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REVIEW 3 major objections 7 minor 1 cited by

Revisiting Uncertainty Estimation and Calibration of Large Language Models

T0 review · 3 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that across 80 large language models, the most reliable uncertainty signal is the model's own hedging language—words like "probably" and "might"—outperforming token probabilities and numerical self-scores on calibration…

desk verdict A genuinely broad and useful benchmark whose 'LVU consistently wins' headline is overstated; the honest version is that LVU wins on average, with judge-validity and instruction-following artifacts still to be resolved. read the letter →

arxiv 2505.23854 v1 pith:CM6U2UR3 submitted 2025-05-29 cs.CL cs.AIcs.LG

Linwei Tao , Yi-Fan Yeh , Minjing Dong , Tao Huang , Philip Torr , Chang Xu This is my paper · ORCID
classification cs.CLcs.AIcs.LG
keywords uncertaintyestimationlargelanguagemodelscalibrationselectiveclassificationlinguisticverbalMMLU-ProexpectederrorAUROC
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 tries to establish that the most reliable black-box way to know when a large language model is uncertain is to listen to the words it uses, not its token probabilities or its self-reported numbers. The authors evaluate 80 models from 0.6B to 671B parameters on the MMLU-Pro benchmark, comparing three single-pass methods: token probability-based uncertainty (TPU), numerical verbal uncertainty (NVU), and linguistic verbal uncertainty (LVU). Their central result is that LVU consistently beats the other two methods on both calibration (lower expected calibration error) and selective classification (higher AUROC), by roughly 10% over the second-best method, while also being more interpretable. A sympathetic reader would care because LVU works with any API-only model and produces a signal humans can understand, making it a plausible practical tool for deciding when to abstain, flag, or defer.

What carries the argument

The load-bearing mechanism is the LVU judge: a separate LLM, LLaMA-4-Maverick-17B-128E-Instruct, that reads a model's response and converts hedging language into a confidence score in [0,1], after the numeric confidence line has been stripped from the response. This is compared against TPU, defined as one minus the exponentiated average log-likelihood of the generated response, and NVU, the model's self-reported numeric score extracted by regular expression from a prompt that asks for confidence from 0 to 100. All three methods share the same single sampled response, prompted with a concise chain-of-thought template, and are scored by expected calibration error (ECE) with 10 bins and by AUROC for selective classification.

What would settle it

Re-evaluate LVU on a sample of MMLU-Pro responses using a different judge, or human-annotated hedging scores, and check whether LVU still beats NVU and TPU by the reported margin; if the ranking flips or the advantage shrinks to noise, the central claim fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that natural-language hedging is a stronger and more general uncertainty signal than either token-level likelihood or explicit numerical self-assessment. Across all 80 models and all subjects in MMLU-Pro, responses containing hedging expressions such as "probably", "might", and "possibly" are scored by a separate judge model and turn out to be better calibrated and better ranked than the two competing baselines. The paper also reports that model size, post-training, reasoning mode, and quantization each shift uncertainty quality, that reasoning tasks yield more reliable uncertainty estimates than knowledge-heavy tasks by over 10% AUROC, and that good calibration does not imply good error ranking. It takes these findings as evidence that accuracy is not a proxy for uncertainty reliability and that LVU deserves a central place in future uncertainty-aware LLM design.

Load-bearing premise

The entire LVU result rests on the judge model reading hedging words as a faithful sign of uncertainty; the paper validates that judge on only 20 crafted sentences and concedes its general reliability is unclear.

Editorial extensions

If this is right

  • LVU can be used out-of-the-box with any API-only model, since it needs no logits, hidden states, or multiple generations.
  • Reasoning-enhanced models are better calibrated without necessarily being more accurate, so reasoning mode is a practical lever for improving uncertainty.
  • Accuracy should not be used as a proxy for reliability: high-accuracy models can be poorly calibrated, while moderate-accuracy models can have top-tier uncertainty estimates.
  • Calibration and selective classification are distinct capabilities, so deployment evaluation needs both metrics rather than either one alone.
  • Uncertainty signals are more trustworthy on reasoning tasks than on knowledge-heavy tasks, implying that abstention policies should be task-aware.

Reading between the lines

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

  • If the LVU advantage comes partly from a judge that flags format violations as uncertainty, then models that follow instructions poorly may look uncertainty-aware for the wrong reasons; this is a testable failure mode the paper notes only for small models under LVU AUROC.
  • If hedging language genuinely tracks uncertainty, a natural next step the paper leaves implicit is to train models to hedge appropriately during post-training, rather than only detecting hedges after generation.
  • A different judge model—or human-annotated hedging scores—could reverse the reported LVU advantage, so the headline result should be read as contingent on the specific judge used.
  • Because the judge was validated on only 20 non-verifiable sentences, extending LVU to open-ended generation or new domains would require a standardized judge-evaluation protocol before deployment.
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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 / 7 minor

Summary. The paper presents a large empirical benchmark of uncertainty estimation for 80 LLMs on MMLU-Pro, comparing token probability-based uncertainty (TPU), numerical verbal uncertainty (NVU), and linguistic verbal uncertainty (LVU). The authors report that LVU consistently outperforms TPU and NVU in calibration (ECE) and selective classification (AUROC), and they examine the effects of model scale, post-training, reasoning mode, MoE architecture, quantization, and task type. The evaluation uses a shared prompt with chain-of-thought and confidence elicitation, LLaMA-4-Maverick as the LVU judge, and includes code and full per-model results.

Significance. If the central result were established, the paper would make a valuable practical contribution: LVU is a black-box, interpretable, single-pass uncertainty signal that does not require token-level access. The benchmark's breadth (80 models, multiple families and scales, per-subject analysis, code release) is a genuine resource for the field. However, the headline conclusion is not currently supported by the evidence: the paper's own tables contain many per-model cases where LVU loses to TPU, and the authors explicitly identify an instruction-violation artifact that inflates LVU for small models. The judge validation is too thin to carry the load. The data and framing are salvageable, but the central claims need re-analysis and careful qualification.

major comments (3)
  1. [§3.6, Tables 3–4] The abstract and Section 3.6 state that LVU 'consistently outperforms' TPU and NVU, but Tables 3 and 4 contain numerous per-model counterexamples. For example, GPT-4.1 has TPU ECE 0.074 versus LVU ECE 0.166; Gemini-2.0-flash has TPU ECE 0.091 versus LVU ECE 0.162; Qwen3-32b-think has TPU AUROC 0.791 versus LVU AUROC 0.726 and TPU ECE 0.042 versus LVU ECE 0.092; Qwen3-14b-think has TPU AUROC 0.809 versus LVU AUROC 0.752; and Phi-4-reasoning has TPU AUROC 0.640 versus LVU AUROC 0.601. The word 'consistently' is therefore not a faithful summary of the data. I recommend reporting the full distribution of per-model differences (e.g., win rates, paired bootstrap or signed-rank tests) and either removing the word 'consistently' or explicitly discussing which model classes drive the aggregate advantage.
  2. [§3.1, §F.3, §G] Section 3.1 acknowledges a serious confound: for smaller models, the judge 'tends to assign high LVU uncertainty to such non-compliant outputs, many of which are indeed incorrect,' producing strong discriminative uncertainty 'not because their uncertainty estimates are intrinsically better, but because instruction violations correlate strongly with failure.' Since the 80-model roster includes many small or weak models, this artifact can dominate the average AUROC/ECE advantage claimed in Section 3.6. The concern is compounded by the extraction protocol in Appendices F.3 and G: outputs with failed extractions are dropped, and the paper reports that on average 17% of responses are dropped; because NVU requires a parsable numeric confidence value while the LVU judge can score free text, the LVU evaluation set may contain non-compliant responses that NVU/TPU exclude. I ask the authors to recompute all three methods on a common subset of responses with successful extractions for every method, and to report LVU results stratified by instruction-compliance (e.g., compliant versus non-compliant outputs) so that the artifact is separated from genuine uncertainty signal.
  3. [§2.1, Appendix H, §4] The validity of LVU as a general uncertainty measure rests on the LLaMA-4-Maverick judge, but the only validation (Appendix H) shows that the judge ordinally orders individual hedge words on 20 non-verifiable daily-life sentences. It does not show that judge scores track actual correctness of model responses on MMLU-Pro, nor that the mapping is stable across domains, model families, or output styles. The Conclusion explicitly says 'its general reliability across tasks, domains, and model families remains unclear,' which is in tension with the abstract's 'consistently outperforms' claim. The authors should validate the judge against correctness on the benchmark (e.g., calibration of judge scores with true accuracy per model), or provide a sensitivity analysis using an alternative LVU judge, before claiming LVU is a practical general-purpose uncertainty signal.
minor comments (7)
  1. [Figure 1 caption] The caption contains a typo: 'T oken Probability-Based Uncertainty' should be 'Token Probability-Based Uncertainty.'
  2. [Reference [8]] Reference [8] appears to be a BBC article on the US debt ceiling, but the text cites it for the story of a lawyer relying on ChatGPT for legal research; please replace it with the correct source.
  3. [§3.4, Table 4] The statement that Qwen3-30B-A3B 'consistently outperforms' Qwen3-32B in both reasoning and non-reasoning tasks under LVU is contradicted by Table 4 for the non-reasoning pair, where LVU ECE is 0.243 for Qwen3-30b-a3b versus 0.218 for Qwen3-32b; please adjust the claim.
  4. [§3.5, Table 4] Section 3.5 describes Qwen3-235B-A22B (Reasoning) as having 'moderate accuracy (67%),' but Table 4 lists its accuracy as 0.880 for the think variant and 0.728 for the non-think variant; please reconcile the numbers.
  5. [Tables 3–4] The '/' entries for TPU values are not explained in the table captions; Appendix E notes that DeepSeek does not provide valid token probabilities, but a general legend for missing values should be added.
  6. [Appendix G] The stratified-sampling validation is performed with GPT-4.1-Mini only; the claim that 50% subsets are sufficient for all models should be presented as a single-model analysis rather than a general guarantee.
  7. [§3.3] The claim that reasoning mode reduces the proportion of highly overconfident predictions by 'more than 20%' is not supported by a numerical table or statistical test; please provide the underlying numbers.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is an empirical benchmark whose headline comparison is computed from held-out MMLU-Pro responses, not derived from its own inputs.

full rationale

The paper contains no fitted-parameter derivation, no equation whose output is defined by the target claim, and no load-bearing self-citation. TPU, NVU, and LVU scores are computed from responses to MMLU-Pro prompts and benchmark labels (Eq. 3, Eq. 5, Appendix F), so the ECE/AUROC comparisons are externally falsifiable measurements rather than identities. The only author self-citation is reference [13], used as an example of an internal-state method in related work; it is not load-bearing. The judge-validation concern (Appendix H, only 20 sentences) and the acknowledged small-model artifact (Section 3.1: 'instruction violations correlate strongly with failure') are validity and confound risks, not circular derivation: they do not make the LVU number equal to another input by construction. The conclusion also acknowledges that judge reliability remains unclear. Under the stated rules, a confound or weak validation is a correctness concern, not circularity; therefore the score is 0.

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

The paper introduces no fitted parameters, new entities, or new theoretical constructs. The evaluation rests on standard metrics, the MMLU-Pro benchmark, and the assumed reliability of the LVU judge, which the authors themselves flag as only lightly validated.

assumptions (4)
  • domain assumption MMLU-Pro ground-truth labels are correct and answer extraction via regex identifies the model's intended choice.
    The evaluation treats MMLU-Pro as ground truth and regex matches as valid answers. Incorrect extraction is treated as non-response and dropped, which can bias the remaining set (Appendix F.3, G).
  • domain assumption The judge model LLaMA-4-Maverick-17B-128E-Instruct maps hedging language to confidence scores reliably beyond the small validation set.
    Appendix H validates on 20 non-verifiable statements; the paper states in the conclusion that judge reliability across tasks and models remains unclear. The central LVU claims depend on this mapping.
  • domain assumption ECE with 10 fixed bins and AUROC adequately capture calibration and discrimination for this comparison.
    These are standard metrics (References 32, 33), though the paper also reports adaptive ECE in Appendix D. The adequacy of fixed-bin ECE is assumed.
  • domain assumption The shared prompt that explicitly asks models to hedge when uncertain does not invalidate comparison among LVU, NVU, and TPU.
    The prompt instructs 'convey this uncertainty linguistically', and the LVU judge then scores these hedges. If this instruction changes generation behavior differently across models, the relative ranking could be confounded (Section 2.2, Appendix F.1).

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Cite this review

Pith. "Pith review of Revisiting Uncertainty Estimation and Calibration of Large Language Models." pith.science (2026). https://pith.science/paper/CM6U2UR3

@misc{pith2026250523854,
  author       = {Pith},
  title        = {Pith review of: Revisiting Uncertainty Estimation and Calibration of Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CM6U2UR3}},
  note         = {Machine review of arXiv:2505.23854}
}
read the original abstract

As large language models (LLMs) are increasingly deployed in high-stakes applications, robust uncertainty estimation is essential for ensuring the safe and trustworthy deployment of LLMs. We present the most comprehensive study to date of uncertainty estimation in LLMs, evaluating 80 models spanning open- and closed-source families, dense and Mixture-of-Experts (MoE) architectures, reasoning and non-reasoning modes, quantization variants and parameter scales from 0.6B to 671B. Focusing on three representative black-box single-pass methods, including token probability-based uncertainty (TPU), numerical verbal uncertainty (NVU), and linguistic verbal uncertainty (LVU), we systematically evaluate uncertainty calibration and selective classification using the challenging MMLU-Pro benchmark, which covers both reasoning-intensive and knowledge-based tasks. Our results show that LVU consistently outperforms TPU and NVU, offering stronger calibration and discrimination while being more interpretable. We also find that high accuracy does not imply reliable uncertainty, and that model scale, post-training, reasoning ability and quantization all influence estimation performance. Notably, LLMs exhibit better uncertainty estimates on reasoning tasks than on knowledge-heavy ones, and good calibration does not necessarily translate to effective error ranking. These findings highlight the need for multi-perspective evaluation and position LVU as a practical tool for improving the reliability of LLMs in real-world settings.

Figures

Figures reproduced from arXiv: 2505.23854 by the authors.

Figure 1
Figure 1. AUROC vs. ECE across various LLMs, evaluated using Linguistic Verbal Uncer￾tainty (LVU), Numerical Verbal Uncertainty (NVU) and Token Probability-based Uncertainty (TPU). Model families are distinguished by color and marker shape. Reasoning-focused models are highlighted with thick black borders, while non-reasoning models are shown with dashed gray borders. Marker size reflects model size. calibration), but also to… view at source ↗
Figure 2
Figure 2. Uncertainty estimation performance of Qwen3 across three variants: no post-training [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Reliability diagram and bin density between reasoning and non-reasoning LLMs. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Left: Comparison of Reasoning vs. Non-Reasoning on ECE and AUROC. Results are averaged over all reasoning/non-reasoning models. Right: Comparison between MoE and dense models within the Qwen3 series under LVU. To understand this effect in depth, we analyze reliability …
Figure 5
Figure 5. Figure 5: Left: Comparison of top-tier models under LVU. Right: Comparison of different uncer￾tainty estimation methods. ECE (TPU) ECE (NVU) ECE (LVU) AUROC (TPU) AUROC (NVU) AUROC (LVU) ECE (TPU) ECE (NVU) ECE (LVU) AUROC (TPU) AUROC (NVU) AUROC (LVU) 1 0.74 0.76 -0.52 -0.64 -0…
Figure 6
Figure 6. Figure 6: Left: Kendall Rank Correlation among Uncertainty Estimation Methods. Right: LLMs exhibit better uncertainty estimates in reasoning tasks, as measured by AUROC using LVU. LVU remains underexplored in the literature, underscoring its potential as a promising direction fo…
Figure 7
Figure 7. Figure 7: Uncertainty estimation performance of Qwen3 across quantization variants: no quantization [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Comparison with multi-generation based uncertainty estimation. [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: AdaptiveECE vs AUROC across all methods. [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: Comparison of top-tier models under NVU. [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Comparison of top-tier models under TPU. [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: GPT-4.1-Mini’s spread of confidence distributions from different stratified subsets sizes. Each box represents 50 stratified samples. The AUROC and ECE distributions start to stabilize and trend towards those of the full set when the sample proportion exceeds 50%. 22 …
Figure 13
Figure 13. Figure 13: LLaMa-4-Maverick-17B-128E’s mapping of hedging words to LVU demonstrates that [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.