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Great Models Think Alike and this Undermines AI Oversight

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read This paper argues that functional similarity between language models, measured by overlap in mistakes, biases AI judges, drives weak-to-strong training gains, and is increasing with capability, so AI oversight will inherit shared blind…

desk verdict CAPA is a real metric and the capability-similarity trend is a genuine finding; the uniform-chance baseline is a soft spot but not fatal, since discrete error consistency corroborates the trend. read the letter →

arxiv 2502.04313 v2 pith:CSWETT4L submitted 2025-02-06 cs.LG cs.AIcs.CL

Shashwat Goel , Joschka Struber , Ilze Amanda Auzina , Karuna K Chandra , Ponnurangam Kumaraguru , Douwe Kiela , Ameya Prabhu , Matthias Bethge
show 1 more author
Jonas Geiping
This is my paper · ORCID
classification cs.LGcs.AIcs.CL
keywords CAPAmodelsimilarityAIoversightLLM-as-a-judgeweak-to-stronggeneralizationcorrelatederrorserrorconsistencyfunctional
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces CAPA (Chance Adjusted Probabilistic Agreement), a metric that measures how similarly two language models fail by checking whether the mistakes they make overlap more than expected from their accuracies alone. Using CAPA, the paper studies 'AI oversight', the practice of having one language model evaluate or teach another, and reports three findings. LLM judges give systematically higher scores to models whose errors resemble their own, even after controlling for capability. Training a strong student on a weak supervisor's annotations yields larger gains when the two models make different mistakes. Across 130 models on MMLU-Pro and BigBench Hard, mistakes become more correlated as capability increases, which the paper reads as a warning that AI oversight will inherit shared blind spots just when it is most needed.

What carries the argument

CAPA (Chance Adjusted Probabilistic Agreement), denoted $\kappa^p$, is the paper's central object: an agreement metric of the form $(\text{observed} - \text{chance})/(1 - \text{chance})$. Observed agreement $c^p_{obs}$ is the average, over samples, of the inner product of the two models' output probability distributions over the answer options; chance agreement $c^p_{exp}$ assumes independent models that put their average correct probability $p_j$ on the ground-truth option and spread the remaining probability uniformly over the wrong options. This adjusts for accuracy, distinguishes different wrong answers from each other, and uses probabilities rather than hard predictions. The metric generalizes error consistency and is the instrument used to detect judge affinity bias, measure supervisor-student complementarity, and trace the capability-similarity trend.

What would settle it

Run the capability-similarity analysis on models whose wrong-answer choices are heavily concentrated on one option (e.g., a positional bias), and recompute CAPA with the uniform-error null replaced by empirical wrong-option marginals; if the rising trend with capability weakens or reverses, the trend is an artifact of the null model rather than a property of model errors.

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Extended reading notes

Core claim

The paper's central claim is that functional similarity between language models, properly measured, is a hidden confounder in both halves of AI oversight. In evaluation, judges are biased toward similar models: the affinity bias extends beyond self-preference to any model whose error pattern resembles the judge's, with significant partial correlation after controlling for accuracy. In training, complementarity explains weak-to-strong generalization: the less similar the weak supervisor and strong student, the larger the gain, and this complementary knowledge raises the estimated ceiling beyond pure elicitation. Most concerningly, similarity is not fixed: across five capability buckets of 130 models, average pairwise CAPA rises with accuracy, indicating that as models get better they fail in more alike ways. The paper concludes that reporting and correcting for model similarity should become standard practice in AI oversight.

Load-bearing premise

The chance-agreement baseline in CAPA assumes that when a model is wrong, its probability mass is spread evenly over all wrong answer choices; if real models have systematic preferences among wrong options, the computed similarity values and all three trends could be biased.

Editorial extensions

If this is right

  • Leaderboard scores produced by LLM-as-a-judge inherit the judge's error pattern: excluding the judge's own family from a ranking is not enough, and similarity should be reported or regressed out.
  • Weak-to-strong training gains can be predicted before training from supervisor-student CAPA, and the previously estimated ceiling from elicitation is too low; exploiting complementary knowledge is a concrete avenue for better weak-to-strong methods.
  • If correlated errors keep rising with capability, LM juries are less independent than they appear, and majority-vote oversight can amplify a shared blind spot rather than cancel it.
  • Model diversity itself becomes a safety-relevant property: measuring CAPA between candidate models can flag when an oversight stack is about to lose its independent checkers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The uniform-error null model is the piece most worth stress-testing: if real models concentrate wrong-answer probability on particular options (a position bias), CAPA could be systematically inflated, so re-deriving CAPA with empirical wrong-option marginals is a natural robustness check.
  • The paper's finding that instruction-tuned models show a steeper similarity trend suggests a testable intervention: training with deliberately diversified instruction data or distinct alignment targets might slow error convergence and preserve oversight value.
  • The affinity-bias result implies a concrete debiasing recipe the paper does not test: assembling a jury whose members have low pairwise CAPA and comparing its verdicts against a single judge.
  • Extending CAPA to free-text responses, via embedding-based agreement, would connect similarity analysis to the oversight setups (debate, process supervision) that the paper names as future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces Chance Adjusted Probabilistic Agreement (CAPA), a pairwise similarity metric for language models defined on MCQ output probabilities. CAPA extends error consistency by counting different wrong predictions as disagreement and by using probabilistic predictions rather than hard labels. The authors apply CAPA to three questions: (i) LLM-as-a-judge scores are positively correlated with judge-model similarity after controlling for accuracy; (ii) weak-to-strong generalization gains are larger when the weak supervisor and the strong student are less similar; and (iii) average pairwise CAPA among 130 open LMs increases with accuracy, implying that model mistakes are becoming more correlated as capabilities improve. The paper concludes that reliance on other LMs for AI oversight carries risks from correlated failures and recommends reporting sample-wise predictions.

Significance. If the empirical findings hold, this is a timely and useful contribution: CAPA is a clean, bounded, probabilistic generalization of error consistency; the affinity-bias result extends self-preference findings to a broader class of similarity; the weak-to-strong analysis offers a new predictor of training gains; and the capability-similarity trend is a falsifiable warning about correlated failures. Strengths include the explicit derivation and simulation of CAPA, partial correlations controlling for accuracy and model size, per-category robustness checks, and the use of multiple alternative agreement metrics in the appendices. The main caveat is that all headline numbers inherit the uniform-distractor chance baseline in Eq. (3), whose validity is not established; the weak-to-strong analysis also excludes several runs in a way that may bias the reported correlation.

major comments (3)
  1. [Section 2.2, Eq. (3), Appendix A.4] The chance-agreement term for incorrect options assumes that a wrong model distributes its error mass uniformly over the |O(x)|-1 non-ground-truth options. This is the only chance baseline in CAPA and is inherited by all three empirical findings. In MMLU-Pro and BBH, wrong options are not semantically exchangeable: models systematically prefer certain distractors, so two conditionally independent models that share a distractor preference will agree on wrong options more often than the uniform null predicts, inflating kappa_p. The defense in Appendix A.4, that MCQ options can be permuted and that answer options are balanced by design, addresses the marginal frequency of correct options, not the conditional distribution of errors over wrong options. Because the Section 5.2 capability trend is the headline safety claim, the paper should show that the trend is not an artifact of this prior. Concretely, I ask for a null or sensitivity analysis that matches per-question accuracy and empirical distractor margins (e.g., permuting wrong-option labels within questions across models or estimating a data-driven wrong-option prior) and for a report of whether the Figure 6 trend and the Table 2 partial correlations survive. The error-consistency result in Appendix D.3 is relevant because it does not use the uniform-wrong-option assumption, but it is presented only qualitatively and should be quantified and tied to this concern.
  2. [Section 4, Appendix C.1] Appendix C.1 reports that three weak models (SmolLM-1.7B, Qwen2.5-0.5B, Llama-3.2-1B) and the Hellaswag dataset were discarded after observing negative weak-to-strong gains or low accuracies. The main Section 4 claim, that lower similarity predicts larger gains, is estimated only on the remaining 12 model pairs. Excluding runs because the outcome variable is unfavorable can induce selection bias and may overstate the strength of the correlation. The paper should either provide a pre-specified inclusion criterion or report a sensitivity analysis that includes the discarded runs, with gains computed on the same scale, so readers can judge whether the qualitative conclusion survives.
  3. [Section 5.2, Figure 6] The headline trend is reported as a 'strong positive correlation' without a correlation coefficient, confidence interval, or p-value, and the 130 plotted points are not independent because each model's mean similarity is computed against overlapping sets of partners from the same bucket. The paper should report the exact statistic (e.g., Pearson or Spearman r with CI) and use a bootstrap or mixed-effects procedure that accounts for the non-independence of pairwise similarities. The per-category analyses in Appendix D.4 are supportive but inherit the same dependence structure.
minor comments (5)
  1. [Abstract and Section 1] The metric is called 'Chance Adjusted Probabilistic Agreement' in the abstract and 'Chance Adjusted Probabilistic Alignment' in the introduction; the name should be unified.
  2. [Appendix A.7] The sentence 'Results are reported in main paper in Sec. A.7' appears to refer to Section 2.2 and Figure 2, not to an appendix section; the cross-reference should be corrected.
  3. [Section 6] The phrase 'canapriori predict gains' is missing a space and should read 'can a priori predict gains'.
  4. [Figure 3 caption] The caption 'Judgment Score Relation with Model Similarity on only across family pairs' is grammatically awkward and should be rewritten as 'on across-family pairs only'.
  5. [Appendix C.5] The phrase 'The astute observer may be confused' is informal for a refereed paper; the point about the bottom-right quadrant can be stated directly.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity; the only by-construction element is a sanity-check simulation that uses the metric's own null model, while the three empirical findings are external correlational analyses.

  1. self definitional [Section 2.2, Eq. 3 and Figure 2 (simulation of independent models)]
    "Then, we define independent models as assigning pj probability to the correct option, and uniformly distributing the remaining 1 − pj probability over the incorrect options. ... In this simulation, for each model we select an independent random subset of samples as correct ... CAPA correctly reports 0 similarity when models have uncorrelated errors."

    The simulated data-generating process is exactly the null model used to define chance agreement c_exp in Eq. 3 (uniform error mass over wrong options). Therefore κp = (c_obs^p − c_exp^p)/(1 − c_exp^p) = 0 follows by construction, not by empirical test. This validates internal consistency but does not independently confirm the metric's interpretation. It is not load-bearing for the paper's main empirical findings, which use CAPA on real model outputs and correlate it with external labels (judge scores, weak-to-strong gains, capability buckets).

full rationale

The paper's central derivation chain is: define CAPA (Eq. 2-4), then use it as a fixed, parameter-free similarity measure in three external correlational analyses. No constant is fitted to produce the reported correlations; p_j is computed from model probabilities, and the weak-to-strong similarity is measured on validation data before training, making it a genuine a priori predictor. The judge-affinity, complementary-knowledge, and capability-similarity findings are empirical associations with independent content. The uniform-error chance baseline in Eq. 3 is an explicit modeling assumption (Appendix A.4); if real models share systematic distractor preferences, κp is biased, but this is a validity or correctness concern rather than circularity, since the result does not reduce to its inputs by construction. The only by-construction element is the Figure 2 simulation, which verifies that CAPA returns 0 on its own null model; this is a sanity check, not a prediction. No load-bearing self-citation or imported uniqueness theorem appears; citations to Geirhos et al. (2020, 2021) and Burns et al. (2024) provide external baselines and setup. Overall circularity is minimal and non-central.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to data: CAPA is computed directly from model probabilities and the uniform-prior null model is a domain assumption, not a fitted value. No new physical or conceptual entities are postulated; the metric itself is an aggregation formula, not an entity.

assumptions (5)
  • domain assumption Independent models distribute their incorrect predictions uniformly over the non-ground-truth options in a multiple-choice question.
    This defines the chance agreement cp_exp in Eq. 3. If real models concentrate their errors on particular wrong options, CAPA's chance baseline is off and all kappa_p measurements are biased.
  • domain assumption Softmaxed log-likelihoods from the OpenLLM Leaderboard are a valid probability distribution over MCQ options.
    Used to compute cp_obs and p_j. The authors note instruct models are overconfident (Appendix B.3.1), which can inflate cp_exp and compress kappa_p values.
  • domain assumption The 130 models in OpenLLM Leaderboard and the 12 W2S model pairs form a representative sample of capability levels and families.
    The capability-similarity trend and the W2S correlations are inferred from these model sets; the W2S set excludes models that produced negative gains (Appendix C.1), narrowing representativeness.
  • domain assumption The LLM-as-a-judge binary choice (0/1) without reference answers is a meaningful proxy for response correctness.
    Used in Section 3. The authors validate against an ensemble with reference answers (Appendix B.3.2), but the main analysis uses the ungrounded judge version to mimic real-world leaderboard settings.
  • domain assumption Standard inter-rater agreement framework (observed agreement minus chance agreement scaled by maximum excess agreement, Eq. 5) applies to model similarity.
    CAPA inherits the kappa-style normalization from Cohen's kappa and error consistency. This framework assumes chance agreement is independent and additive.

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Cite this review

Pith. "Pith review of Great Models Think Alike and this Undermines AI Oversight." pith.science (2026). https://pith.science/paper/CSWETT4L

@misc{pith2026250204313,
  author       = {Pith},
  title        = {Pith review of: Great Models Think Alike and this Undermines AI Oversight},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CSWETT4L}},
  note         = {Machine review of arXiv:2502.04313}
}
read the original abstract

As Language Model (LM) capabilities advance, evaluating and supervising them at scale is getting harder for humans. There is hope that other language models can automate both these tasks, which we refer to as ''AI Oversight''. We study how model similarity affects both aspects of AI oversight by proposing Chance Adjusted Probabilistic Agreement (CAPA): a metric for LM similarity based on overlap in model mistakes. Using CAPA, we first show that LLM-as-a-judge scores favor models similar to the judge, generalizing recent self-preference results. Then, we study training on LM annotations, and find complementary knowledge between the weak supervisor and strong student model plays a crucial role in gains from ''weak-to-strong generalization''. As model capabilities increase, it becomes harder to find their mistakes, and we might defer more to AI oversight. However, we observe a concerning trend -- model mistakes are becoming more similar with increasing capabilities, pointing to risks from correlated failures. Our work underscores the importance of reporting and correcting for model similarity, especially in the emerging paradigm of AI oversight.

Figures

Figures reproduced from arXiv: 2502.04313 by the authors.

Figure 1
Figure 1. Our Main Contributions. We develop a novel proba￾bilistic metric for model similarity, CAPA (κp), which adjusts for chance agreement due to accuracy. Using this, we find (1) LLM-as￾a-judge scores are biased towards more similar models controlling for the model’s capability (2) Gain from training strong models on annotations of weak supervisors (weak-to-strong generalization) is higher when the two models are more di… view at source ↗
Figure 2
Figure 2. Metric comparison for independent models with un￾correlated predictions. In this simulation, for each model we select an independent random subset of samples as correct, with the first having a fixed 90% accuracy, while for the second ac￾curacy is varied from 50% to 90%. CAPA correctly reports 0 similarity when models have uncorrelated errors. Finally, the equation for CAPA is: κp = c p obs − c p exp 1 − c p exp (4)… view at source ↗
Figure 3
Figure 3. Judgment Score Relation with Model Similarity on only across family pairs. Each line is a regression model fit between judgment and similarity scores. The circle shape indicates that only across-family judge-model pairs are plotted. We report for each fit the corresponding Pearson correlation values, r. We found significant positive correlation between judgment scores and CAPA across all judges, ∗∗ indicates p < 0.0… view at source ↗
Figures from the paper (18 more)
Figure 5
Figure 5. Figure 5: Role of Complementary Knowledge and Elicitation in Weak-to-Strong Generalization. We decompose the accuracy of the weak-to-strong trained model on four parts of the test data distribution, based on the correctness of the weak supervisor and an oracle strong elicited mo…
Figure 6
Figure 6. Figure 6: Average Similarity (κp) vs Model Capability. We split 130 LMs into 5 buckets based on their accuracy percentile. For each LM we compute its mean similarity within the bucket (across models from different developers), and plot it against model ac￾curacy. The size of the…
Figure 7
Figure 7. Figure 7: Metric comparison when two models tend towards agreement. For model A we set accuracy to 90% and calibration to 0.99 of the correct answer. For model B we increase its calibration from 0.01 to 0.99 of the correct answer, so its answer distribution becomes increasingly …
Figure 8
Figure 8. Figure 8: Metric comparison when models tend towards disagree￾ment (Read plot from right to left). We compare different metric values for two models in a binary setting. For model A, we set accuracy to 90% and calibration to 0.99 (the model is highly confi￾dent in its answers). …
Figure 10
Figure 10. Figure 10: Judgment Scores vs CAPA and vs Error Consistency. We compare the relationship of judge scores on the filtered MMLU-Pro to our improved error consistency and to the original version of Geirhos et al. (2020) [PITH_FULL_IMAGE:figures/full_fig_p028_10.png]
Figure 11
Figure 11. Figure 11: Accuracy of free-form responses compared with multiple-choice accuracy on MMLU-Pro. The free-form responses were rated using an ensemble of five capable LM judges. Each judge was given access to the original MMLU-Pro reference answers and their decisions whether a giv…
Figure 12
Figure 12. Figure 12: Judgment Scores compared with the ensemble judgment accuracy given access to reference answers. We compare the judgment scores of each judge using only their own knowledge and capabilities to the rating of a judge ensemble that has access to the ground-truth options. …
Figure 13
Figure 13. Figure 13: Elo of LMs on AlpacaEval 2.0 as judged by different LLM-as-judges in relation with our similarity metric on MMLU￾Pro. We compare the Elo obtained by using different judges for binary preference pairs on Alpaca Eval to their similarity on the filtered MMLU-Pro dataset.…
Figure 14
Figure 14. Figure 14: Judgment Score Relation with Model Similarity per Category. This plot shows the same experiment as [PITH_FULL_IMAGE:figures/full_fig_p031_14.png]
Figure 15
Figure 15. Figure 15: We decompose the accuracy of the weak to strong trained model on four parts of the train data distribution based on whether the weak supervisor and an oracle strong elicited model (using ground-truth annotations) are correct or wrong. All results are averaged over 15 …
Figure 16
Figure 16. Figure 16: Various Similarity Metrics vs Weak-to-Strong gain. The highest correlation is seen for CAPA κp, though in the binary classification setup of weak-to-strong generalization the probabilistic information does not add much value compared to error consistency. 1 − JSD give…
Figure 17
Figure 17. Figure 17: Test Accuracies for various models and ceiling estimates in Weak-to-Strong training. The accuracies are averaged over 12 model pairs. The initial strong student model has consistently lower accuracy than the weak supervisor consistent with Burns et al. (2024); Scherli…
Figure 18
Figure 18. Figure 18: LM Similarity (κp) vs Capabilities in Instruct-tuned and Base models on MMLU pro and BBH. After applying the same model binning stratergy and pairwise similarity, a steeper trend is observed in the instruct-tuned models compared to base models for both datasets. Instr…
Figure 19
Figure 19. Figure 19: (a) demonstrates that the overall average similarity remains consistent across different levels of question hardness, with only a slight increase observed for the hardest questions (100th percentile). This consistency indicates that the hardness of the questions does …
Figure 20
Figure 20. Figure 20: Error consistency and JSD for model similarity on BBH and MMLU Pro. The y-axis represents the similarity computed using JSD and Error consistency. JSD exhibits high variance and a flat trend, whereas Error Consistency shows an increasing trend with model capability, s…
Figure 21
Figure 21. Figure 21: Discrete κp and κp for M > 2 values computed on the MMLU Pro and BBH dataset. An increasing trend in similarity is observed across both datasets in accordance with the hypothesis. Discrete κp uses similar averaging idea as used in κp while in κp for M > 2, the similar…
Figure 22
Figure 22. Figure 22: LM Similarity (κp) vs Capability on MMLU pro for each subject. The increasing trend holds for all 14 subjects in MMLU pro. The similarity trend is therefore not a consequence of a particular domain or subject in MMLU Pro. 57 [PITH_FULL_IMAGE:figures/full_fig_p057_22.png]
Figure 23
Figure 23. Figure 23: LM Similarity (κp) vs Capability on each Big-Bench Hard task. The increasing trend holds for most BBH tasks. Each task has atmost 250 questions, resulting in minimal data to compute similarity for the individual tasks. 58 [PITH_FULL_IMAGE:figures/full_fig_p058_23.png]

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Forward citations

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.