Improved Confidence Estimates for Black-Box Large Language Models

Sokhna Diarra Mbacke; Mouloud Belbahri; Gabriel Loaiza-Ganem

cs.LGAug 19, 2026

Improved Confidence Estimates for Black-Box Large Language Models

Authors: Sokhna Diarra Mbacke, Mouloud Belbahri, Gabriel Loaiza-Ganem

Organizations: Layer 6 AI · TD Insurance

Abstract

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

Panel of Figure 1 — Figure 1: Most UQ methods use a given query $q$ and one or more corresponding LLM-generated responses $\mathbf{r}$ to obtain uncertainty scores $\mathbf{s}$ 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 $\mathbf{s}$ , to produce features $\mathbf{x}$ ; we then train a classifier predicting $y$ from $\mathbf{x}$ .

GPT4.1
	AUROC ( $\uparrow$ )				ECE ( $\downarrow$ )
	$P_{\mathrm{true}}$	Semantic	APRICOT	Auto-ML	$P_{\mathrm{true}}$	ts- $P_{\mathrm{true}}$	APRICOT	Auto-ML
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.

LLaMA4Maverick
	AUROC ( $\uparrow$ )			ECE ( $\downarrow$ )
	$P_{\mathrm{true}}$	Semantic	Auto-ML	$P_{\mathrm{true}}$	Auto-ML
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.

GPT4.1
	AUROC ( $\uparrow$ )			ECE ( $\downarrow$ )
	$P_{\mathrm{true}}$	Semantic	Auto-ML	$P_{\mathrm{true}}$	ts- $P_{\mathrm{true}}$	Auto-ML
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
$P_{\mathrm{true}}$	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
$P_{\mathrm{true}}$	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
$P_{\mathrm{true}}$	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
$P_{\mathrm{true}}$	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.

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Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering

Tiejin Chen, Longchao Da, Xiaoou Liu, Hua Wei

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LLM Evaluation Uncertainty Quantification Confidence Estimation in Language Models LLM Reliability LLM Hallucination Detection LLM Uncertainty Estimation

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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.

Abstract

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