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

This paper investigates the divergence between humans and large language models in verbal uncertainty quantification by introducing an optimization-based algorithm, METHODNAME, which learns optimal probability mappings for verbal markers directly from model outputs to reveal systematic confidence disparities without relying on repeated sampling.

Original authors: Jinhao Duan, Zicheng Liu, Zijie Liu, Kaidi Xu, Tianlong Chen

Published 2026-10-02

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CC BY 4.0

Original authors: Jinhao Duan, Zicheng Liu, Zijie Liu, Kaidi Xu, Tianlong Chen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

When we speak, we often hedge our bets. We say something is "likely," "possible," or "almost certain," using these words to signal how much we truly know. This ability to express doubt is a form of metacognition, a mental check where we acknowledge the boundaries of our own knowledge. It is a crucial part of human communication, allowing us to navigate uncertainty without pretending to have answers we do not possess. In the world of artificial intelligence, specifically with large language models, this same ability is becoming a critical safety feature. These models can sometimes generate confident-sounding but factually incorrect information, a phenomenon known as hallucination. To trust these systems, especially in sensitive fields like medicine or law, we need to know when they are unsure. The challenge lies in figuring out if the words an AI uses to express doubt mean the same thing to a human listener as they do to the machine itself.

A team of researchers set out to investigate whether the verbal uncertainty expressed by large language models aligns with human understanding. They began by gathering a massive collection of how people interpret phrases like "very likely" or "uncertain." Drawing from decades of psychological and decision-science research, they compiled a reference guide that maps these common phrases to specific numerical probabilities. For instance, in the human mind, the phrase "very likely" corresponds to a high degree of confidence, while "possible" sits somewhere in the middle. The researchers then tested several advanced language models, asking them to answer questions and explain their confidence using these same natural language phrases. They compared the models' answers against the human reference guide to see if the machines were speaking the same language as their users.

The results revealed a significant disconnect. While the models could use the words, they assigned different levels of certainty to them than humans do. For example, when a human hears "very likely," they interpret it as a strong probability, but the models in the study often used this phrase to describe situations where they were actually quite unsure. Conversely, the models might express a high degree of confidence for phrases that humans consider to be mere guesses. This mismatch means that simply reading a model's output and assuming its verbal cues reflect its internal state can be misleading. The study showed that relying on a human-made dictionary of uncertainty words was not enough to accurately gauge a machine's confidence; the models had their own, distinct internal logic for what those words meant.

To bridge this gap, the researchers developed a new method called VOCAL. Instead of forcing the models to conform to human definitions, this approach learns the specific meaning of uncertainty words directly from the model's own behavior. The system analyzes thousands of the model's responses, noting which phrases it uses when it is right and which it uses when it is wrong. It then builds a custom map that translates the model's specific verbal habits into accurate probability scores. This process involves a mathematical optimization that smooths out the data, ensuring that similar-sounding phrases receive similar scores, even if the model uses them rarely. By tailoring the interpretation to the specific machine, the method creates a much more reliable way to detect when the model is unsure.

The experiments demonstrated that this customized approach works significantly better than trying to force a human standard onto the machine. In tests across various datasets, including complex math problems and medical questions, the new method was far more accurate at predicting whether a model's answer was correct or incorrect compared to using the human reference guide alone. In some cases, the improvement was substantial, turning a method that barely performed better than random guessing into one that could reliably spot errors. The researchers found that this technique could achieve performance levels comparable to much more expensive methods that require the model to generate multiple answers and compare them, but without the extra time or computing power.

The study concludes that while large language models can mimic human speech patterns, their internal understanding of uncertainty is fundamentally different from our own. A phrase like "very likely" does not carry the same weight for the machine as it does for a person. To make these systems truly trustworthy, we cannot simply ask them to speak like humans and expect them to mean the same thing. Instead, we must learn to read their specific dialect of uncertainty. By creating custom maps that translate a model's unique verbal signals into clear signals of confidence, we can better distinguish between a correct answer and a confident hallucination, making the technology safer and more reliable for real-world use.

Technical Summary: "Very Likely" Means "Uncertain"? How LLMs Diverge from Humans in Linguistic Uncertainty Quantification

Problem Statement

While Large Language Models (LLMs) have achieved remarkable success, a fundamental challenge remains in determining when to trust their responses, particularly regarding hallucinations. Existing Uncertainty Quantification (UQ) methods generally fall into two categories: sampling-based (e.g., Semantic Entropy, ensemble variance) and logits-based (e.g., Predictive Entropy, Perplexity). However, these approaches suffer from significant limitations: sampling methods are computationally expensive and introduce latency, while logits-based methods often suffer from lexical sensitivity and fail to capture the nuance of human reasoning.

Humans naturally express uncertainty using verbal markers (e.g., "possible," "likely," "almost certain"). While recent work has explored verbalized UQ, a critical gap exists: LLMs diverge from humans in how they interpret and utilize these linguistic markers. Current methods often rely on lookup tables derived from human psychology literature to map verbal phrases to numerical probabilities. The authors posit that these human-derived mappings do not accurately reflect the internal uncertainty states of LLMs, leading to unreliable quantification.

Methodology

1. Human Verbal Uncertainty Benchmark (UM-Lookup)

The authors first constructed a large-scale Verbal Uncertainty Marker Lookup Table (UM-Lookup). This resource aggregates data from foundational studies in psychology and decision science (e.g., Lichtenstein & Newman, 1967; Beyth-Marom, 1982; Vogel et al., 2022).

Construction: The table maps 115 distinct verbal uncertainty expressions to numerical probability scores based on an average of 336 human ratings per phrase.
Aggregation: When an LLM generates a response containing multiple markers, the method (denoted as $Q_{VU-H}$ ) averages the numerical scores of the extracted markers to produce a final uncertainty estimate.
Initial Evaluation: The authors evaluated $Q_{VU-H}$ against standard baselines (Predictive Entropy, Semantic Entropy) across various models (GPT-4o, DeepSeek-V3.1) and datasets (GSM8K, MedQA, SciQ). While $Q_{VU-H}$ demonstrated non-trivial performance in some cases, it frequently underperformed compared to sampling-based methods and, in some instances (e.g., GPT-4o on GSM8K), performed worse than random chance. This confirmed a fundamental misalignment between human linguistic intuition and LLM internal confidence.

2. VOCAL: Optimized Verbal Uncertainty Quantification

To address this misalignment, the authors propose VOCAL, a novel optimization-based algorithm that learns an LLM-specific mapping between verbal markers and numerical uncertainty levels.

Objective: VOCAL learns a set of numerical scores ( $c_i$ ) for each verbal marker ( $u_i$ ) such that the aggregated uncertainty score ( $q_y$ ) faithfully reflects the model's actual correctness. The goal is to assign higher uncertainty scores to incorrect generations and lower scores to correct ones.
Optimization Formulation: The problem is formulated as minimizing a Binary Cross-Entropy (BCE) loss:
$\mathcal{L}(c) = \min_{c} \mathbb{E}_{(x,y)} \left[ -z \log c_y - (1-z) \log(1-c_y) \right]$
Where $z$ is the correctness indicator (1 for correct, 0 for incorrect), and $c_y$ is the aggregated uncertainty derived from the learned scores of the markers in generation $y$ .
Semantic Smoothing: To handle data sparsity (where rare markers like "faint chance" have few training examples), VOCAL incorporates a Graph Laplacian Regularizer. This enforces smoothness by penalizing large discrepancies between semantically similar markers (measured via 3-gram Jaccard similarity). The total objective is $\mathcal{L}(c) + \gamma \mathcal{L}_{lap}(c)$ .
Efficiency: Unlike sampling-based methods, VOCAL requires only a single model response to generate an uncertainty score, avoiding the computational overhead of multiple generations.

Key Contributions

Human Verbal Uncertainty Lookup Table: The paper presents a curated resource of 115 verbal markers mapped to numerical probabilities, grounded in psychological literature. This serves as a foundational benchmark for analyzing human-LLM divergence in metacognitive monitoring.
VOCAL Algorithm: The authors introduce VOCAL, a lightweight, optimization-based method that tailors verbal uncertainty mappings to specific LLMs without requiring parameter updates or fine-tuning. It learns the optimal probability mass each marker should convey based on empirical correctness.
Comprehensive Empirical Analysis: The study provides an in-depth analysis of how LLMs diverge from humans. For instance, the paper demonstrates that while humans rate "very likely" as highly confident (~~0.85), GPT-4o associates it with significantly lower confidence (~~0.35) in its internal state.

Results

Superiority over Human Lookup: VOCAL consistently outperforms the human-sourced UM-Lookup ( $Q_{VU-H}$ ). On the GSM8K dataset, VOCAL improved the AUROC for GPT-4o from 0.41 (using human lookup) to approximately 0.60.
Comparison with Single-Sample Baselines: VOCAL significantly outperforms single-sample UQ methods such as G-NLL and Perplexity (PPL). In 5 out of 6 evaluated settings, VOCAL achieved the highest AUROC. For example, on GSM-Hard with DeepSeek-V3.1, VOCAL achieved an AUROC of 0.715, compared to 0.520 for G-NLL.
Competitiveness with Multi-Sample Methods: Despite using only a single response, VOCAL achieves performance comparable to expensive multi-sample methods (e.g., Semantic Entropy, Semantic Density). In several cases (e.g., SciQ with Qwen2.5-72B), VOCAL achieved the top AUROC (0.717), surpassing sampling-based baselines.
Calibration: VOCAL demonstrates strong calibration properties. When combined with post-hoc calibration methods like Isotonic Regression (IR), it achieved an average Expected Calibration Error (ECE) of 0.0281, outperforming other baselines.
Transferability: Experiments show that while verbal uncertainty indicators are largely transferable across different LLMs (AUROC remains in the 0.60–0.72 range when training on one model and testing on another), model-specific tuning via VOCAL yields superior results.

Significance and Claims

The paper claims that verbal uncertainty expressions are model-dependent, and relying on fixed, human-defined tables is insufficient for reliable UQ in LLMs. The significance of this work lies in:

Bridging the Human-LLM Gap: It reveals that "very likely" does not mean the same thing to an LLM as it does to a human, highlighting a critical disconnect in current trust mechanisms.
Efficiency and Practicality: VOCAL offers a strong accuracy-efficiency trade-off. It provides near state-of-the-art uncertainty discrimination without the latency and cost of multi-sample semantic-consistency pipelines, making it more practical for real-world deployment.
Metacognitive Insight: The findings suggest that while LLMs can express uncertainty verbally, their internal mapping of these expressions to confidence levels is distinct from human cognition. VOCAL provides a mechanism to align these expressions with the model's actual reliability, supporting more trustworthy AI interactions.

The authors conclude that grounding LLM uncertainty in verbal expressions, when properly calibrated to the specific model, offers a viable path toward more trustworthy and responsible generative AI.