Towards Reliable Truth-Aligned Uncertainty Estimation in Large Language Models

Ponhvoan Srey; Quang Minh Nguyen; Xiaobao Wu; Anh Tuan Luu

cs.AIApr 1, 2026

Towards Reliable Truth-Aligned Uncertainty Estimation in Large Language Models

Authors: Ponhvoan Srey, Quang Minh Nguyen, Xiaobao Wu, Anh Tuan Luu

Organizations: Nanyang Technological University, Singapore · KAIST, South Korea · Shanghai Jiao Tong University

Abstract

Uncertainty estimation (UE) aims to quantify uncertainty in large language model (LLM) outputs to flag potential hallucinations and support reliable deployment. However, UE metrics often exhibit unstable performance across models and datasets, limiting their practical utility. We formalise this phenomenon as proxy failure, arising because UE metrics are derived from model behaviour rather than being explicitly grounded in factual correctness. We show that when mutual information between a UE score and correctness is low, the score's discriminability must be close to chance. To address this, we propose Truth AnChoring (TAC), a lightweight post-hoc calibration method that maps raw UE scores to truth-aligned correctness probabilities. Even with noisy and few-shot supervision, TAC continues to improve calibration, providing a practical calibration protocol. Our findings highlight the limitations of treating heuristic UE metrics as direct indicators of uncertainty about factual correctness, and position our TAC as a principled step toward more reliable uncertainty estimation for LLMs. The code repository is available at https://github.com/ponhvoan/TruthAnchor/.

Figures & tables

Panel of Figure 1 — Figure 1: Reliability diagrams of widely used and recent uncertainty methods, and our Truth-AnChored (TAC) scores.

Panel of Figure 2 — Figure 2: Our proposed TAC significantly reduces ECE ( $\downarrow$ ) and frequently increases AUC ( $\uparrow$ ), improving calibration and discrimination.

	TriviaQA						SciQ						PopQA
Method	ECE ( $\downarrow$ )			AUC ( $\uparrow$ )			ECE ( $\downarrow$ )			AUC ( $\uparrow$ )			ECE ( $\downarrow$ )			AUC ( $\uparrow$ )
	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$
Qwen-3-4B
MSP	63.68	5.52	-58.16	73.82	73.58	-0.24	55.97	3.89	-52.08	70.07	70.02	-0.05	80.21	6.07	-74.13	33.02	69.14	36.12
Perplexity	62.71	6.12	-56.59	73.60	73.48	-0.12	51.53	9.95	-41.58	69.98	69.98	0.00	80.03	4.65	-75.38	30.43	61.09	30.66
Entropy	53.45	5.97	-47.47	73.51	73.87	0.37	42.20	2.05	-40.15	69.04	67.19	-1.85	72.57	3.70	-68.87	33.93	63.13	29.20

Table 1: Main results.

\Delta

denotes the change of ECE and AUC after truth anchoring (TAC), with improvements in green .

Panel of Figure 3 — Figure 3: Performance of vanilla, CUE, and truth-anchored scores.

Table 2: Performance (average

\Delta

) under few-shot and noisy label constraints.

Table 3: Average performance and

\Delta

compared to vanilla scores under transfer settings.

Figure 4: Pairwise TAC. Upper triangle shows ECE, and lower triangle shows AUC. Darker colours indicate more favourable results.

Panel of Figure 5 — Figure 5: Performance on GSM8K with Ministral-3-8B.

Dataset	ECE ( $\downarrow$ )			AUC ( $\uparrow)$
Dataset	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$
CSQA	14.16	4.03	-10.13	56.85	63.10	+6.25
MedMCQA	23.12	5.59	-17.53	56.16	64.28	+8.12

Table 4: Average performance and change on CSQA and MedMCQA with Gemma-2-9B.

Figure 6: Sensitivity analysis of $\phi_{\textrm{rank}}$ .

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	$\Delta$ (AUC) (SD)	$\Delta$ (ECE) (SD)
TriviaQA	+3.24 (0.14)	-19.35 (1.16)
SciQ	+5.01 (0.36)	-25.69 (1.37)
PopQA	+2.85 (0.14)	-18.76 (2.77)

Appendix

Table 5: Five-seed average changes with Ministral-3-8B.

Panel of Figure 7 — Figure 7: Performance of vanilla, CUE, and truth-anchored scores.

Panel of Figure 8 — Figure 8: Performance of vanilla, CUE, and truth-anchored scores.

	TriviaQA						SciQ						PopQA
Method	ECE ( $\downarrow$ )			AUC ( $\uparrow$ )			ECE ( $\downarrow$ )			AUC ( $\uparrow$ )			ECE ( $\downarrow$ )			AUC ( $\uparrow$ )
	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$	Vanilla	TAC	$\Delta$
Llama-3.2-3B
MSP	48.25	13.41	-34.84	76.15	76.15	0.00	47.96	13.23	-34.73	75.79	75.79	0.00	70.96	2.74	-68.22	53.46	61.51	8.05
Perplexity	58.46	6.51	-51.95	69.19	67.11	-2.09	50.47	8.70	-41.77	72.88	72.25	-0.63	80.05	2.28	-77.76	48.25	57.41	9.16
Entropy	37.83	18.88	-18.95	84.60	84.60	0.00	35.06	15.56	-19.49	76.28	76.28	0.00	58.48	1.71	-56.77	65.41	64.20	-1.21

Appendix

Table 6: Additional results with Llama models.

Question	LLM Answer	Label	Vanilla $\rightarrow$ TAC Confidence
Which businessman on his elevation to the House of Lords, by Gordon Brown, in 2009, took the title Baron of Clapton?	Lord Alan Sugar	Correct	0.172 $\rightarrow$ 0.271
Which 19th century British novelist, who worked as a Surveyor for the Post Office, was reputedly instrumental in the introduction of the pillar box in 1852?	Charles Dickens	Incorrect (Anthony Trollope)	0.877 $\rightarrow$ 0.591
Approximately 20% of the atmosphere is made of which element?	Nitrogen	Incorrect (Oxygen)	0.890 $\rightarrow$ 0.594
What model describing atomic structure is often referred to as a planetary model?	Rutherford model	Incorrect (Bohr model)	0.692 $\rightarrow$ 0.267
What is another word for cellular drinking?	Pinocytosis	Correct	0.632 $\rightarrow$ 0.416 (false negative)

Appendix

Table 7: Qualitative examples of proxy failure and subsequent TAC calibration. Vanilla confidence is derived from entropy. Green indicates movement toward the correctness label, with 1 representing correct generations.

Figure 9: $\Delta$ (ECE) and $\Delta$ (AUC) on TriviaQA with few-shot supervision.

Figure 10: $\Delta$ (ECE) and $\Delta$ (AUC) on TriviaQA with noisy supervision.

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Between the Layers Lies the Truth: Uncertainty Estimation in LLMs Using Intra-Layer Local Information Scores

Zvi N. Badash, Yonatan Belinkov, Moti Freiman

Faculty of Data and Decision Sciences, Technion — Israel Institute of Technology, Haifa, Israel · Faculty of Computer Science, Technion — Israel Institute of Technology, Haifa, Israel · Faculty of Biomedical Engineering, Technion — Israel Institute of Technology, Haifa, Israel

Uncertainty Quantification LLM Uncertainty Estimation

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Large language models (LLMs) are often confidently wrong, making reliable uncertainty estimation (UE) essential. Output-based heuristics are cheap but brittle, while probing internal representations is effective yet high-dimensional and hard to transfer. We propose a compact, per-instance UE method that scores cross-layer agreement patterns in internal representations using a single forward pass. Across three models, our method matches probing in-distribution, with mean diagonal differences of at most

-1.8

AUPRC percentage points and

+4.9

Brier score points. Under cross-dataset transfer, it consistently outperforms probing, achieving off-diagonal gains up to

+2.86

AUPRC and

+21.02

Brier points. Under 4-bit weight-only quantization, it remains robust, improving over probing by

+1.94

AUPRC points and

+5.33

Brier points on average. Beyond performance, examining specific layer--layer interactions reveals differences in how disparate models encode uncertainty. Altogether, our UE method offers a lightweight, compact means to capture transferable uncertainty in LLMs.

Abstract

LLM Uncertainty Estimation

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