As Large Language Models (LLMs) are increasingly deployed in real-world applications, reliable uncertainty quantification (UQ) becomes critical for safe and effective use. Most existing UQ approaches for language models aim to produce a single confidence score -- for example, estimating the probability that a model's answer is correct. However, uncertainty in natural language tasks arises from multiple distinct sources, including model knowledge gaps, output variability, and input ambiguity, which have different implications for system behavior and user interaction. In this work, we study how the source of uncertainty impacts the behavior and effectiveness of existing UQ methods. To enable controlled analysis, we introduce a new dataset that explicitly categorizes uncertainty sources, allowing systematic evaluation of UQ performance under each condition. Our experiments reveal that while many UQ methods perform well when uncertainty stems solely from model knowledge limitations, their performance degrades or becomes misleading when other sources are introduced. These findings highlight the need for uncertainty-aware methods that explicitly account for the source of uncertainty in large language models.
Figures & tables
Figure 1: Question generation pipeline used to construct question triplets.
Setting
Question Types
Desciption
MK
Type 1
Well-formed questions with a unique correct answer. Model knowledge is the sole source of uncertainty.
MK + OV
Type 2
Questions admitting multiple valid answers. Output variability is introduced alongside model knowledge uncertainty.
MK + IA
Type 1 + Type 3
Mix of well-formed and underspecified questions. A well-calibrated method must remain confident on correctly answered Type 1 and assign high uncertainty to Type 3.
MK + OV + IA
Type 1 + Type 2 + Type 3
All question types combined, reflecting realistic deployment conditions where all uncertainty sources co-occur.
Table 1: Evaluation settings. Model knowledge (MK) uncertainty is present in all settings as an inherent property of any deployed system; remaining settings layer output variability (OV) and input ambiguity (IA) on top.
Figure 2: Prediction–Rejection Ratio (PRR) curve of non-rejected prediction quality vs. rejection rate. Oracle denotes the optimal strategy; Random and UQ correspond to random and uncertainty-based rejection.
Metric
MK
MK+OV
MK+IA
MK+OV+IA
SP
0.580
0.417 ↓ 0.163
0.438 ↓ 0.142
0.415 ↓ 0.165
PPL
0.556
0.372 ↓ 0.184
0.415 ↓ 0.141
0.372 ↓ 0.184
MTE
0.593
0.405 ↓ 0.188
0.445 ↓ 0.148
0.401 ↓ 0.192
MCSE
0.587
0.425 ↓ 0.162
0.439 ↓ 0.149
0.426 ↓ 0.161
MCNSE
0.561
0.371 ↓ 0.190
0.400 ↓ 0.161
0.368 ↓ 0.193
Consistency
0.511
0.386 ↓ 0.125
0.358 ↓ 0.153
0.320 ↓ 0.191
Table 2: PRR scores averaged across all five models. Inline arrows show drop from MK setting. Bold and underline denote best and second-best per column.
Figure 3: Examples of UQ failure modes across question types. Type 1: consistent, high-probability answers are correct. Type 2: inconsistency reflects valid output diversity, not poor quality. Type 3: the model commits to one interpretation of an ambiguous input, producing falsely confident, consistent answers.
Figure 4: Density of UQ scores for correct single- and multi-answer, and incorrect responses. Output variability shifts the correct distribution toward higher uncertainty, increasing overlap with incorrect answers. Model – Gemma-3-12b-Instruct.
Figure 5: Density of UQ scores for correct, incorrect answers and answered ambiguous questions. Models commit to an arbitrary interpretation and answer with apparent confidence – uncertainty estimates for ambiguous inputs are lower than for incorrect answers, indicating overconfidence. Model – Gemma-3-12b-Instruct.
Appendix figures & tables17 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Agreement between human annotations and LLM-as-Judge across question types.
Model
HuggingFace Endpoint
Llama-3.1-8b-Instruct
meta-llama/Llama-3.1-8B-Instruct
Gemma-3-12b-Instruct
google/gemma-3-12b-it
Qwen-2.5-14b-Instruct
Qwen/Qwen2.5-14B-Instruct
llamaseventy
meta-llama/Llama-3.3-70B-Instruct
Appendix
Table 3: HuggingFace Inference Endpoints used in our experiments.
Model
Single-answer
Multi-answer
Clarification rate
Llama-3.1-8b-Instruct
68.6% (370/539)
76.3% (411/539)
3.5% (19/539)
Gemma-3-12b-Instruct
69.0% (372/539)
76.6% (413/539)
0.0% (0/539)
Qwen-2.5-14b-Instruct
64.7% (349/539)
70.5% (380/539)
0.7% (4/539)
Llama-3.3-70b-Instruct
88.5% (477/539)
84.6% (456/539)
0.0% (0/539)
GPT-4.1
94.8% (511/539)
91.8% (495/539)
0.0% (0/539)
Appendix
Table 4: Quality of generations across models. For single- and multi-answer questions we report accuracy; for ambiguous inputs we report the clarification rate (fraction of outputs that explicitly ask for clarification).
Figure 7: Distributions of generation lengths across models.
Metric
Single
Ambi
Multi
Combined
SP
0.594
0.503 ↓ 0.091
0.585 ↓ 0.009
0.501 ↓ 0.093
PPL
0.503
0.434 ↓ 0.069
0.457 ↓ 0.046
0.413 ↓ 0.090
MTE
0.568
0.492 ↓ 0.076
0.541 ↓ 0.027
0.485 ↓ 0.083
MCSE
0.608
0.522 ↓ 0.086
0.643 ↑ 0.035
0.543 ↓ 0.065
MCNSE
0.524
0.472 ↓ 0.052
0.464 ↓ 0.060
0.443 ↓ 0.081
Consistency
0.490
0.419 ↓ 0.072
0.479 ↓ 0.012
0.384 ↓ 0.107
Appendix
Table 5: PRR scores for Llama-8b-it. Inline arrows show drop from Single.
Metric
Single
Ambi
Multi
Combined
SP
0.564
0.394 ↓ 0.170
0.461 ↓ 0.103
0.358 ↓ 0.206
PPL
0.544
0.357 ↓ 0.187
0.456 ↓ 0.088
0.325 ↓ 0.219
MTE
0.587
0.378 ↓ 0.209
0.499 ↓ 0.089
0.346 ↓ 0.242
MCSE
0.587
0.413 ↓ 0.174
0.471 ↓ 0.117
0.374 ↓ 0.213
MCNSE
0.551
0.355 ↓ 0.197
0.467 ↓ 0.085
0.330 ↓ 0.221
Consistency
0.519
0.394 ↓ 0.125
0.424 ↓ 0.095
0.328 ↓ 0.191
Appendix
Table 6: PRR scores for Gemma-12b-it. Inline arrows show drop from Single.
Metric
Single
Ambi
Multi
Combined
SP
0.539
0.395 ↓ 0.145
0.550 ↑ 0.010
0.394 ↓ 0.145
PPL
0.544
0.392 ↓ 0.152
0.524 ↓ 0.020
0.371 ↓ 0.173
MTE
0.570
0.423 ↓ 0.146
0.568 ↓ 0.001
0.408 ↓ 0.162
MCSE
0.520
0.381 ↓ 0.140
0.531 ↑ 0.010
0.381 ↓ 0.140
MCNSE
0.524
0.380 ↓ 0.144
0.519 ↓ 0.005
0.358 ↓ 0.166
Consistency
0.467
0.327 ↓ 0.140
0.498 ↑ 0.031
0.329 ↓ 0.138
Appendix
Table 7: PRR scores for Qwen-14b-it. Inline arrows show drop from Single.
Metric
Single
Ambi
Multi
Combined
SP
0.707
0.476 ↓ 0.231
0.206 ↓ 0.501
0.428 ↓ 0.279
PPL
0.680
0.483 ↓ 0.197
0.213 ↓ 0.467
0.409 ↓ 0.271
MTE
0.702
0.514 ↓ 0.188
0.213 ↓ 0.489
0.423 ↓ 0.279
MCSE
0.751
0.490 ↓ 0.261
0.240 ↓ 0.511
0.447 ↓ 0.304
MCNSE
0.704
0.446 ↓ 0.258
0.222 ↓ 0.482
0.385 ↓ 0.318
Consistency
0.682
0.376 ↓ 0.305
0.290 ↓ 0.392
0.311 ↓ 0.371
Appendix
Table 8: PRR scores for Llama-70b. Inline arrows show drop from Single.
Metric
Single
Ambi
Multi
Combined
SP
0.495
0.424 ↓ 0.071
0.284 ↓ 0.210
0.392 ↓ 0.102
PPL
0.510
0.409 ↓ 0.101
0.209 ↓ 0.302
0.342 ↓ 0.168
MTE
0.537
0.419 ↓ 0.118
0.202 ↓ 0.335
0.341 ↓ 0.196
MCSE
0.470
0.388 ↓ 0.082
0.242 ↓ 0.228
0.386 ↓ 0.084
MCNSE
0.503
0.347 ↓ 0.156
0.185 ↓ 0.318
0.325 ↓ 0.178
Consistency
0.395
0.273 ↓ 0.122
0.237 ↓ 0.157
0.246 ↓ 0.149
Appendix
Table 9: PRR scores for GPT-4.1. Inline arrows show drop from Single.
Figure 8: Density of uncertainty scores for correct (single answer), correct (multi answer), and incorrect (pooled) responses. Model - Llama-3.1-8b-Instruct.
Figure 9: Density of uncertainty scores for correct (single answer), incorrect, and answered (ambiguous) responses. Model - Llama-3.1-8b-Instruct.
Figure 10: Density of uncertainty scores for correct (single answer), correct (multi answer), and incorrect (pooled) responses. Model - Qwen-2.5-14b-Instruct.
Figure 11: Density of uncertainty scores for correct (single answer), incorrect, and answered (ambiguous) responses. Model - Qwen-2.5-14b-Instruct.
Figure 12: Density of uncertainty scores for correct (single answer), correct (multi answer), and incorrect (pooled) responses. Model - Llama-3.3-70b-Instruct.
Figure 13: Density of uncertainty scores for correct (single answer), incorrect, and answered (ambiguous) responses. Model - Llama-3.3-70b-Instruct.
Figure 14: Density of uncertainty scores for correct (single answer), correct (multi answer), and incorrect (pooled) responses. Model - GPT-5.
Figure 15: Density of uncertainty scores for correct (single answer), incorrect, and answered (ambiguous) responses. Model - GPT-5.
Uncertainty Quantification (UQ) is widely regarded as the primary safeguard for deploying Large Language Models (LLMs) in high-stakes domains. However, we argue that the field suffers from a category error: mainstream UQ methods for LLMs are just unsupervised clustering algorithms. We demonstrate that most current approaches inherently quantify the internal consistency of the model's generations rather than their external correctness. Consequently, current methods are fundamentally blind to factual reality and fail to detect ``confident hallucinations,'' where models exhibit high confidence in stable but incorrect answers. Therefore, the current UQ methods may create a deceptive sense of safety when deploying the models with uncertainty. In detail, we identify three critical pathologies resulting from this dependence on internal state: a hyperparameter sensitivity crisis that renders deployment unsafe, an internal evaluation cycle that conflates stability with truth, and a fundamental lack of ground truth that forces reliance on unstable proxy metrics to evaluate uncertainty. To resolve this impasse, we advocate for a paradigm shift to UQ and outline a roadmap for the research community to adopt better evaluation metrics and settings, implement mechanism changes for native uncertainty, and anchor verification in objective truth, ensuring that model confidence serves as a reliable proxy for reality.
Tiejin Chen, Longchao Da, Xiaoou Liu +1
School of Computing and Augmented Intelligence, Arizona State University
Uncertainty quantification (UQ) is essential for the safe deployment of large language models (LLMs). Existing methods, from verbalized confidence to ones requiring multiple generations, are often zero-shot and produce scores quantifying uncertainty without the need for labelled data. Nonetheless, in practice one must always evaluate their performance on a dataset of interest before deployment. In this work we show that, by leveraging this dataset, we consistently outperform these existing scores. Specifically, we build simple classifiers that predict LLM response correctness by using these scores and the correctness of similar queries as features. Our method produces minimal computational overhead, making it a cheap and straightforward enhancement for UQ in LLMs for real-world applications.
Sokhna Diarra Mbacke, Mouloud Belbahri, Gabriel Loaiza-Ganem
Large Language Models (LLMs) demonstrate remarkable capabilities in generative tasks but pose potential risks due to their tendency to generate hallucinatory responses. Therefore, Uncertainty Quantification (UQ), which aims to distinguish the validity of answers, is crucial for ensuring the safety and robustness of AI systems. However, existing methods primarily rely on measuring the entropy of multiple stochastic samples to represent uncertainty, often overlooking the specific uncertainty information associated with the candidate answer under evaluation. This oversight can lead to biased classification outcomes. In this paper, we investigate the discrepancy between global entropy from multiple samples and local confidence of candidate answer, and propose a Label-Confidence-Aware Uncertainty Quantification (LCA-UQ) method based on Pointwise Kullback-Leibler (PKL) divergence. Our method effectively bridges the gap between the consistency of sampled outputs and the calibration of the candidate answer, thereby enhancing the reliability and stability of uncertainty assessments. Empirical evaluations across a range of popular LLMs and NLP datasets reveal that label sources significantly impact classification. Furthermore, our approach effectively captures the nuances between sampling results and label sources, demonstrating superior performance in uncertainty estimation.
Qinhong Lin, Yinglun Feng, Yuhao Zhang +2
School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing, China · QuanCheng Laboratory, Jinan, China