Pith. sign in

REVIEW 4 major objections 6 minor 2 cited by

Simple Yet Effective: An Information-Theoretic Approach to Multi-LLM Uncertainty Quantification

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read MUSE aggregates JSD-selected LLM subsets to produce better-calibrated binary predictions than single models or naive ensembles.

desk verdict A genuinely new subset-selection method for multi-LLM calibration, but the unreachable msize=20 configuration and overclaimed results make the empirical story untrustworthy as written. read the letter →

arxiv 2507.07236 v2 pith:2OU7NMBZ submitted 2025-07-09 cs.LG cs.AIcs.CL

Maya Kruse , Majid Afshar , Saksham Khatwani , Anoop Mayampurath , Guanhua Chen , Yanjun Gao This is my paper
classification cs.LGcs.AIcs.CL
keywords uncertaintyquantificationlargelanguagemodelsJensen-Shannondivergencemodelcalibrationensemblemethodssubsetselectionclinicalpredictionchain-of-thoughtdistillation
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

This paper proposes MUSE, an inference-time algorithm that quantifies uncertainty in binary predictions by measuring disagreement among several large language models. The central claim is that disagreement between LLM predictive distributions signals epistemic uncertainty, while consensus indicates reliable generalization, so averaging a selectively chosen low-disagreement subset of models yields better-calibrated probabilities. On TruthfulQA, EHRShot, and MIMIC-Extract, MUSE improves AUROC, expected calibration error, and Brier score over single-LLM baselines and naive mean or majority ensembles. The paper also tests MUSE consensus probabilities as supervision for fine-tuning and chain-of-thought distillation, finding model-dependent benefits; if the central claim holds, model diversity becomes a practical, no-retraining route to trustworthy confidence in high-stakes settings.

What carries the argument

The load-bearing object is MUSE, a subset-ensemble algorithm built on Jensen-Shannon Divergence (JSD), a symmetric, bounded measure of disagreement between probability distributions. For each input, MUSE treats each LLM's yes-probability as a distribution, defines epistemic uncertainty as the average JSD between each selected model and the subset mean, and aleatoric uncertainty as average binary entropy; a greedy or conservative procedure then selects a subset that keeps disagreement below a tolerance, and the final probability is the unweighted or entropy-weighted average of the subset. The single-model inputs come from self-consistency, ten stochastic decodes with bootstrap re-sampling (GENBS), or from sequence-likelihood scoring (SLL), the two uncertainty estimators the paper compares.

What would settle it

Run MUSE and a plain average of all LLM probabilities on held-out binary data and compare ECE and AUROC across random seeds; if the plain average matches or beats MUSE, or if the reported subset-size parameter (msize=20) cannot be reproduced with a four-model pool, the central claim fails.

Watch

Extended reading notes

Core claim

The paper's central discovery is that a simple information-theoretic selection rule—start from the most confident LLM prediction and add models only while average Jensen-Shannon divergence to the subset mean stays within tolerance—produces an aggregated probability that is better discriminated (AUROC) and better calibrated (ECE, Brier) than any individual LLM or naive ensemble in the binary tasks tested. The authors frame this as evidence that LLMs make complementary errors and that consensus across a diverse pool is a trustworthy uncertainty signal. They also show that using MUSE's consensus probabilities as silver labels for fine-tuning individual LLMs can improve calibration, but the effect depends on the model, the prompt format, and whether chain-of-thought reasoning is included.

Load-bearing premise

The method assumes that when several different LLMs agree, the answer is more likely to be correct, and that disagreement is genuine uncertainty; if consensus does not track correctness, the subset-selection objective has no basis.

Editorial extensions

If this is right

  • On TruthfulQA, MUSE reaches AUROC 72.35 with ECE 38.15, close to the best single-LLM AUROC (72.89) but with much lower calibration error, so selective aggregation can buy calibration without sacrificing discrimination.
  • Agreement among a small, per-input subset of LLMs becomes a usable uncertainty signal, meaning confidence scores from such ensembles can inform when to trust an answer.
  • Per-input subset selection beats fixed global ensembles, so adding more models does not automatically help; the pool must be filtered by disagreement rather than by model identity.
  • MUSE-derived probabilities can act as silver supervision for fine-tuning individual LLMs, but the benefit depends on model and prompt format, so the signal is useful rather than universally sufficient.

Reading between the lines

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

  • An abstention rule follows naturally from the method: inputs with high total uncertainty (epistemic plus aleatoric) could be flagged for human review, a use the paper touches on when it compares prediction probability against total uncertainty as a scoring signal.
  • The complementarity hypothesis predicts that MUSE's margin over naive averaging grows as the model pool becomes more diverse; this can be tested by ablating pool composition across architectures and training data.
  • The same JSD-plus-entropy selection objective should transfer beyond binary labels, with binary entropy replaced by the appropriate divergence for multiclass or regression targets.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes MUSE, a method for multi-LLM uncertainty quantification that selects a subset of LLM predictive distributions via Jensen-Shannon Divergence and entropy, then aggregates the selected predictions. The authors claim improved AUROC and calibration over single-model and naive-ensemble baselines on TruthfulQA, EHRShot, and MIMIC-Extract, and they additionally explore using MUSE-derived probabilities as supervision for fine-tuning with chain-of-thought distillation. The supervised fine-tuning exploration is reported transparently as mixed, while the central uncertainty-selection claim is the main contribution.

Significance. If MUSE worked as claimed, it would offer a simple, code-released baseline for combining diverse LLM outputs in high-stakes binary settings. The information-theoretic framing is natural, and the appendix's inclusion-frequency analysis (Table 4) and failure-case discussion (Table 7) show an attempt to understand when selection helps. However, the empirical support is currently inconsistent: the headline claim is contradicted by the paper's own tables, the main parameter configuration is incompatible with the stated pool size, and key hyperparameters are unreported, so the paper's contribution is not yet established.

major comments (4)
  1. [Section 5.1; Tables 1 and 7] The unqualified claim in Section 5.1 that 'MUSE improves both AUROC and calibration metrics compared to single LLMs and naive ensembling baselines' is contradicted by the paper's own results. In Table 7 (hyperlipidemia), MUSE Greedy mean AUROC is 33.16, far below the best single LLM (Mistral, 52.53). In Table 1, DS-Qwen GENBS achieves ECE 18.83 and Brier 30.32, while the highlighted MUSE Conservative Top 2 row reports ECE 38.15 and Brier 38.55, and MUSE Greedy All LLMs has AUROC 57.57 versus DS-Qwen SLL's 72.89. The Limitation section's assertion that MUSE 'consistently improves both accuracy and calibration' is therefore unsupported; please report error bars, paired significance tests, and a revised conditional claim that acknowledges the hyperlipidemia and TruthfulQA results.
  2. [Section 3.2, Algorithm 1, Figure 2, Appendix A.2] The stated main configuration msize=20 is incompatible with the described prediction set. Algorithm 1 operates on P_x of N predictive distributions and the experiments use four LLMs; with mmin=20 the condition on line 6 can never be satisfied and the loop terminates only after all four items are added. Figure 2 and Appendix A.2 therefore cannot describe the algorithm's behavior as written. If P_x actually contains bootstrap replicates (e.g., B=100 per LLM), this must be stated explicitly and Table 4's 'LLM inclusion frequencies' must be redefined accordingly; otherwise the main results are not tied to a well-specified selection procedure.
  3. [Section 3.2; Algorithms 1 and 2; Section 4] The values of beta, tau, epsilon_tol, and mmin are not reported for the main experiments, and the definition of U_epis is inconsistent between the text (average JSD) and Algorithm 1 line 4 / Algorithm 2 line 4 (average squared JSD). These choices change the selected subsets and the weighted results, so the experiments are not reproducible. Please report the exact objective and all hyperparameter values per dataset, and state whether they were chosen on a dev set.
  4. [Section 5.1; Tables 1 and 2] The favorable configurations labeled 'Excl. Outlier' and 'Top 2' are fixed subsets, not outputs of Algorithms 1 or 2, yet they are presented as MUSE settings and used to support the headline claim. Without a held-out rule for choosing these subsets, this conflation makes the comparison look like post hoc selection. The main text should separate algorithm-selected results from ablations and report the algorithm's actual subset performance on every dataset; similarly, Table 2's statement that Greedy and Conservative non-weighted results are identical needs an explanation.
minor comments (6)
  1. [Table 9 caption] The caption ends with 'LLM notation is consistent with table??'; please replace the placeholder with the correct table number.
  2. [Section 5.1] The sentence 'Mistral is chosen less often than Greedy, only when it improves subset consistency' is garbled; please rephrase to state which MUSE variant selects Mistral less often and under what condition.
  3. [Section 3.2] The description of aleatoric-aware weighting first says each prediction is weighted by U_alea(S), then says it is weighted by 1−H(ˆpyes_i); please give the exact aggregation formula.
  4. [Throughout] Notation is inconsistent: 'GEN BS' and 'GENBS' are used interchangeably, as are 'GEM' and 'Gemma'; please harmonize the notation.
  5. [Appendix A.5] The text refers to 'Greedy v2' but no version v2 is defined; please either define it or remove the label.
  6. [Section 4] Please provide the exact prompts, decoding parameters (temperature, top-p, max tokens), and label-mapping rules for the GEN and SLL evaluations, as these details are needed for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: MUSE's predictions are evaluated against external labels, and the selection objective does not encode the target results.

full rationale

The paper's derivation chain is self-contained against external benchmarks. MUSE's subset selection uses only per-model predictive distributions and confidence scores, not ground-truth labels; the final probability is an average of selected models' probabilities, and AUROC, ECE, and Brier are computed against held-out labels. The central hypothesis that consensus tracks reliability is an empirical claim tested by those external metrics, not built into the objective by definition. The only self-citations (e.g., Gao et al. 2024b in the introduction) motivate high-stakes healthcare uncertainty and are not load-bearing; no uniqueness theorem or ansatz is imported from prior work by the same authors. Hyperparameters (msize, epsilon_tol, beta, tau) are tuned on dev sets, which is standard practice and does not make the test-set predictions forced. The paper does have a serious internal inconsistency: Figure 2 states 'Main results use msize=20, epsilon_tol=0.04' while the pool has only four LLMs, and Algorithm 1 cannot reach msize=20 with N=4; this undermines reproducibility and the parameter-sensitivity analysis, and Table 7 shows MUSE underperforming all single LLMs on hyperlipidemia, contradicting the unqualified improvement claim. These are correctness and consistency problems, not circularity: no equation reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The algorithm rests on two unproven modeling assumptions (consensus reliability and entropy as aleatoric), plus several hand-set hyperparameters, of which beta and tau are unreported and msize is inconsistent with the model pool size.

free parameters (4)
  • epsilon_tol (epistemic noise threshold) = 0.04 in main results; range 0.04-0.08 explored
    Controls when the greedy and conservative subset stops adding models; tuned on TQA dev and EHRShot lupus (Figure 2, Appendix A.8).
  • m_min / msize (minimum subset size) = 20 as reported in Figure 2 caption
    Algorithm 1 and 2 define m_min; the stated value 20 is inconsistent with a 4-LLM pool, so either the parameter is wrong or the pool is not the four listed models.
  • beta (aleatoric weight) = Not reported
    Used in the conservative variant and total uncertainty (Algorithm 2 and U(S)); no value or sensitivity analysis is given.
  • tau (conservative stopping threshold) = Not reported
    Used in Algorithm 2 stopping rule; value not reported.
assumptions (5)
  • domain assumption LLMs make complementary predictions due to training differences and Zipfian language statistics, making consensus a reliable signal.
    Stated in Section 1 as hypothesis; used to justify why multi-LLM aggregation should improve uncertainty estimation.
  • domain assumption Low JSD among selected models indicates low epistemic uncertainty and reliable generalization.
    Section 3.2: 'disagreement among LLM predictive distributions signals epistemic uncertainty, while consensus indicates more reliable generalization.' This premise is load-bearing for MUSE's subset selection.
  • domain assumption Mean binary entropy of LLM output distributions approximates aleatoric uncertainty of the task.
    Section 3.2 defines U_alea(S) as average H(p_i), treating model uncertainty as irreducible data noise; this identification is assumed, not verified.
  • ad hoc to paper Bootstrapped empirical frequencies from k=10 stochastic decodes approximate stable predictive distributions.
    Section 3.1 sets k=10, B=100, 90% resampling; no justification is given that these choices yield stable probabilities.
  • standard math JSD is symmetric and bounded, making it suitable for comparing LLM distributions.
    Section 3.1 cites Cover 1999; standard property, no issue.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Simple Yet Effective: An Information-Theoretic Approach to Multi-LLM Uncertainty Quantification." pith.science (2026). https://pith.science/paper/2OU7NMBZ

@misc{pith2026250707236,
  author       = {Pith},
  title        = {Pith review of: Simple Yet Effective: An Information-Theoretic Approach to Multi-LLM Uncertainty Quantification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2OU7NMBZ}},
  note         = {Machine review of arXiv:2507.07236}
}
read the original abstract

Large language models (LLMs) often behave inconsistently across inputs, indicating uncertainty and motivating the need for its quantification in high-stakes settings. Prior work on calibration and uncertainty quantification often focuses on individual models, overlooking the potential of model diversity. We hypothesize that LLMs make complementary predictions due to differences in training and the Zipfian nature of language, and that aggregating their outputs leads to more reliable uncertainty estimates. To leverage this, we propose MUSE (Multi-LLM Uncertainty via Subset Ensembles), a simple information-theoretic method that uses Jensen-Shannon Divergence to identify and aggregate well-calibrated subsets of LLMs. Experiments on binary prediction tasks demonstrate improved calibration and predictive performance compared to single-model and na\"ive ensemble baselines. In addition, we explore using MUSE as guided signals with chain-of-thought distillation to fine-tune LLMs for calibration. MUSE is available at:https://github.com/LARK-NLP-Lab/MUSE.

Figures

Figures reproduced from arXiv: 2507.07236 by the authors.

Figure 1
Figure 1. Comparative results of supervised fine-tuning with MUSE-derived probabilities. Common settings at both panels: Md indicates the default consensus probability input, while RP uses the raw bootstrapped probabilities from the model pool. Left (4 panels): Direct SFT performance shown as changes in AUROC and ECE (bottom row) for Mistral and Qwen, when using model SLL and GEN output under settings with and without pˆ. Imp… view at source ↗
Figure 2
Figure 2. Contour plot of AUROC and ECE as MUSE param￾eters (msize, ϵtol) vary, based on a TQA dev set. Main results use msize=20, ϵtol=0.04. See Appendix for further analysis. 2024a. Fact-and-reflection (far) improves confidence calibration of large language models. In Findings of the Association for Computational Linguistics ACL 2024, pages 8702–8718. Yukun Zhao, Lingyong Yan, Weiwei Sun, Guoliang Xing, Shuaiqiang Wang, Cho… view at source ↗
Figure 3
Figure 3. Contour plot for parameter sensitivity analysis using lupus prediction task from EHRShot. We report MUSE-Greedy with both weighted and unweighted version, to showcase the differences. LLMs AUROC ↑ ECE ↓ Brier Score ↓ Hyperlipidemia (weak models dominate) Qwen 46.91 38.92 50.88 Mistral 52.53 14.47 25.69 Gemma 45.18 25.72 35.36 Deepseek-Distill 43.92 22.46 40.97 Greedy (mean) 33.16 24.51 29.13 (weighted) 33.17 27.24 3… view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uncertainty-Aware Trust Estimation for Multi-LLM Systems via Structured Expert Judgement

    cs.LG 2026-07 conditional novelty 4.0 of 10

    Multi-LLM ensembles can be made robust to weak or adversarial members by weighting each model by its per-subject log score on a small set of calibration questions, instead of trusting all models equally.

  2. The Alignment Auditor: A Bayesian Framework for Verifying and Refining LLM Objectives

    cs.LG 2025-10 conditional novelty 4.0 of 10

    Bayesian IRL with sequential posterior updates can recover a usable toxicity-reduction reward from LLM demonstrations and reproduce ground-truth RLHF detoxification.

Reference graph

Works this paper leans on

16 extracted references · 11 canonical work pages · cited by 2 Pith papers

  1. [2]

    Preprint, arXiv:2501.12948

    Deepseek-r1: Incentivizing rea- soning capability in llms via reinforcement learning. Preprint, arXiv:2501.12948. Prasenjit Dey, Srujana Merugu, and Sivaramakrishnan Kaveri

    arXiv

  2. [3]

    Xiang Gao, Jiaxin Zhang, Lalla Mouatadid, and Kama- lika Das

    Uncertainty-aware fusion: An ensem- ble framework for mitigating hallucinations in large language models.arXiv preprint arXiv:2503.05757. Xiang Gao, Jiaxin Zhang, Lalla Mouatadid, and Kama- lika Das. 2024a. Spuq: Perturbation-based uncer- tainty quantification for large language models. In Proceedings of the 18th Conference of the European Chapter of the ...

    arXiv

  3. [6]

    InPro- ceedings of the 1st Workshop on Uncertainty-Aware NLP (UncertaiNLP 2024), pages 1–14

    Calibration-tuning: Teaching large lan- guage models to know what they don’t know. InPro- ceedings of the 1st Workshop on Uncertainty-Aware NLP (UncertaiNLP 2024), pages 1–14. Stephanie Lin, Jacob Hilton, and Owain Evans

    work page 2024

  4. [7]

    Uncer- tainty quantification for in-context learning of large language models. InProceedings of the 2024 Con- ference of the North American Chapter of the Asso- ciation for Computational Linguistics: Human Lan- guage Technologies (Volume 1: Long Papers), pages 3357–3370. Shudong Liu, Zhaocong Li, Xuebo Liu, Runzhe Zhan, Derek Wong, Lidia Chao, and Min Zhang

    work page 2024

  5. [8]

    InProceedings of the 2024 Conference on Empiri- cal Methods in Natural Language Processing, pages 21635–21645

    Can llms learn uncertainty on their own? express- ing uncertainty effectively in a self-training manner. InProceedings of the 2024 Conference on Empiri- cal Methods in Natural Language Processing, pages 21635–21645. Steven T Piantadosi

    work page 2024

  6. [9]

    InFindings of the Association for Computational Linguistics: EMNLP 2024, pages 2520–2537

    En- hancing healthcare llm trust with atypical presenta- tions recalibration. InFindings of the Association for Computational Linguistics: EMNLP 2024, pages 2520–2537. Mauricio Rivera, Jean-Fran c ¸ois Godbout, Reihaneh Rabbany, and Kellin Pelrine

    work page 2024

  7. [10]

    InProceedings of the 1st Workshop on Uncertainty- Aware NLP (UncertaiNLP 2024), pages 114–126

    Combining confi- dence elicitation and sample-based methods for un- certainty quantification in misinformation mitigation. InProceedings of the 1st Workshop on Uncertainty- Aware NLP (UncertaiNLP 2024), pages 114–126. Thomas Savage, John Wang, Robert Gallo, Abdessalem Boukil, Vishwesh Patel, Seyed Amir Ahmad Safavi- Naini, Ali Soroush, and Jonathan H Chen

    work page 2024

  8. [11]

    Shirly Wang, Matthew BA McDermott, Geeticka Chauhan, Marzyeh Ghassemi, Michael C Hughes, and Tristan Naumann

    Gemini: a family of highly capable multimodal models.arXiv preprint arXiv:2312.11805. Shirly Wang, Matthew BA McDermott, Geeticka Chauhan, Marzyeh Ghassemi, Michael C Hughes, and Tristan Naumann

    arXiv

Show all 16 references
  1. [14]

    5-math technical report: Toward mathe- matical expert model via self-improvement.arXiv preprint arXiv:2409.12122

    Qwen2. 5-math technical report: Toward mathe- matical expert model via self-improvement.arXiv preprint arXiv:2409.12122. Caiqi Zhang, Fangyu Liu, Marco Basaldella, and Nigel Collier. 2024a. Luq: Long-text uncertainty quantifi- cation for llms. InProceedings of the 2024 Con- fe...

    2024 arXiv

  2. [16]

    Original Bayesian Noˆp Model SFT Output AUROC Brier ECE AUROC Brier ECE AUROC Brier ECE Mistral default SLL 54.2242.90 42.97 42.1443.04 41.03 39.27 35.09 31.23 GENBS 51.9127.9714.66 49.30 28.8016.48 48.52 41.73 31.03 RawProb SLL 44.7957.75 57.78 58.7328.9021.88 64.5151.46 52.8...

  3. [20]

    stronger

    promotes diversity by including more models, while a moderate ϵtol ([0.04, 0.08]) allows controlled disagreement without overwhelming the ensemble with noise. The best performance is achieved when both parameters are carefully bal- anced. This supports our hypothesis that LLMs...

  4. [2020]

    InProceedings of the ACM conference on health, inference, and learning, pages 222–235

    Mimic-extract: A data extraction, preprocessing, and representation pipeline for mimic-iii. InProceedings of the ACM conference on health, inference, and learning, pages 222–235. Xinglin Wang, Yiwei Li, Shaoxiong Feng, Peiwen Yuan, Boyuan Pan, Heda Wang, Yao Hu, and Kan Li. 20...

    2024

  5. [2022]

    InFindings of the Association for Computational Linguistics: EMNLP 2022, pages 7273–7284

    Uncertainty quantification with pre-trained language models: A large-scale em- pirical analysis. InFindings of the Association for Computational Linguistics: EMNLP 2022, pages 7273–7284. An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jian...

    2022

  6. [2023]

    Alistair EW Johnson, Tom J Pollard, Lu Shen, Li-wei H Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G Mark

    Mistral 7b.Preprint, arXiv:2310.06825. Alistair EW Johnson, Tom J Pollard, Lu Shen, Li-wei H Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G Mark

    arXiv

  7. [2024]

    InPro- ceedings of the 2024 Conference on Empirical Meth- ods in Natural Language Processing, pages 284–312

    Uncertainty in language mod- els: Assessment through rank-calibration. InPro- ceedings of the 2024 Conference on Empirical Meth- ods in Natural Language Processing, pages 284–312. Albert Q. Jiang, Alexandre Sablayrolles, Arthur Men- sch, Chris Bamford, Devendra Singh Chaplot, ...

    2024

  8. [2025]

    InFindings of the Association for Computa- tional Linguistics: NAACL 2025, pages 7512–7523, Albuquerque, New Mexico

    Uncertainty quantification for clinical outcome predictions with (large) language models. InFindings of the Association for Computa- tional Linguistics: NAACL 2025, pages 7512–7523, Albuquerque, New Mexico. Association for Compu- tational Linguistics. Thomas M Cover. 1999.Elem...

    2025

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.