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"very likely" Means "uncertain"? How LLMs Diverge from Humans in Linguistic Uncertainty Quantification

Jinhao Duan, Zicheng Liu, Zijie Liu, Kaidi Xu, Tianlong Chen

arXiv:2610.00083v1cs.LG

TL;DR

LLM uncertainty estimates often rely on likelihood or consistency signals, while human verbal markers can carry different meanings for models. The paper builds a human-derived marker resource and introduces VOCAL to adapt uncertainty mappings to model outputs; it reports gains over single-sample UQ and performance comparable to multi-sample methods at lower computational cost.

  • Problem

    Human-derived verbal uncertainty markers do not always match LLM uncertainty, leaving open whether verbal expressions can reliably quantify model uncertainty.

    Source: §1 · pp. 1–2, §3.3 · p. 4

  • Method

    VOCAL optimizes marker uncertainty scores from correctness-labeled model generations and applies the learned lookup at test time without additional sampling.

    Source: §4.1 · p. 5, §4.3 · p. 6

  • Results

    VOCAL outperforms single-sample UQ methods and achieves performance comparable to multi-sample UQ with lower computational overhead.

    Source: §1 · p. 2, §6 · p. 9

  • Takeaways & Limitations

    The findings support grounding LLM uncertainty in verbal expressions, with practical relevance to trustworthy deployment and human–AI alignment research.

    Source: §6 · p. 9

    Verbal markers provide coarse signals, can be ambiguous or overlapping, and vary across domains and cultural contexts, limiting a single UM-Lookup’s generalizability.

    Source: Limitations · p. 9

Abstract

from arXiv · show

Humans express uncertainty verbally via markers (e.g., "possible," "likely"), yet most LLM uncertainty quantification (UQ) relies on costing likelihood- or consistency-based signals. From a cognitive perspective, accurate verbal uncertainty reflects metacognitive monitoring, representing knowledge boundaries ("knowing that you don't know") to support regulation and information seeking. In this paper, we investigate how LLMs diverge from humans in verbal uncertainty quantification and whether verbal markers can reliably quantify LLM uncertainty. We curate a corpus of human uncertainty markers from psychology and decision-science literature and benchmark LLMs against it. We observe that LLMs encode verbal uncertainty with numerical levels that differ substantially from those of humans. We then introduce METHODNAME, a novel optimization-based algorithm that learns an optimal uncertainty profile over uncertainty markers directly from LLM outputs. By fitting a marker-uncertainty mapping to best explain empirical correctness, METHODNAME discovers how much probability mass each verbal marker should convey, rather than estimating uncertainty via repeated sampling. METHODNAME enables a direct, marker-level comparison of confidence semantics between humans and LLMs, disentangling mismatch and revealing systematic confidence disparities in verbal expressions.

1. Introduction

The introduction frames a gap between human verbal uncertainty and LLM quantification, then presents a model-adapted verbal mapping that improves on single-sample UQ and matches multi-sample methods.

1. Introduction

  • LLM verbal UQ is proposed as a more natural alternative to costly sampling and lexically sensitive logits methods, but precise verbal quantification remains unresolved.The motivating gap contrasts qualitative expressions such as “possible” and “likely” with numerical uncertainty scores.Source: §1 · p. 1
  • 4.7% AUROC over PE and 5.6% AUROC over SE: verbal uncertainty improved on both for GPT-4o on SciQ, but remained weaker than strong UQ baselines broadly.These improvements are reported against representative logits-based and sampling-based methods, respectively.Source: §1 · p. 2
  • UM-Lookup combines literature review and debiasing with judgments from more than 300 annotators, yielding 115 markers with numerical interpretations.Its sources are psychology and decision-science literature.Source: §1 · p. 2
  • LLMs interpret markers such as “possible” as less uncertain than humans and typically use one marker where humans may combine several.VOCAL addresses this mismatch by adapting marker-to-uncertainty mappings to each model’s uncertainty distribution.Source: §1 · p. 2
  • VOCAL significantly outperforms single-sample UQ methods and achieves performance comparable to multi-sample methods with reduced computational cost.The introduction says it does so without additional sampling or inference-time computation.Source: §1 · p. 2

2. Related Work

Related work traces LLM UQ from lexical and sampling methods toward semantic, verbal, and model-internal approaches; the paper positions VOCAL as a lightweight alternative that learns verbal uncertainty mappings without fine-tuning.

2. Related Work

  • Sampling-based UQ addresses semantic variation across equivalent answers, while other approaches measure semantic density, generation consistency, relevance, uncertainty propagation, or single-output likelihood.Predictive entropy can mistake benign lexical variation for semantic uncertainty; G-NLL is presented as an efficient single-greedy-output alternative.Source: §2 · p. 3
  • Verbalized UQ ranges from prompting and aggregation to fine-tuning and RLHF, yet studies report faithfulness gaps between verbal decisiveness and intrinsic or internal uncertainty.Other cited work examines chain-of-thought calibration, pretraining mimicry, encoded priors, and effects of phrasing on user reliance and trust.Source: §2 · p. 3
  • VOCAL treats verbal uncertainty as an inherent predictive signal and optimizes a lookup table without parameter updates or multiple generations.The method is positioned as an efficient alternative to expensive fine-tuning and sampling-based UQ.Source: §2 · p. 3

3. Preliminary: How LLMs Diverge from Humans in Verbal Uncertainty

This section introduces human-based verbal uncertainty scoring and evaluates its use for LLM uncertainty quantification. QVU-H often predicts correctness meaningfully, but its performance is uneven, and marker diversity differs across model sizes.

3.1. Problem Statement: Uncertainty Quantification

  • UQ scores model doubt about a generation, and evaluation tests whether those scores predict correctness using AUROC or hallucination-detection accuracy.Higher AUROC or detection accuracy indicates better correctness prediction.Source: §3.1 · p. 3

3.2. Human Verbal Uncertainty and its Numerical Representation

  • Verbal UQ requires numerical interpretations for human uncertainty markers and a way to aggregate scores when a generation contains multiple markers.Source: §3.2 · pp. 3–4
  • UM-Lookup maps 115 distinct markers to probabilities on a 0–1 scale, with each phrase's value derived from an average of 336 human ratings.Examples include “impossible” at 0.0, “tossup” at 0.50, and “definite” at 0.99.Source: §3.2 · p. 4
  • QVU-H averages scores for multiple markers and converts lookup confidence to uncertainty using 1 − UM-Lookup(ui).The paper adopts averaging because listeners and coders tend to combine multiple verbal probability terms into a middle probability.Source: §3.2 · p. 4

3.3. Analytical Insights

  • QVU-H yields AUROC significantly above 0.5 in 7 of 8 model-dataset configurations; it beats PE and SE on GPT-4o/SciQ and matches both on DeepSeek-V3.1/MedQA.Figure 2 presents the QVU-H results using the human UM-Lookup table.Source: Figure 2 · p. 4, §3.3 · p. 4
  • Across evaluated models on GSM8K, verbal-uncertainty prompting leaves accuracy on par with standard CoT, with no statistically significant degradation.Source: §3.3 · p. 4
  • The human lookup can misalign with an LLM’s internal uncertainty when it generates a marker; QVU-H can fall below chance on GPT-4o/GSM8K.QVU-H is also frequently outperformed by PE.Source: §3.3 · p. 4
  • On GSM8K, GPT-4o and DeepSeek-V3.1 have the highest entropy-based marker-diversity scores, while smaller models express less nuanced uncertainty.The paper characterizes smaller models as tending toward overconfidence.Source: §3.3 · pp. 4–5

4. VOCAL: Optimizing the Numerical Scores of Verbal Uncertainty Markers for LLMs

Because a human-derived marker lookup can lag logit- and sampling-based UQ, VOCAL learns marker scores tailored to each LLM from its generations. It optimizes those scores against correctness and smooths them across semantically similar markers.

4.1. Setup

  • VOCAL collects generations across mathematics, science, and medical domains, then elicits verbal uncertainty markers and pairs them with generation correctness.The domains include GSM8K and GSM-Hard, PIQA and SciQ, and MedQA.Source: §4.1 · p. 5

4.2. Optimized Uncertainty Levels for LLMs

  • VOCAL optimizes marker scores so aggregated verbal uncertainty is higher for incorrect generations and lower for correct ones.It uses a Binary Cross-Entropy objective with a correctness indicator.Source: §4.2 · p. 5

4.3. Semantic Smoothing via Graph Laplacian Regularization

  • Graph Laplacian regularization penalizes large score differences between semantically similar markers, promoting smoother assignments that are more robust for rare markers.The method builds a weighted marker-similarity graph using 3-gram Jaccard similarity and applies a convex quadratic penalty.Source: §4.3 · pp. 5–6

4. VOCAL: Optimizing the Numerical Scores of Verbal Uncertainty Markers for LLMs

  • VOCAL jointly minimizes the correctness loss and smoothing regularizer, learns the lookup table once, and requires no additional sampling or inference-time computation at test time.Adam optimizes the uncertainty scores.Source: §4.3 · p. 6

5. Experiments

Across models and datasets, VOCAL’s learned uncertainty mapping generally performs better than a human-sourced lookup and single-sample baselines, while remaining competitive with multi-sample UQ. Experiments also find calibration gains and cross-model transfer alongside persistent differences between human and LLM marker meanings.

5.1. Experimental Setup

  • VOCAL consistently improves AUROC over human-sourced QVU-H across models and datasets; for GPT-4o on GSM8K, AUROC rises from 0.41 to around 0.6.The comparison suggests that a fixed human-defined lookup is less reliable when its marker scores do not match model behavior.Source: Figure 4 · p. 6, §5.1 · p. 7
  • Using one response, VOCAL is competitive with multi-sample UQ methods, often tracks their upper envelope, and sometimes performs best, though several baselines surpass it on TriviaQA.Multi-sample methods require multiple generations and expensive semantic-consistency computations.Source: Figure 5 · p. 7, §5.1 · pp. 7–8
  • VOCAL achieves the highest AUROC in 5 of 6 evaluated settings, including 0.715 on GSM-Hard with DeepSeek-V3.1 versus 0.520 for G-NLL and 0.567 for PPL.PPL is marginally better on Trivia QA with GPT-4o.Source: §5.1 · p. 7, Table 1 · p. 7
  • With post-hoc calibration, VOCAL w/ TS has the lowest average ECE among TS-calibrated methods, and VOCAL w/ IR achieves the best overall calibration with average ECE 0.0281.The calibration evaluation covers GPT-4o on GSM-Hard, GSM8K, and MedQA.Source: §5.1 · p. 8
  • Cross-model transfer on SciQ yields competitive AUROC values of 0.60–0.72, but model-specific expression differences prevent a fully universal mapping.The experiments train and test VOCAL on responses from different LLMs.Source: Figure 6 · p. 8, §5.1 · p. 8
  • GPT-4o and humans assign substantially different probabilities to markers: GPT-4o gives “almost certain” 0.677 versus humans’ 0.92, and “very likely” 0.355 versus humans’ 0.853.The comparison is between the GPT-4o-optimized mapping and the human-sourced lookup on SciQ.Source: §5.1 · p. 8, Table 2 · p. 8

6. Conclusion

The paper investigates how LLMs’ verbal uncertainty differs from humans’ and whether model-specific calibration can improve quantification. It concludes that human-derived mappings only partially capture model behavior, while VOCAL offers more reliable quantification and performance comparable to costly multi-sample methods with lower computational overhead.

6. Conclusion

  • The work investigates how LLMs diverge from humans in expressing verbal uncertainty.It introduces a large-scale human uncertainty-marker lookup table and VOCAL, an optimization-based alignment algorithm.Source: §6 · pp. 8–9
  • Human-derived mappings only partially capture model behavior, while LLM-specific calibrations offer more reliable uncertainty quantification.The paper presents the human lookup table as the first large-scale resource of its kind.Source: §6 · p. 9
  • VOCAL performs comparably to costly multi-sample UQ methods with much lower computational overhead, supporting practical benefits for trustworthy deployment and directions for human–AI alignment research.Source: §6 · p. 9

Limitations

The section reviews limits of verbal uncertainty, contrasts predictive and semantic uncertainty measures, describes how human verbal markers are mapped to probabilities, and outlines prompts used to elicit them from models.

Limitations

  • Verbal uncertainty is coarse, marker extraction can be ambiguous, and domain- and culture-dependent interpretations limit the generalizability of a single lookup table.The section identifies these issues as directions for more expressive, robust, and context-aware verbal UQ methods.Source: Limitations · p. 9

A. Uncertainty Quantification in LLMs

  • Predictive Entropy measures uncertainty in the predictive distribution, while Semantic Entropy aggregates probability mass over output clusters sharing the same semantics.The section notes that these realizations target distinct aspects of output uncertainty.Source: A. Uncertainty Quantification in LLMs · p. 14

B. Human Verbal Uncertainty Expression

  • The human-grounded lookup table consolidates verbal-marker probabilities from empirical studies, rescaling reported ranges and scales and averaging processed values into Table 4.For example, “likely” is assigned 0.72 from a reported mean or 0.70 as the midpoint of a reported range.Source: B. Human Verbal Uncertainty Expression · p. 14, Table 4 · p. 15

C. Prompt LLMs to Express Verbal Uncertainty

  • The baseline prompt requests conversational answers and a specific final answer in two-field JSON, while the verbal-uncertainty prompt adds uncertainty phrases and a separate list of those phrases.The latter also requests a final answer in a three-field JSON response.Source: C. Prompt LLMs to Express Verbal… · p. 17
  • The verbal-uncertainty prompt requires valid JSON with answer, vue, and final_answer fields, including naturally embedded uncertainty expressions listed in vue.It asks for the most specific answer possible in final_answer.Source: C. Prompt LLMs to Express Verbal… · p. 17

D. Experimental Settings

The experimental settings use separate generation configurations for correctness assessment and uncertainty quantification.

D. Experimental Settings

  • Correctness was assessed with greedy decoding, while uncertainty quantification used five multinomial samples at temperature 0.8; outputs were capped at 512 tokens with top_p 1.0.Source: §D.1 · p. 18

D.2. Datasets

The dataset suite covers mathematical reasoning, medical knowledge, commonsense, science, and reading comprehension.

D.2. Datasets

  • The evaluation spans GSM8K and GSM-Hard math reasoning, MedQA, PIQA, SciQ, and TriviaQA, covering multi-step problems, medical questions, physical commonsense, science exams, and evidence-based reading comprehension.GSM-Hard is a challenging GSM8K subset, and TriviaQA uses large, unstructured evidence documents.Source: §D.2 · p. 18

E. Failure Case Analysis

The failure-case analysis examines both low-confidence correct answers and high-confidence incorrect answers.

E. Failure Case Analysis

  • The analysis presents one correct answer with a low confidence score and one incorrect answer with a high confidence score to clarify when verbal uncertainty fails.The authors say these cases point toward possible directions for addressing such failures.Source: E. Failure Case Analysis · p. 18

E.1. Under-Confidence Despite Correctness

A DeepSeek-V3.1 example on PIQA contrasts confidence from consistent, correct sampled answers with VOCAL’s hedged verbal output for the same correct answer.

E.1. Under-Confidence Despite Correctness

  • The sampling-based baseline shows high confidence because its generations are consistent and match the ground truth.Source: §E.1 · p. 18
  • VOCAL uses hedges such as “not completely confident” and “I think,” lowering confidence despite the correct final answer.Its output gives the same final answer as the baseline.Source: §E.1 · pp. 18–19
  • The example is DeepSeek-V3.1 on PIQA, where the final answer is correct.The question asks how to trigger a sneeze when one feels unable to sneeze.Source: §E.1 · p. 19

E.2. Over-Confidence Despite Incorrectness

A MedQA example shows verbal confidence can be high on an incorrect answer, and the discussion notes that verbal expressions may not align with internal confidence. The later sections report that verbal uncertainty prompting maintains general performance and describe marker distributions and optimized lookup tables.

E.2. Over-Confidence Despite Incorrectness

  • On MedQA, VOCAL uses high-confidence phrases for an incorrect final answer, while sampled answers disagree and only one matches the ground truth.The example identifies “fairly confident” and “most likely” as the verbal phrases.Source: §E.2 · pp. 19–20

E.3. Discussion.

  • The discussion says verbal uncertainty expressions may misalign with internal confidence and calls for domain-specific signals and clearer prompting strategies.Source: §E.3 · p. 20

F.1. Verbal Uncertainty Prompting Maintains General Performance

F.2. Advanced LLMs Express Diverse Uncertainty Markers

G. Optimized UM-Lookup Table

H. The Use of Large Language Models (LLMs)

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