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.
Figures & tables
Figure 1: Most UQ methods use a given query q and one or more corresponding LLM-generated responses r to obtain uncertainty scores s whose goal is to correlate with y (a correctness label for the response). Instead, we retrieve similar queries from an existing dataset, and use the retrieved queries, alongside s , to produce features x ; we then train a classifier predicting y from x .
AUROC ( ↑ )
ECE ( ↓ )
Ptrue
Semantic
APRICOT
Auto-ML
Ptrue
ts- Ptrue
APRICOT
Auto-ML
GPT4.1
CS_QA
0.743
0.645
0.494
0.770
0.069
0.023
0.660
0.024
NQ
0.715
0.709
0.457
0.774
0.322
0.016
0.148
0.029
SciQ
0.895
0.653
0.452
0.911
0.021
0.008
0.966
0.008
SimpleQA
0.632
0.769
0.489
0.782
0.325
0.183
0.312
0.040
Table 1: AUROC ( higher is better ) and ECE ( lower is better ) across methods. For each method family, we report the best score (highest AUROC, lowest ECE), averaged over five independent runs with different random seeds. Semantic UQ scores are included as features in the Auto-ML method.
Figure 2: AUROC ( higher is better ) across methods. Each bar shows the average AUROC over five independent runs with different random seeds for each dataset/LLM combination. Red integers above the bars indicate "win" counts, i.e., the number of times a method achieved the highest AUROC among all methods. Semantic UQ scores are included as features in the Auto-ML method.
AUROC ( ↑ )
ECE ( ↓ )
Ptrue
Semantic
Auto-ML
Ptrue
Auto-ML
LLaMA4Maverick
NQ
0.727
0.762
0.796
0.077
0.029
SciQ
0.853
0.580
0.857
0.003
0.003
SimpleQA
0.624
0.778
0.787
0.336
0.027
Table 2: AUROC ( higher is better ) and ECE ( lower is better ) across methods with LLaMA4Maverick generations.
AUROC ( ↑ )
ECE ( ↓ )
Ptrue
Semantic
Auto-ML
Ptrue
ts- Ptrue
Auto-ML
GPT4.1
CS_QA
0.743
0.645
0.747
0.069
0.023
0.036
NQ
0.715
0.709
0.735
0.322
0.016
0.025
SciQ
0.895
0.653
0.894
0.021
0.008
0.009
SimpleQA
0.632
0.769
0.667
0.325
0.183
0.088
Table 3: AUROC ( higher is better ) and ECE ( lower is better ) across methods without semantic features for Auto-ML.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Method
CS_QA
NQ
SciQ
SimpleQA
Ptrue
0.743 (0.024)
0.715 (0.008)
0.895 (0.011)
0.632 (0.009)
Logistsic Regression
0.764 (0.023)
0.747 (0.008)
0.903 (0.011)
0.780 (0.023)
Random Forest
0.770 (0.020)
0.774 (0.008)
0.906 (0.023)
0.779 (0.022)
Laplacian Degree
0.644 (0.011)
0.697 (0.006)
0.564 (0.035)
0.766 (0.016)
Laplacian Eigenvalue
0.630 (0.007)
0.708 (0.013)
0.653 (0.011)
0.766 (0.016)
Semantic Entropy
0.614 (0.014)
0.646 (0.009)
0.625 (0.023)
0.754 (0.019)
Appendix
Table 4: Mean (standard deviation) AUROC of the different methods and datasets with GPT4.1 generations.
Method
CS_QA
NQ
SciQ
SimpleQA
Ptrue
0.697 (0.019)
0.703 (0.018)
0.837 (0.033)
0.640 (0.026)
Logistsic Regression
0.736 (0.025)
0.754 (0.008)
0.869 (0.028)
0.786 (0.027)
Random Forest
0.737 (0.030)
0.762 (0.013)
0.874 (0.027)
0.774 (0.035)
Laplacian Degree
0.646 (0.025)
0.721 (0.005)
0.622 (0.057)
0.788 (0.022)
Laplacian Eigenvalue
0.631 (0.029)
0.722 (0.006)
0.699 (0.046)
0.785 (0.024)
Semantic Entropy
0.622 (0.027)
0.691 (0.005)
0.674 (0.031)
0.778 (0.025)
Appendix
Table 5: Mean (standard deviation) AUROC of the different methods and datasets with GPT4.1-mini generations.
Method
CS_QA
NQ
SciQ
SimpleQA
Ptrue
0.626 (0.010)
0.734 (0.015)
0.769 (0.017)
0.644 (0.020)
Logistsic Regression
0.707 (0.009)
0.778 (0.009)
0.838 (0.024)
0.748 (0.035)
Random Forest
0. 709 (0.010)
0.790 (0.011)
0.838 (0.029)
0.745 (0.044)
Laplacian Degree
0.684 (0.019)
0.751 (0.013)
0.668 (0.041)
0.703 (0.033)
Laplacian Eigenvalue
0.691 (0.015)
0.741 (0.013)
0.716 (0.038)
0.718 (0.038)
Semantic Entropy
0.660 (0.008)
0.706 (0.014)
0.708 (0.026)
0.725 (0.040)
Appendix
Table 6: Mean (standard deviation) AUROC of the different methods and datasets with GPT4.1-nano generations.
Method
NQ
SciQ
SimpleQA
Ptrue
0.727(0.010)
0.853(0.037)
0.624(0.019)
Logistic Regression
0.792(0.010)
0.817(0.078)
0.787(0.010)
Random Forest
0.796(0.010)
0.842(0.038)
0.771(0.017)
Laplacian Degree
0.758(0.006)
0.476(0.037)
0.776(0.013)
Laplacian Eigenvalue
0.762(0.008)
0.550(0.075)
0.768(0.006)
Semantic Entropy
0.725(0.005)
0.535(0.023)
0.746(0.012)
Appendix
Table 7: Mean (standard deviation) AUROC of the different methods and datasets with LLaMA4Maverick generations.
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
In high-stakes decision-making applications of large language models (LLMs), practitioners require not only accurate LLMs but also uncertainty estimates for their predictions. Existing approaches to uncertainty estimation for LLMs require access to log-probabilities output by the model or require fine-tuning access. However, many industrial LLM products use closed-source API models, and many such API models like GPT do not return log-probabilities and may not allow fine-tuning. We introduce Pinocchio, an external calibrator that estimates the correctness of responses from black-box API models. Trained jointly on responses from seven LLMs, it achieves 0.862 AUROC predicting the correctness of held-out responses from those same models, and shows zero-shot transfer to thirteen unseen models across eight organizations. Our model needs only a single forward pass to generate an uncertainty estimate and requires no access to the target model's logits, weights, or internal states. A lightweight text only 0.8B checkpoint matches our largest model's AUROC. We release code for adding uncertainty estimation to existing repos in only two additional lines of code.
Kevin David Hayes, Arka Pal, Haosong Zhang +2
Department of Computer Science, University of Maryland · Ritual AI · Fudan University +1
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.
Maiya Goloburda, Roman Vashurin, Fedor Chernogorskii +4
Mohamed bin Zayed University of Artificial Intelligence