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Don't Always Pick the Highest-Performing Model: An Information Theoretic View of LLM Ensemble Selection

Yigit Turkmen, Baturalp Buyukates, Melih Bastopcu

arXiv:2602.08003v1cs.LGcs.AIcs.DCcs.ITmath.ITstat.ML

TL;DR

Choosing models under a query budget is difficult when model outputs are correlated and querying the full pool is costly. The paper selects models by their information about a binary ground truth, models error dependence with a Gaussian copula, and shows correlated ensembles can retain a non-vanishing error probability as their size grows.

  • Problem

    Which models to select under a query budget is a challenge because LLM outputs can be unstable, models are correlated, and querying the full pool can be costly.

    Source: §1 · p. 1

  • Method

    The paper uses mutual information about a binary ground-truth label to select models, accounting for how much information each adds beyond the current subset.

    Source: §1 · p. 1

  • Results

    Correlated models can leave a non-vanishing ensemble error probability, while under independent errors the optimal selection is the most accurate models.

    Source: §1 · p. 2, §7 · p. 9

  • Takeaways & Limitations

    The authors suggest complementing selection strategies with greater model diversity and more data to estimate the required information-theoretic quantities as routes to further improvement.

    Source: §8 · p. 9

    The analysis focuses on binary decisions; richer output spaces and alternative dependency structures remain directions for future work.

    Source: §8 · p. 9

Abstract

from arXiv · show

Large language models (LLMs) are often ensembled together to improve overall reliability and robustness, but in practice models are strongly correlated. This raises a fundamental question: which models should be selected when forming an LLM ensemble? We formulate budgeted ensemble selection as maximizing the mutual information between the true label and predictions of the selected models. Furthermore, to explain why performance can saturate even with many models, we model the correlated errors of the models using Gaussian-copula and show an information-theoretic error floor for the performance of the ensemble. Motivated by these, we propose a simple greedy mutual-information selection algorithm that estimates the required information terms directly from data and iteratively builds an ensemble under a query budget. We test our approach in two question answering datasets and one binary sentiment classification dataset: MEDMCQA, MMLU, and IMDB movie reviews. Across all datasets, we observe that our method consistently outperforms strong baselines under the same query budget.

1. Introduction

The introduction frames model selection under a query budget as difficult because LLM errors are correlated, making accuracy-only selection unreliable. It motivates information-theoretic selection and a Gaussian-copula account of saturation, then reports consistent gains over strong baselines.

1. Introduction

  • Under a per-query budget, selecting a subset is difficult because models can share error patterns, so another high-accuracy model may add little new information.The paper notes that querying the full model pool is often infeasible because of latency and monetary costs.Source: §1 · p. 1
  • A Gaussian-copula representation captures individual model accuracies and correlations, and simulated errors effectively reproduce real-model error behavior.The paper uses this model to study correlated errors and ensemble saturation.Source: §1 · pp. 1–2
  • With independent LLM decisions, selecting the most accurate models is optimal; the introduction attributes Top-k's practical breakdown to error correlation.The independent case is established in Theorem 4.1.Source: §1 · p. 2
  • Greedy selection maximizes mutual-information gain, and Theorem 4.3 connects the rule to mRMR feature selection.In the correlated regime, a model's value depends on the new information it contributes relative to the current subset.Source: §1 · pp. 1–2
  • Under uniform pairwise correlation, adding models does not necessarily drive error probability to zero; it converges to a fundamental limit.The introduction says this limit explains why adding correlated models may fail to further reduce error.Source: §1 · p. 2
  • The method consistently improves over strong baselines, including Top-k by accuracy, under identical query budgets.It is evaluated on MEDMCQA, MMLU, and IMDB movie reviews.Source: §1 · p. 2

2. Related Work

Related work covers LLM ensemble aggregation and selection, mutual-information feature selection, and Gaussian-copula modeling. The paper distinguishes its focus on selecting models using their cross-model error structure.

LLM Ensembles

  • Prior LLM ensemble work includes voting, cascaded selection, diversity-based pruning, and aggregation; this paper instead asks which models to select using Gaussian-copula correlation structure.The related work notes evidence of diminishing or negative returns from adding models and identifies error correlation as a likely culprit.Source: §2 · p. 2

Information-Theoretic Feature Selection

  • Mutual-information feature selection methods such as mRMR balance relevance against redundancy, but the paper says this intuition does not transfer to ensemble selection.The related work describes these methods as approximating conditional mutual information and penalizing inter-feature correlation.Source: §2 · p. 3

Gaussian-Copula Models

  • Earlier Gaussian-copula work models refusal behavior within one LLM or dependent correctness for confidence estimation; this paper applies it to cross-LLM ensemble errors and selection.The paper uses the model for an information-theoretic saturation theorem and mutual-information-driven greedy selection.Source: §2 · p. 3

3. System Model and Problem Formulation

The paper defines a binary LLM classification setting and models dependent errors with a Gaussian copula. It formulates budgeted subset selection by ensemble error, using MAP aggregation when the joint error law is known.

3. System Model and Problem Formulation

  • The system uses a balanced binary label Y and binary model predictions; an error indicator is one when a model's prediction differs from Y.Responses are related to errors by X_j = Y·(-1)^E_j.Source: §3 · p. 3

3.1. Modeling Latent Errors with Gaussian-Copula

  • A Gaussian-copula model represents the joint error distribution with latent Gaussian variables and pairwise correlations between models.The correlation matrix has unit diagonal entries and off-diagonal entries ρ_ij.Source: §3.1 · p. 3
  • With equal pairwise correlations, the latent dependence can also be represented by a shared factor and independent individual noise terms.This is the equicorrelated case described by the factor model.Source: §3.1 · p. 3
  • Thresholds set each model's marginal error probability, while the correlation matrix governs dependence among errors.The Gaussian-copula construction separates marginal error statistics from the dependence structure.Source: §3.1 · p. 3

3.2. Ensemble Aggregation and Selection

  • When the joint error distribution is known, MAP aggregation minimizes decision error; subset performance is measured by its expected MAP error probability.The paper implements Algorithm 3 for MAP aggregation.Source: §3.2 · p. 3

3.3. Problem Formulation

  • Given a budget of k calls from m models, the problem is to select a size-k subset minimizing ensemble error, a combinatorial task dependent on the joint error law.The formulation explicitly allows correlated model errors.Source: §3.3 · p. 4
  • The independent binary symmetric channel case corresponds to Σ = I and ρ = 0; equal pairwise correlation enables closed-form saturation limits.The paper studies the independent case in Theorem 4.1 and the equicorrelated case for Theorem 4.4.Source: §3.3 · p. 4

4. Information-Theoretic Analysis of Ensemble Selection

The analysis shows why accuracy-based selection is optimal under independent errors but insufficient when model errors are correlated. It decomposes information gain under dependence and establishes a non-zero error floor as correlated ensembles grow.

4. Information-Theoretic Analysis of Ensemble Selection

  • The analysis frames error-optimal subset selection as combinatorial and contrasts top-k accuracy heuristics with mutual-information maximization.It examines independent errors, correlation’s information-theoretic penalty, and the limit on achievable error.Source: §4 · p. 4

4.1. Optimal Subset Selection Under Independence

  • Under independent errors, the top-k most accurate models maximize mutual information and minimize error, so accuracy-based and information-theoretic selection coincide.The paper attributes top-k selection’s failure in practice to the correlation structure among models.Source: §4.1 · p. 4

4.2. Decomposition of Correlated Ensembles

  • For correlated models, marginal information gain decomposes into relevance, a redundancy penalty, and an error-correlation term under label-invariant errors.The error-correlation term can be beneficial when structured, because knowing the selected models’ error pattern can help decode the label.Source: §4.2 · pp. 4–5

4.3. Asymptotic Saturation Limit

  • With uniform positive pairwise correlation, the optimal MAP error converges to a non-zero floor as the ensemble grows.The floor reflects the information limit imposed by latent common noise, not suboptimal aggregation; increasing ensemble size cannot overcome structural correlations.Source: §4.3 · p. 5

5. Proposed Selection Algorithm: Greedy Mutual Information (Greedy MI)

Because optimal subset selection is NP-hard, the paper proposes a tractable greedy strategy that builds a model subset by maximizing marginal information gain. Its criterion accounts for redundancy and structured error dependence.

5. Proposed Selection Algorithm: Greedy Mutual Information (Greedy MI)

  • The greedy strategy approximates the optimal subset because the mutual-information optimization is NP-hard.In correlated ensembles, its marginal gain includes dependence terms, so classical mRMR intuition does not directly apply.Source: §5 · p. 5

5.1. Selection Criterion

  • The algorithm iteratively adds the unselected model with the greatest estimated marginal information gain until the target subset size is reached.The paper says it computes full conditional mutual information I(Y; X_j | X_S) in practice to account for potential label-dependent error structure.Source: §5.1 · pp. 5–6
  • The selection score is estimated from training-set empirical mutual information terms without training LLM parameters.Model outputs are treated as discrete random variables, with joint distributions estimated by frequency counts.Source: §5.1 · p. 5

6. Experimental Results

Greedy MI shows its clearest error reductions over baselines at moderate ensemble sizes on MEDMCQA and MMLU. It also consistently outperforms baselines in IMDB’s mid-budget range, where models are highly correlated.

6.1. Experiments on MEDMCQA; 6.2. Experiments on MMLU

  • MEDMCQA evaluation uses 4,183 validation samples converted into 8,366 binary queries; MMLU uses 5,000 test questions converted into 10,000 binary samples, with 80/20 estimation and evaluation splits.The MMLU sample is selected from 14,042 test examples.Source: §6.1 · p. 6, §6.2 · p. 8

6.1. Experiments on MEDMCQA

  • 16.3% test error at k = 5 versus 17.0% for Top-k; Greedy MI’s improvement is most pronounced at k = 3–7.Results are averaged across temperatures, runs, and random splits.Source: Figure 5 · p. 7, §6.1 · p. 7
  • The MEDMCQA copula validation compares empirical and simulated pairwise and higher-order simultaneous error patterns; the fitted 12 × 12 correlation matrix has average correlation ρ̄ = 0.55.Synthetic error indicators are generated from a multivariate normal and thresholded using model-specific accuracy thresholds.Source: Figure 4 · p. 6, §6.1 · p. 7
  • At k = 3 on MEDMCQA, Greedy MI selects Qwen3-235B (77.4%, ranked fifth), while mRMR selects GPT-4.1-nano (66.8%, ranked 11th).At k = 5, Greedy MI spans five model families; Top-k instead stacks four OpenAI models early.Source: §6.1 · pp. 7–8, Table 1 · p. 7

6.2. Experiments on MMLU

  • 0.144 test error at k = 4 and 0.141 at k = 6, versus 0.150 and 0.149 for Top-k, respectively.Greedy MI’s clearest gains are in the budget-relevant k = 3–8 range; all methods converge near 0.171 by k = 13.Source: Figure 6 · p. 8, §6.2 · p. 8

6.1. Experiments on MEDMCQA; 6.2. Experiments on MMLU

  • As ensemble size grows, gains diminish and errors approach a non-zero floor; with limited estimation data, rare or unseen output patterns make MAP aggregation noisy.On MMLU, all methods are around 0.171 by k = 13; using all 12 MEDMCQA models also degrades performance.Source: §6.2 · p. 8, §6.1 · p. 8

6.2. Experiments on MMLU

  • On MMLU, Greedy MI adds Qwen3-235B (82.2%) at k = 2 and Kimi-K2 (82.1%) at k = 3, while mRMR selects lower-accuracy alternatives.At k = 5, every Greedy MI model exceeds 79% accuracy across four families; within-family correlations are about 0.8, compared with 0.6–0.7 across families.Source: §6.2 · pp. 8–9, Table 2 · p. 8

6.3. Experiments on IMDB Movie Reviews Dataset

  • On IMDB, Greedy MI consistently outperforms baselines in the mid-budget range, though gains are modest with average pairwise correlation ρ̄ = 0.90.Models have uniformly high accuracies of 91–96%.Source: §6.3 · p. 9

7. Conclusion

The paper studies fixed-budget LLM ensembling with correlated outputs, modeling responses using a Gaussian copula. It proposes Greedy MI and reports that it consistently outperforms strong baselines across multiple datasets.

7. Conclusion

  • Correlations make accuracy alone insufficient for ensemble selection, and even an optimal estimator can have non-vanishing error.For independent decisions, selecting the most accurate models is optimal; the paper develops Greedy MI for the correlated, budget-constrained setting.Source: §7 · p. 9
  • The Gaussian-copula model captures individual model accuracies and inter-model correlations in the binary decision setting.The paper presents the model as an effective representation of LLM responses.Source: §7 · p. 9
  • Greedy MI greedily constructs a near-optimal LLM ensemble under budget constraints and consistently outperforms strong baselines across multiple datasets.Source: §7 · p. 9

8. Limitations and Discussion

The analysis focuses on binary decisions as a foundational step toward more general formulations. The authors identify richer output spaces and alternative dependency structures as directions for future work.

8. Limitations and Discussion

  • The study is limited to a binary decision setting, chosen for a clean and interpretable information-theoretic analysis.The authors describe it as a foundational step toward more general formulations.Source: §8 · p. 9
  • Extending the analysis to richer output spaces and alternative dependency structures remains future work.The authors also suggest model diversity and larger training datasets for estimating information-theoretic quantities as possible ways to improve ensemble performance.Source: §8 · p. 9

Impact Statement

The paper frames its contribution as analytical tools for improving the reliability and efficiency of existing aggregation methods, without introducing new data collection mechanisms or decision policies that directly affect individuals.

Impact Statement

  • The framework may help practitioners design more reliable and cost-effective LLM systems and reduce unnecessary computational and environmental costs from indiscriminate model querying.Source: Impact Statement · p. 9
  • The framework does not introduce new data collection mechanisms or decision policies that directly affect individuals.Source: Impact Statement · p. 9

Appendix

A. Proof of Theorem 4.1

The proof shows that, for independent binary symmetric channels, selecting the k channels with the smallest error rates is optimal. It establishes this by constructing a stochastic degradation from the top-k outputs to those of any competing subset.

A. Proof of Theorem 4.1

  • A BSC flips each input symbol independently with crossover probability ϵ, so its error rate is ϵ.Source: A. Proof of Theorem 4.1 · p. 14
  • When ϵ1 ≤ ϵ2 < 1/2, a BSC with error rate ϵ2 is obtained by further corrupting the output of the ϵ1 BSC with independent noise.The proof uses this stochastic degradation to construct outputs with the competing channels’ error rates.Source: A. Proof of Theorem 4.1 · pp. 14–15
  • Theorem 4.1 states that for independent BSCs, the top-k channels with the smallest error rates achieve at least as much mutual information as any size-k subset.The proof constructs a degraded version of any competing subset from the top-k outputs, then applies the Data Processing Inequality.Source: A. Proof of Theorem 4.1 · pp. 14–15
  • The constructed degradation preserves each competing channel’s error rate and yields outputs with the joint distribution of the competing subset.The proof pairs channels by error rate and adds independent degradation noise.Source: A. Proof of Theorem 4.1 · pp. 14–15
  • Any decision rule on a competing subset can be replicated from the top-k outputs by generating the degraded outputs first, so the top-k estimator has no greater error.Source: A. Proof of Theorem 4.1 · p. 15
  • The inequalities are equalities when the subset is the top-k set, while any other subset strictly degrades at least one component.Source: A. Proof of Theorem 4.1 · p. 15
  • The result extends to any prior probability P(Y = 1) = p in (0, 1), because the proof relies on the Markov chain and Data Processing Inequality.Source: A. Proof of Theorem 4.1 · p. 15
  • For the example with error rates 0.1, 0.2, and 0.4, the top-k subset {1, 2} has at least as much mutual information and no greater error than {1, 3}.The construction degrades the second model’s output with crossover probability 1/3 to match the novice channel.Source: A. Proof of Theorem 4.1 · p. 16

B. Proof of Theorem 4.3

The proof decomposes a model’s information gain into accuracy, redundancy, error dependence, and a label-dependent correction; the Gaussian-copula analysis establishes an asymptotic error floor under correlated errors.

B. Proof of Theorem 4.3

  • Conditioning on the true label makes each model output bijective with its error indicator, allowing entropy identities to rewrite the information gain in error terms.The proof uses this correspondence and mutual-information chain rules to derive the decomposition.Source: B. Proof of Theorem 4.3 · pp. 17–18
  • The decomposition separates a model’s accuracy, prediction redundancy, error correlation, and label-dependent correction when measuring its incremental information gain.The proof expresses the gain as I(Y; Xj) − I(Xj; XS) + I(Ej; ES | Y), with the correction accounting for label-dependent error behavior.Source: B. Proof of Theorem 4.3 · p. 18
  • When model errors are independent of the label, the correction vanishes and the gain reduces to accuracy minus redundancy plus error correlation.The simplified expression is Δ(j | S) = I(Y; Xj) − I(Xj; XS) + I(Ej; ES).Source: B. Proof of Theorem 4.3 · p. 18
  • For balanced binary classification, the correction is bounded in magnitude by 1 bit and vanishes as joint label-dependence in error patterns approaches zero.The authors suggest ignoring the correction when empirical estimates indicate weak joint dependence between errors and labels.Source: B. Proof of Theorem 4.3 · p. 19

C.1. Model recap and notation

  • The Gaussian-copula model uses a balanced binary label, a common latent factor, independent Gaussian factors, and thresholds chosen to match marginal accuracy.The common factor yields equicorrelated latent scores; thresholding defines errors, and model outputs are sign-flips of the label.Source: §C.1 · p. 20

C.2. Proof of Theorem 4.4

This section presents proofs characterizing an asymptotic error floor under correlated model errors and decomposing ensemble information into difficulty-aware information and a difficulty penalty, alongside implementation details for information estimation and aggregation. It also describes Gaussian-copula fitting, synthetic error generation, and additional MEDMCQA and MMLU procedures and results, including aggregation comparisons and copula validation.

C.2. Proof of Theorem 4.4

  • For ρ>0 and α∈(1/2,1), the asymptotic MAP/majority error floor lies in (0,1/2), vanishes as ρ→0, and tends to 1−α as ρ→1.MAP and majority have equal error probabilities for every ensemble size; as ρ→1, perfectly correlated models provide no ensemble gain.Source: §C.2 · p. 21

D. Difficulty-Aware Decomposition and the Price of Difficulty

  • I(Y;X_S)=I(Y;X_S|D)−I(Y;D|X_S): the first term is difficulty-aware information, while the second is the Price of Difficulty.A nonvanishing Price of Difficulty means adding models cannot fully remove label uncertainty, explaining ensemble saturation.Source: D. Difficulty-Aware Decomposition and… · p. 22

D.1. Proof of Theorem D.1

  • Conditional independence given (Y,D) makes F(S)=I(Y;X_S|D) monotone submodular, so greedy selection has a (1−1/e) approximation guarantee under a cardinality constraint.The proof uses an entropy representation: conditional entropy given (Y,D) is modular, while H(X_S|D) is submodular.Source: D. Difficulty-Aware Decomposition and… · p. 22, §D.1 · p. 23

E. Implementation Details

  • The implementation section covers mutual-information estimation, MAP, majority and weighted-majority aggregation, and Gaussian-copula parameter estimation for correlated errors.It presents the estimation method before aggregation pseudocode and concludes with copula-estimation details.Source: E. Implementation Details · p. 24

E.1. Mutual Information Estimation

  • With α=1 add-one smoothing, mutual-information estimation uses empirical marginal and joint counts, keeping probabilities positive to avoid log 0 and stabilize estimates for rare or absent outcomes.It computes I(A;B)=H(A)+H(B)−H(A,B) from the smoothed distributions.Source: §E.1 · p. 24

E.2. Aggregation Methods

  • MAP uses smoothed empirical prediction-pattern counts without a conditional-independence assumption; majority weights models equally, while weighted voting uses accuracy log-odds optimal under independent errors.Majority breaks ties randomly when the ensemble size is even; weighted-vote accuracies are estimated from the training split.Source: §E.2 · p. 25
  • The weighted-majority aggregation expression is equivalent to the sign of a weighted majority vote.Source: §E.2 · p. 27

E.3. Gaussian-Copula Fitting and Sampling Algorithm

  • The copula procedure estimates marginal error rates and thresholds, fits pairwise latent correlations, regularizes the correlation matrix, then samples and thresholds latent Gaussian variables to generate synthetic errors.It uses tetrachoric correlations to match observed joint error probabilities and projects the estimated matrix to positive semidefinite form by clipping negative eigenvalues and renormalizing diagonals.Source: §E.3 · p. 28

F. Additional Experimental Details for the MEDMCQA Dataset

  • MEDMCQA uses a binary True/False prompt that asks whether the candidate answer is correct and requests a single-word response.The paper states that models were accessed through OpenRouter to standardize inference.Source: F. Additional Experimental Details for… · p. 29

F.1. Experiments across Temperature and Runs (the MAP aggregation)

  • MEDMCQA MAP experiments aggregate test error across 30 evaluations, covering three temperatures, two runs, and five random 80/20 splits.Figure 7 presents per-condition curves, while Table 4 reports mean ± std test error at each ensemble size k.Source: §F.1 · p. 29, Figure 7 · p. 29

F.2. Alternative Aggregation Rules

  • Greedy MI remains most competitive at moderate budgets under alternative aggregation rules, while mRMR is unstable and methods converge at larger budgets.Under MV, Terms 1+2 has 0.264 error at k = 2, versus 0.181 for Top-k and Term 1 and 0.171 for Greedy MI (MAP); at k = 5, Greedy MI has 0.163 versus 0.170 for Top-k. Under W-MV, Terms 1+2 has 0.204 error at k = 4 and 0.197 at k = 6, while Greedy MI (MAP) achieves 0.163 ± 0.008 at k = 4 and 0.164 at k = 6. At k ≥10, methods begin to converge; the passage attributes some large-k Greedy MI underperformance to near-optimal selection and increasingly difficult joint-distribution estimation.Source: Figure 8 · p. 30, §F.2 · p. 30, Figure 9 · p. 31

F.3. Copula Validation Plots across Temperatures and Runs

  • Copula predictions closely match MEDMCQA pairwise joint error probabilities and distributions of simultaneous errors across the evaluated settings.The pairwise comparison covers 66 model pairs across six temperature-run conditions; the simultaneous-error plots compare empirical and copula-generated frequencies.Source: §F.3 · p. 31, Figure 10 · p. 32, Figure 11 · p. 32

G. Additional Experimental Details for the MMLU Dataset

  • MMLU uses a binary True/False prompt asking whether a candidate answer is correct and requiring a single-word response.The paper states that models were accessed through OpenRouter to standardize inference.Source: G. Additional Experimental Details for… · p. 33

G.1. Experiments across Temperature and Runs (the MAP Aggregation)

  • MMLU MAP experiments aggregate test error across 30 evaluations, with three temperatures, two runs, and five random 80/20 splits.Figure 12 shows per-condition curves, and Table 8 aggregates mean ± std test error by ensemble size k.Source: §G.1 · p. 33, Figure 12 · p. 33

G.2. Experiments with Alternative Aggregation Rules

On MMLU, Greedy MI remains competitive under alternative aggregation rules, particularly at moderate budgets, while Gaussian-copula predictions closely match observed pairwise and simultaneous-error patterns. On IMDB, selection gains are modest and often within noise, where methods perform similarly and error structure is also captured by the copula.

G.2. Experiments with Alternative Aggregation Rules

  • Under MV, Greedy MI's MMLU error was 0.148 at k = 3 versus 0.219 for Terms 1+2; under W-MV, it was 0.144 ± 0.007 at k = 4 versus 0.174 for Terms 1+2.At larger budgets, W-MV can narrow the gap for simpler selectors; Greedy MI remains most competitive in the moderate-budget regime.Source: §G.2 · p. 34, Figure 13 · p. 34, Figure 14 · p. 35

G.3. Copula Validation across Temperature and Runs

  • Across six MMLU conditions, 78 pairwise error fits cluster near the ideal diagonal, and copula-predicted simultaneous-error frequencies closely match observed frequencies.The simultaneous-error diagnostic counts how many models err on the same instance, exposing higher-order dependencies relevant to ensemble performance.Source: §G.3 · p. 35, Figure 15 · p. 36, Figure 16 · p. 36

H. Experimental Details for the IMDB Movie Reviews Dataset

  • IMDB evaluation sampled 10,000 of 25,000 test queries, balanced 5,000 positive and negative examples, across three temperatures and two runs.The positive and negative sentiment labels were mapped to true and false, respectively, for the binary-classification framework.Source: H. Experimental Details for the IMDB… · p. 37

H.2. Experiments with Alternative Aggregation Rules

H.3. Copula Validation

  • On IMDB, pairwise fits stay near the diagonal; simultaneous errors concentrate at k = 0 and are accurately captured by the copula, with k ≥ 2 nearly absent.The authors connect the near-absence of multiple simultaneous errors to limited gains from selection.Source: §H.3 · p. 37, Figure 20 · p. 40, Figure 21 · p. 40

H.1. Experiments Across Temperatures and Runs (MAP aggregation)

  • On IMDB, 91–96% model accuracy and mean correlation 0.90 accompany modest, often noise-level selection gains; high correlations and shared ambiguous reviews leave little room to improve.The authors connect the limited gains to the error floor under near-uniform high correlation and to intrinsically difficult reviews that models tend to misclassify together.Source: §H.1 · p. 37, Figure 17 · p. 38, Table 12 · p. 45

I. Supplementary Tables

  • For IMDB, supplementary Table 12 averages test errors over 30 evaluations, while Table 15 lists 12 models' accuracies and copula parameters averaged over six runs.Table 12 covers three temperatures, two runs, and five splits; Table 15 sorts the model pool by accuracy.Source: Table 12 · p. 45, Table 15 · p. 47
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