimation in. 2026 , doi =
2026
-
[45]
and Wang, Rui , booktitle =
Wang, Yiming and Zhang, Pei and Yang, Baosong and Wong, Derek F. and Wang, Rui , booktitle =. Latent Space Chain-of-Embedding Enables Output-Free. 2025 , url =
2025
-
[46]
Are the Hidden States Hiding Something? Testing the Limits of Factuality-Encoding Capabilities in
Servedio, Giovanni and De Bellis, Alessandro and Di Palma, Dario and Anelli, Vito Walter and Di Noia, Tommaso , booktitle =. Are the Hidden States Hiding Something? Testing the Limits of Factuality-Encoding Capabilities in. 2025 , publisher =. doi:10.18653/v1/2025.acl-long.304 , url =
-
[47]
Schouten and Peter Bloem and Ilia Markov and Piek Vossen , booktitle=
Stefan F. Schouten and Peter Bloem and Ilia Markov and Piek Vossen , booktitle=. Truth-value judgment in language models:. 2025 , url=
2025
-
[48]
Masked by Consensus: Disentangling Privileged Knowledge in
Ashuach, Tomer and Gretz, Shai and Katz, Yoav and Belinkov, Yonatan and Ein-Dor, Liat , booktitle =. Masked by Consensus: Disentangling Privileged Knowledge in. 2026 , address =. doi:10.18653/v1/2026.acl-long.483 , pages =
-
[49]
Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , year =
Cognitive Dissonance: Why Do Language Model Outputs Disagree with Internal Representations of Truthfulness? , author =. Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing , year =. doi:10.18653/v1/2023.emnlp-main.291 , pages =
This paper was first reviewed by deepseek-v4-flash on August 1, 2026.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.