Great Models Think Alike and this Undermines AI Oversight

• AI oversight uses LMs to annotate training data and score model outputs, offering a scalable alternative to slow and expensive human preferences or expert annotations.The paper uses “AI oversight” for these training and evaluation techniques together.Source: §1 · p. 1
• CAPA extends error consistency by accounting for prediction differences and output probabilities, enabling chance-adjusted measurement of functional similarity between models.It adjusts for chance agreement arising from model accuracies.Source: §1 · p. 2

LLM-as-a-Judge

• LLM judges assign higher scores to models more similar to themselves, extending concerns about self-preference to affinity between similar models.This finding motivates accounting for model similarity when interpreting LLM-as-a-judge evaluations.Source: §1 · p. 2

Training LMs on annotations of other LMs

• Weak-to-strong training gains are higher when weak supervisors and strong student models are more different, because complementary knowledge can improve the student’s performance ceiling.The result concerns setups where a larger student is finetuned on annotations from a smaller supervisor.Source: §1 · p. 2

With increasing LM capability errors are becoming more correlated

• As frontier LMs become more capable, their mistakes become more similar, creating risks of common blind spots and correlated failure modes in AI oversight.The paper therefore emphasizes the risks of correlated mistakes and encourages releasing sample-wise predictions alongside benchmark scores for richer similarity analysis.Source: §1 · p. 2

2.1. Background

• Functional metrics compare input–output behavior, support cross-architecture and API-based comparisons, and use interpretable data samples rather than internal representations.The paper focuses on functional similarity because similar mistakes can proxy similar internal mechanisms despite architectural differences.Source: §2.1 · p. 2
• Error consistency adjusts agreement for chance overlap caused by accuracy but incorrectly treats different wrong predictions as agreement and ignores probability distributions.Thus, models that are always wrong in different ways can receive perfect error consistency, while similar probability distributions may produce different binary labels.Source: §2.1 · p. 2, §2.2 · p. 3

2.2. Our Contribution

• CAPA uses output probabilities to distinguish incorrect options, normalizes agreement against independent models’ expected probabilities, and interprets 0 as chance-level agreement.Positive values indicate agreement beyond independence, negative values indicate disagreement, and increasing values indicate more correlated mistakes.Source: Table 1 · p. 3, §2.2 · pp. 3–4
• CAPA reports 0 similarity for independent models with uncorrelated errors, unlike Cohen’s κ, Jensen Shannon distance, and %Agreement, whose scores rise with accuracy.In the simulation, one model has fixed 90% accuracy while the other varies from 50% to 90%.Source: Figure 2 · p. 4, §2.2 · p. 4

3. Affinity Bias in LLM-as-a-Judge

• The affinity-bias problem means using a held-out language model as judge is insufficient because similarity remains a confounding factor.This motivates accounting for model similarity when interpreting scalable LLM-as-a-judge evaluations.Source: §3 · p. 4

3.1. Experimental Setup

• The experiment evaluates 9 judges and 39 models using CAPA on 8,707 free-response-compatible MMLU-Pro questions, comparing judgments with ground-truth accuracy.Models answer each question in MCQ and open-response formats; judges make binary correctness decisions without access to ground-truth solutions.Source: §3.1 · pp. 4–5

3.2. Results & Discussion

• Average Pearson r=0.84 (p < 0.01) between judgment scores and CAPA shows judges favor functionally similar models across families.Qwen2.5-72B-Instruct judged the less capable Qwen2.5-7B-Instruct 71% correct but Llama-3.1-70B-Instruct 67% correct despite higher MCQ accuracy.Source: Figure 3 · p. 5, §3.2 · p. 5
• After controlling for accuracy, similarity remains significantly associated with judgment scores, with its effect especially large for judges under 32B.Multiple regression finds significant positive effects for both accuracy and similarity, while partial correlations confirm similarity effects even for the best judges.Source: Table 2 · p. 5, §3.2 · p. 5
• Elo scores from binary preference judgments on AlpacaEval also strongly correlate with MMLU-Pro model similarity, extending affinity bias beyond question answering.The result indicates that similarity bias affects preference-based chat evaluation as well as technical correctness judgments.Source: §3.2 · p. 5

4. Learning from Complementary Knowledge of LM Annotators

• The proposed mechanism is that complementary knowledge appears as differing training-set predictions, so lower κp should correspond to larger gains from supervisor annotations.This frames model similarity as an a priori predictor of performance improvement when models learn from one another.Source: §4 · p. 6

4.2. Results & Discussion

• Complementary knowledge contributes beyond elicitation: weak-to-strong accuracy averages 42.2% where the strong elicited model is wrong, while elicitation explains 71.9% where the weak supervisor is wrong.The decomposition averages results across 15 tasks and 12 model pairs, confirming that both mechanisms contribute to weak-to-strong gains.Source: Figure 5 · p. 6, §4.2 · p. 7

4.1. Experimental Setup

• The study evaluates 12 weak–strong model pairs across 15 binary NLP tasks, measuring validation-set similarity before confidence-weighted weak-to-strong training.Weak models contain 1–3B parameters and strong models 7–9B; the setup follows Burns et al. (2024) and the reproduction of Scherlis et al. (2024).Source: §4.1 · p. 6

4.2. Results & Discussion

• Similarity inversely predicts weak-to-strong gains: r = −0.85 across model combinations, remaining significant after controlling for accuracy gaps (r = −0.35, p < 0.01).Less correlated supervisor–student errors tend to produce greater improvements, and the trend also holds with alternate similarity metrics.Source: §4.2 · pp. 6–7
• A ceiling formed by the union of correct predictions from the weak supervisor and strong elicited model is significantly higher than the elicitation-based ceiling.On unseen samples, the trained model more often falls back to its initial priors, identifying complementary-knowledge use as a concrete improvement target.Source: §4.2 · p. 7, Table 3 · p. 7

5.1. Experimental Setup

• The study evaluates 130 official OpenLLM Leaderboard 2 models on MMLU-Pro and Big Bench Hard, grouping them into five performance ranges and measuring cross-developer mean similarity within each range.Cross-developer comparisons reduce confounding from distillation or continual training.Source: §5.1 · p. 8

5.2. Results & Discussion

• Model capabilities show a strong positive correlation with κp, indicating that models make increasingly similar errors beyond chance agreement due to accuracy.This pattern also holds across individual categories in both datasets, not only in aggregate.Source: §5.2 · p. 8
• Increasingly similar mistakes could amplify affinity bias, reduce inter-LM training gains, undermine LM-jury independence, and create safety risks from correlated failures.As blind spots become harder to detect, greater deference to AI oversight could increase the consequences of correlated model failures.Source: §5.2 · p. 8
• Question difficulty is not a significant confounder, while the similarity trend is stronger in instruction-tuned models and alternative Mamba architectures may not sufficiently increase diversity.The analysis finds only a slight similarity increase for harder questions.Source: §5.2 · p. 8

Model similarity

• Prior work examines differences between models for visual comparative analytics, efficient human evaluation, learning-algorithm comparison, API-update side effects, quantization, and qualitative descriptions of data-distribution differences.Source: §6 · p. 8
• Unlike representation-similarity studies, this work finds increasingly correlated LM mistakes as capabilities improve, extending error consistency with probabilistic, mistake-sensitive measurements.It situates this trend alongside homogenized LM decision outcomes and risks from algorithmic monoculture (Kleinberg & Raghavan, 2021).Source: §6 · p. 8

AI judges

• LM judges systematically favor models making similar mistakes, generalizing self-preference findings and motivating formal evaluator checks such as consistency (Fluri et al., 2024).This extends broader work on judge pitfalls, including verbosity and position biases (Koo et al., 2024; Ye et al., 2025), and affinity bias in human selection.Source: §6 · p. 8

Weak-to-strong training

• Prior weak-to-strong work established training on LM annotations and used misfit error to relate student disagreement to the accuracy gap from the weak supervisor.The paradigm builds on weak-to-strong generalization (Burns et al., 2024), with related applications in image classification and alignment (Zhu et al., 2025).Source: §6 · p. 8
• Unlike misfit error, supervisor–student similarity can a priori predict gains from weak-to-strong training, complementing diversity-based findings in distillation and chess training.Related evidence concerns knowledge distillation for image classifiers (Roth et al., 2024) and chess models surpassing their human training data (Zhang et al., 2024).Source: §6 · p. 9

Conclusion

• CAPA measures functional language-model similarity, revealing judge affinity bias, complementary knowledge in LM-annotation training, and increasingly correlated errors as capabilities improve.These findings motivate measuring and accounting for model similarity as AI oversight becomes more important.Source: §7 · p. 9

Establishing Causation

• Similarity correlates with evaluation and training supervision, but establishing causality requires reducing similarity without harming capabilities.The paper identifies this intervention as a challenging open problem.Source: §7 · p. 9

Extending to similarity metrics for free-text outputs

• Because current analyses use multiple-choice tasks, future work should develop free-text and reasoning similarity metrics for oversight settings such as debate and process supervision.Free-text evaluation remains difficult because existing model-free and model-based metrics are sensitive to syntax and style (Biderman et al., 2024; Papineni et al., 2002; Pillutla et al., 2021; Kocmi et al., 2021; He et al., 2023).Source: §7 · p. 9

Generator-Verifier gap

• Similarity may affect generator-verifier oversight by biasing stylistic judge scores and enlarging the generator-verifier gap when models differ more.This extends the paper’s analysis to tasks where validating solutions is easier than generating them (Song et al., 2025).Source: §7 · p. 9

Safety implications

• Measuring similarity after safety interventions could clarify whether combined safeguards decorrelate benefits and side effects, while revealing collective blind spots and interaction risks among agents.The paper connects this agenda to intervention composition, functionally similar unlearning and refusal training, and possible cooperation or scheming.Source: §7 · p. 9

Qualitative analysis of model differences

• Future work could use similarity metrics to qualitatively describe model differences by identifying data distributions where models are least similar.This would complement quantitative similarity measurement on a given data distribution (Dunlap et al., 2025).Source: §7 · p. 9

Impact Statement

• The paper presents its contribution as foundational analysis of AI-oversight mechanisms rather than research tied to particular applications.Source: Impact Statement · p. 9

A.1. Derivation of CAPA

• CAPA applies the chance-adjusted agreement framework to probabilistic model outputs, computing observed overlap per sample and chance agreement from model-specific correctness probabilities.Its chance calculation adjusts incorrect-option agreement by the number of available options, avoiding the overestimation caused by assuming both models choose the same incorrect option.Source: §A.1 · pp. 18–19
• For binary classification without probabilities, CAPA reduces to error consistency because probabilistic observed agreement becomes discrete agreement and its normalization factor simplifies to 1.Source: §A.1 · p. 19

A.2. Extending CAPA to more than two models

• CAPA extends to more than two models by averaging observed pairwise agreements and pairwise chance agreements across all model pairs, using first-principles logic rather than Fleiss’ κ assumptions.This avoids Fleiss’ κ’s use of Scott’s π-style chance agreement, which is unsuitable for the model-similarity setting described earlier.Source: §A.2 · p. 19

A.3. How to use CAPA beyond multiple choice?

• Beyond multiple choice, CAPA is defined for nominal classification by adjusting incorrect-class agreement by the number of classes, while exact-match use is recommended in discrete form and regression requires assumed error distributions.For unconstrained exact or fuzzy match, independent chance agreement approaches zero; regression instead requires a distance-based observed agreement and assumptions such as Gaussian errors for chance agreement.Source: §A.3 · pp. 19–20

A.4. Detailed Discussion on Design Choices

• CAPA uses Cohen’s κ-style chance agreement because MCQ options are permutable and model similarity should account for each model’s accuracy rather than shared marginal class distributions.The motivating example concludes that κ has the more desirable behavior: with fixed observed agreement, it distinguishes pairs according to their differing accuracies, unlike Scott’s π.Source: §A.4 · pp. 20–21
• CAPA favors an interpretable closed-form overlap metric because correlation, regression, and divergence alternatives complicate probabilistic modeling, contextualization, or accuracy-adjusted interpretation.JSD tends to be lower for higher-accuracy models, while incorporating accuracy-adjusted chance agreement into an information-theoretic divergence remains open; the current metric assumes a uniform MCQ error prior but permits alternative priors.Source: §A.4 · pp. 21–22

A.5. Probabilistic versions of popular agreement metrics

• The appendix defines probabilistic Cohen’s κ, Scott’s π, and Fleiss’ κ by replacing discrete observed agreement with probability-based agreement while retaining their respective chance-agreement assumptions.Probabilistic Scott’s π uses a shared marginal distribution, and the multi-model Fleiss formulation computes observed and chance agreement across model pairs assuming all models annotate every question.Source: §A.5 · p. 22

Observed agreement bounds

• CAPA’s observed agreement is strictly greater than 0 and strictly smaller than 1 because probability products are positive and their sum is strictly smaller than the summed probabilities.This establishes the basic range used in the subsequent bounds for κp.Source: §A.6 · pp. 22–23

Bounds for κp

• κp is strictly below 1 but approaches 1 in the limit, while its theoretical lower bound is −1 and the practical lower bound is greater than −1.Achieving κp = −1 would require zero observed agreement, which is impossible because CAPA computes agreement from positive probabilities.Source: §A.6 · pp. 23–24

Perfect agreement and probability sensitivity

• When models assign probabilities approaching [1, 0] to the same classes, κp approaches 1 despite CAPA not attaining perfect agreement as originally defined by Cohen’s k.The metric’s probability-based formulation also captures observed agreement at finer resolution than response-only agreement.Source: §A.6 · p. 23

Probability-sensitive agreement

• Unlike Geirhos et al. (2020), which computes agreement from equal responses independently of output probabilities, CAPA gives higher agreement to more confident matching predictions.For example, matching probabilities [0.999.., 0.000..1] should receive higher agreement than matching [0.8, 0.2], and CAPA captures this distinction.Source: §A.6 · p. 23

A.7. CAPA comparison with other inter-rater metrics

• In the numerical example, Cohen’s κ and Scott’s π report 0.00 similarity, probabilistic variants remain misleading, and only CAPA accounts for sample-level probabilistic similarity.The models both have 50% accuracy, but the classification-based metrics ignore accuracy and output probabilities.Source: §A.7 · p. 24, Table 5 · p. 24
• The agreement simulation uses 10,000 binary observations to compare probabilistic Cohen’s κ, probabilistic Scott’s π, error consistency, Jensen–Shannon distance, and CAPA.Model A has 90% accuracy and calibration 0.99, while Model B’s calibration increases from 0.01 to 0.99, making the models increasingly similar.Source: §A.7 · p. 25
• CAPA captures increasing model similarity that existing metrics miss, while Cohen’s κ prob can remain at 0 and Scott’s π prob can become incorrectly negative.In the agreement simulation, error consistency stops distinguishing models after matched accuracy, Jensen–Shannon distance initially overestimates similarity, and probabilistic metrics rely on unsuitable marginal assumptions.Source: §A.7 · p. 25, Figure 7 · p. 25
• When model accuracies increase while errors remain uncorrelated, the experiment varies Model B from 50% to 90% accuracy across 10,000 uniformly distributed binary observations.Model A remains at 90% accuracy, and Model B’s correct samples are selected randomly at each of 100 steps.Source: §A.7 · p. 25
• CAPA and error consistency fail to reach -1 when models become maximally probabilistically dissimilar, because both use the original Cohen’s κ equation.An adjusted CAPA using obs-min = max(0, p1 + p2 −1) resolves this lower-bound limitation, causing adjusted CAPA to approach -1.Source: §A.7 · pp. 25–26, Figure 8 · p. 26, Figure 9 · p. 26

B. LLM-as-a-Judge

• The LLM-as-a-judge extension compares CAPA with error consistency, analyzes judge quality and behavior, and evaluates models on open-style MMLU-Pro.It presents these experiments as extensions of the Section 3 LLM-as-a-judge results.Source: B. LLM-as-a-Judge · p. 27
• The evaluation section reports Shapiro–Wilk and Breusch–Pagan tests to verify normality and homoscedasticity assumptions for partial correlations and multiple regression.It also documents MMLU-Pro filtering, free-form chain-of-thought inference, the judge framework, prompts, and the language models used.Source: B. LLM-as-a-Judge · p. 27

B.1. Extended Multiple Regression Analysis with Model Size as a Confounder

• After controlling for model accuracy and size, model similarity remains a significant predictor of judgment score, while model size has an effect size around 0.The analysis standardizes model size and removes six outliers, all involving HuggingFaceTB-SmolLM2-135M-Instruct.Source: Table 6 · p. 27, §B.1 · p. 27

B.3.1. MCQ GROUND-TRUTH

• MCQ probabilities are obtained by applying softmax to OpenLLM Leaderboard 2 log-likelihoods, producing calibrated predictions for base models but overconfident predictions for instruct models.This procedure is used for MMLU-Pro and BBH evaluations.Source: §B.3.1 · pp. 27–28

B.2. Comparison of Judge Scores for Our Similarity vs Error Consistency

• 0.90 mean Pearson r for CAPA exceeds 0.85 for Geirhos et al. (2020) error consistency when relating judge scores to model similarity.Both metrics correlate with judgment scores, but CAPA shows the stronger relationship on filtered MMLU-Pro.Source: §B.2 · p. 27, Figure 10 · p. 28

B.3.2. JUDGE ENSEMBLE WITH ACCESS TO REFERENCE ANSWERS

• Using the same MMLU-Pro questions for free-form and multiple-choice evaluation connects functional performance with LLM-as-a-judge behavior and enables analysis against ground truth.The setup is intended to preserve qualitative differences across model sizes and families while studying evaluator affinity biases.Source: §B.3.2 · p. 28
• Open-style accuracy closely tracks multiple-choice accuracy, with open evaluation typically 5–10% lower except for instruction-tuned Qwen2.5 and Gemma-2 models.For most other families, instruction-tuned and base models perform similarly.Source: §B.3.2 · p. 29

B.3.3. JUDGE SCORE VALIDITY AGAINST REFERENCE-BASED ENSEMBLE

• Most LLM judges correctly rank capable versus less capable models when their scores are compared with a reference-based ensemble’s correctness assessments.The ensemble provides a proxy for the real correctness of responses by using five judges with access to ground-truth options and majority voting.Source: §B.3.2 · p. 28, §B.3.3 · p. 29, Figure 12 · p. 29
• As evaluated models become stronger, judges increasingly overrate wrong responses, revealing capability-dependent positivity and affinity biases despite generally accurate rankings.Qwen2.5-72B-Instruct identifies errors in low-capability models more effectively but develops the same bias as smaller judges on stronger models.Source: §B.3.3 · p. 29

B.4. Judge Preference in Chat Generation Tasks Against Similarity

• The free-form evaluation used 23 instruction-tuned models, nine LLM judges, and 203,665 prompt–model-pair judgments from AlpacaFarm prompts.Judgment Elo was computed from shuffled preferences using a re-implementation of AlpacaEval 2.0.Source: §B.4 · p. 29
• On AlpacaEval 2.0, Judgment Elo shows a clear positive correlation with CAPA similarity measured on MMLU-Pro, despite the domain gap between evaluation tasks.This provides evidence that similarity on a diverse MCQ benchmark can transfer as a predictor across tasks.Source: §B.4 · pp. 29–30, Figure 13 · p. 30

B.5. Judge Score Against Similarity per Category

• Category-level analysis recomputed Judgment Scores and CAPA using only questions and responses from each original MMLU-Pro category.This tests whether filtering questions for free-form evaluation introduced aggregation artifacts such as Simpson’s paradox.Source: §B.5 · p. 30
• Affinity bias persists across every MMLU-Pro category, with nearly all category-level Pearson correlations above 0.75 and statistically significant.The sole exception is google/gemma-2-9b-it on engineering, with r = 0.28 and p = 0.211.Source: §B.5 · p. 30, Figure 14 · p. 31
• The category-level results show affinity bias is not confined to the aggregated filtered MMLU-Pro benchmark, but holds irrespective of category.Each plotted line corresponds to one judge model’s relationship between CAPA and Judgment Score.Source: §B.5 · p. 30, Figure 14 · p. 31

B.6. Statistical Testing

• The statistical validation uses partial correlation and multiple regression to test affinity bias while controlling for MCQ ground-truth accuracy.It also verifies the normality and homoscedasticity assumptions required for these tests across all nine judges.Source: §B.6 · p. 30

B.6.1. QUANTIFYING CORRELATION STRENGTH USING PARTIAL CORRELATION

• Partial correlations remain positive and statistically significant for all judges after controlling for ground-truth accuracy, with r ranging from 0.35 to 0.65.The strongest correlations occur for smaller gemma-2 judges, while Qwen2.5 judges show moderate correlations; all p-values are below 0.05.Source: §B.6.1 · p. 30

B.6.2. MULTIPLE REGRESSION

• Similarity and accuracy significantly predict judgment scores for every judge (p < 0.05), with adjusted R2 values from 0.87 to 0.92; similarity remains significant when controlling for model capability.Reported results include similarity β = 0.59 and accuracy β = 0.51, both p < 0.001, and R2 = 0.91.Source: §B.6.2 · p. 32

B.7. Experimental Setup for Filtering MMLU-Pro

• Filtering retains 8707 of 12032 MMLU-Pro questions judged answerable without reference options, using binary and confidence assessments from Qwen-2.5-32B-Instruct.The filtered benchmark supports evaluation in both MCQ and open-style formats.Source: §B.7 · p. 36

B.8. Experimental Setup to Perform Free-Form Inference on Filtered MMLU-Pro

• Free-form inference removes answer options from five-shot CoT prompts, extracts final answers automatically, and uses vLLM through the LM Evaluation Harness.CoT prompting was included because free-form generation is harder for small base models; prompt-template options were omitted because response quality sometimes decreased.Source: §B.8 · p. 37

B.9. Experimental Setup for LLM-as-a-Judge on Filtered MMLU-Pro

• LLM judges rate responses as correct or incorrect without ground-truth answers or MCQ options, and average binary decisions into Judge Scores after CAPA-based similarity analysis.Samples with differing ground-truth options are excluded from model-judge pair analyses.Source: §B.9 · p. 37

B.10. List of Judges and Evaluated Language Models

• The study uses nine instruction-tuned, open-weight judges from four model families, spanning very small models to 72 billion parameters, while evaluated models also include base models.Both base and instruction-tuned variants were evaluated when available.Source: §B.10 · p. 37

B.11.1. LM-JUDGE PROMPT WITHOUT REFERENCE ANSWER

• The reference-free judge prompt supplies only a question and response, requiring a single-token judgment: “0” for incorrect or “1” for correct.The prompt explicitly forbids justification.Source: §B.11.1 · p. 39

B.11.2. LM-JUDGE PROMPT WITH MCQ OPTIONS

• The reference-aware judge prompt provides the question, ground-truth response, incorrect options, and evaluated response, defining correctness by matching the ground truth.It likewise requires outputting only “0” or “1”.Source: §B.11.2 · p. 39

B.11.3. ORIGINAL MCQ COT PROMPT

• Original five-shot MCQ CoT prompts include answer options and option-letter references, whereas transformed open-style prompts remove options and replace those references with answer text.Final answers remain automatically extractable, and the evaluated models generally follow the transformed instructions.Source: §B.11.3 · p. 40

B.11.4. OPEN-STYLE COT PROMPT

• The open-style chain-of-thought prompt asks models to reason step by step and finish with the selected answer, with minimal adjustments from the original MMLU-Pro prompts.The prompt examples include anatomy and disease questions.Source: §B.11.4 · p. 42

B.11.5. COARSE FILTERING PROMPT

• Coarse filtering labels questions YES when they can be answered from the stem alone and NO when they depend on the answer choices, while fine-grained filtering scores answerability from 1 to 10.The fine-grained rubric ranges from entirely choice-dependent to confidently answerable without options.Source: §B.11.5 · p. 43, §B.11.6 · p. 44

C.1. Setup

• The setup trains a weak supervisor on Dtr1, uses it to annotate Dtr2, and fine-tunes the strong model on those annotations to obtain the weak-to-strong student.The study uses pretrained weak and strong models with training, validation, and test splits of 10,000, 1,000, and 5,000 samples, respectively.Source: §C.1 · p. 45
• The training procedure uses LoRA and a confidence-weighted loss that aligns strong-model predictions with both weak-model outputs and thresholded hardened predictions.The hardened-prediction weight α increases during the initial training phase.Source: §C.1 · p. 45
• Weak-to-strong gain is consistently higher on tasks where models are less similar, while similarity varies mainly by task rather than model pair.This relationship is reported using weak-to-strong gain on the y-axis and similarity κp on the x-axis.Source: §C.1 · p. 46

C.2. Elicitation vs Complementary Knowledge

• On the training distribution, complementary knowledge transfer contributes at least as much as elicitation, while the trained student generalizes more like the elicited strong model than the weak supervisor.Figure 15 reports mean accuracies of 0.59 for complementary knowledge transfer and 0.56 for elicitation across 15 datasets.Source: §C.2 · p. 47, Figure 15 · p. 47

C.3. Effect of Different similarity metrics

• CAPA has the highest correlation with weak-to-strong gain, although binary classification leaves little advantage over error consistency, whereas 1 −JSD produces a noisier, lower-correlation relationship.All metrics show larger gains when models differ more.Source: §C.3 · p. 47, Figure 16 · p. 48

C.4. Accuracies in Weak-to-Strong training

• Across 15 datasets and 12 model pairs, the initial strong student starts below the weak supervisor, surpasses it after weak-to-strong training, but remains below ground-truth elicitation; combining their correct predictions yields a higher ceiling.The ordering is consistent across datasets, and the union of weak-supervisor and elicited-model predictions defines an even higher performance ceiling.Source: §C.4 · p. 48

C.5. Weak-to-strong Accuracy Value Details in Elicitation vs Complementary Knowledge Analysis

• Complementary knowledge transfer explains much of the beyond-chance accuracy not accounted for by elicitation, beyond roughly 11% random label flips from retraining on another data subset.The approximately 12% both-wrong accuracy is therefore substantially attributable to binary-classification chance effects.Source: §C.5 · p. 48
• Weak-to-strong training surpasses the weak supervisor but remains below the elicitation ceiling, while the complementary-knowledge ceiling is higher still.Figure 17 averages accuracies across 12 model pairs and shows additional scope for improvement from complementary knowledge.Source: Figure 17 · p. 49
• Weak-to-strong training exploits more possible gains from elicitation than from complementary knowledge transfer, although it is nearly always correct when both reference models are correct.It performs better when only the strong elicited model is correct than when only the weak supervisor is correct.Source: Table 11 · p. 50

D.1. Setup Details

• The analysis uses MMLU Pro and 23 multiple-choice BBH tasks, retaining 11,828 MMLU Pro questions with consistent text and correct-option indices across models.These datasets provide the evaluation basis for studying similarity and capability.Source: §D.1 · p. 52
• The study bins 130 models into five accuracy-percentile groups, compares within-bin model pairs, and excludes same-family pairs to reduce family-based confounding.The binning maintains approximately equal model counts and representative pair accuracies across capability levels.Source: §D.1 · p. 52

D.2.1. INSTRUCTION-TUNING EXACERBATES THE TREND

• Instruction-tuned model pairs show a steeper similarity-capability trend than base-model pairs, plausibly because they were fine-tuned on similar instruction datasets.The comparison restricts pairs to the same model type while using the shared capability-binning strategy.Source: §D.2.1 · p. 52, Figure 18 · p. 52

D.2.2. IS THE TREND CONFOUNDED BY QUESTION DIFFICULTIES?

• Average CAPA remains consistent across question-hardness levels, with only a slight increase on the hardest questions, so question difficulty does not significantly confound increasing similarity.Hardness is defined by the percentage of models answering each question correctly, and the result is shown across capability bins.Source: §D.2.2 · p. 53, Figure 19 · p. 53

D.2.3. CAN CHANGING ARCHITECTURE REDUCE MODEL SIMILARITY?

• Among base models, Falcon3 Mamba–Falcon Transformer pairs are most similar, whereas Mamba–Mistral/Llama pairs are least similar; among instruct models, Falcon3 Transformer–Mistral/Llama pairs are most similar.The compared non-Falcon transformers were selected to have accuracies within ±5% of Falcon3 Mamba for comparable capabilities.Source: §D.2.3 · p. 53
• Base models are less similar overall than instruction-tuned models, while Falcon3 Mamba and Falcon3 Transformer retain high similarity despite different architectures.Falcon3 Mamba–Falcon Transformer similarity is attributed potentially to their shared model family, suggesting training data and fine-tuning may matter more than architecture.Source: §D.2.3 · p. 53, Table 13 · p. 54

D.3. Alternative Similarity Metrics

• Discrete κp and κp for M > 2 both increase with capability, while Error Consistency follows the same upward trend and JSD remains flat with high variance.κp for M > 2 directly measures agreement among all models in a capability bin rather than averaging pairwise similarities.Source: §D.3 · p. 54, Figure 20 · p. 54, Figure 21 · p. 55
• κp for M > 2 provides an all-model similarity measure within each capability bin, whereas Discrete κp omits logit information and relies on a similar averaging strategy.The alternative metrics were evaluated under the same binning and averaging settings on MMLU Pro and BBH.Source: §D.3 · p. 54

D.4. Model capability vs similarity across domains

• The capability–similarity increase appears after aggregating across MMLU Pro subjects and BBH tasks, with the within-subject trend consistent across MMLU Pro and significant for most BBH tasks.Limited questions per BBH task reduce result reliability relative to the more robust MMLU Pro analysis.Source: §D.4 · pp. 54–55

D.5. List of models

• The model set spans families, architectures, sizes, versions, and available base and fine-tuned variants to test the capability–similarity trend broadly.These models were drawn from the OpenLLM leaderboard.Source: Table 14 · p. 56

D.4. Model capability vs similarity across domains

• Increasing similarity with model capability holds across all 14 MMLU Pro subjects and most BBH tasks, supporting a domain-robust trend.The BBH results are less pronounced for some tasks because each has at most 250 questions, producing wider confidence intervals and lower reliability than MMLU Pro.Source: §D.4 · pp. 54–55, §D.5 · p. 57, Figure 22 · p. 57