NOVA: NOise-aware Verbal Confidence CAlibration for Robust Large Language Models in RAG Systems

Jiayu Liu; Rui Wang; Qing Zong; Yumeng Wang; Cheng Qian; Qingcheng Zeng; Tianshi Zheng; Haochen Shi

cs.CLJan 16, 2026

NOVA: NOise-aware Verbal Confidence CAlibration for Robust Large Language Models in RAG Systems

Authors: Jiayu Liu, Rui Wang, Qing Zong, Yumeng Wang, Cheng Qian, Qingcheng Zeng, Tianshi Zheng, Haochen Shi, +4 more

Organizations: HKUST · UIUC · Northwestern University

Abstract

Accurately assessing model confidence is essential for deploying large language models (LLMs) in mission-critical factual domains. While retrieval-augmented generation (RAG) is widely adopted to improve grounding, confidence calibration in RAG settings remains poorly understood. We conduct a systematic study across four benchmarks, revealing that LLMs exhibit poor calibration performance especially when noisy contexts are retrieved. Specifically, contradictory or irrelevant evidence tends to exacerbate the model's overconfidence issue. To address this, we propose NOVA Rules (NOise-Aware Verbal Confidence CAlibration Rules) to provide a principled foundation for resolving overconfidence under noise. We further design NOVA, a noise-aware calibration framework that synthesizes supervision from ~2K HotpotQA examples guided by these rules. By performing supervised fine-tuning (SFT) with this data, NOVA equips models with intrinsic noise awareness without relying on stronger teacher models. Empirical results show that NOVA yields substantial gains, improving ECE scores by 10.9% in-domain and 8.0% out-of-domain. By bridging the gap between retrieval noise and verbal calibration, NOVA paves the way for both accurate and epistemically reliable LLMs.

Figures & tables

Figure 1: An illustrative example of model responses before and after NOVA . By explicitly training the model to assess passage and group level utility prior to answering, NOVA enables more reliable confidence expression under noisy retrieval. The performance plots report results on NQ for Llama-3.1-8B-Instruct and DeepSeek-R1-Distill-Llama-8B , where SFT corresponds to the Label-only SFT setting in Table 2 , and illustrate how NOVA promotes more transparent and grounded human–computer interaction in real-world scenarios.

Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
BM25 (CoT)	0.205	0.485	0.496	0.552	0.369	0.688	0.566	0.557	0.409	0.571
Contriever (CoT)	0.167	0.550	0.585	0.476	0.347	0.649	0.592	0.535	0.423	0.552
Qwen2.5-7B-Instruct
BM25 (CoT)	0.190	0.620	0.439	0.683	0.473	0.747	0.650	0.670	0.438	0.680

Table 1: Real-world RAG results across four datasets demonstrate consistently poor calibration. Notably, average ECE exceeds 0.4, highlighting severe misalignment between verbal confidence and empirical correctness.

Figure 2: Calibration performance of Llama-3.1-8B-Instruct and DeepSeek-R1-Distill-Llama-8B on NQ and Bamboogle under controlled noise settings. The plots display ECE, AUROC, and Average Confidence across four retrieval settings: Gold-only , Gold+Irrelevant (Irr), Gold+Relevant (Rel), and Gold+Counterfactual (Cf). Results show that introducing noise, particularly counterfactual passages, substantially degrades calibration performance.

Figure 3: Overview of the NOVA data pipeline, consisting of three stages: RAG Passage Construction, Training Response Generation, and Multi-stage Data Filtering. In Training Response Generation, the model takes a query $q$ and retrieved passages $\mathcal{P}$ with $k=3$ as input (Input: Q+3P), generates passage-level and group-level judgments $J_{p},J_{g}$ (P Type), then predicts the answer $\hat{a}$ (A) and verbal confidence $\hat{c}$ (C). The pipeline ultimately yields 2K high-quality trajectories for fine-tuning.

Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
Vanilla	0.396	0.602	0.460	0.605	0.465	0.577	0.324	0.636	0.411	0.605
CoT	0.354	0.555	0.444	0.645	0.423	0.611	0.288	0.552	0.377	0.591
Noise-aware	0.376	0.615	0.309	0.642	0.351	0.618	0.217	0.793	0.314	0.667
Ensemble	0.370	0.609	0.397	0.650	0.428	0.619	0.214	0.713	0.352	0.648

Table 2: Calibration performance of various models on four datasets. Scores in bold indicate the best performance, while underlined scores denote the second-best. Results show that NOVA substantially improves calibration and consistently outperforms several baselines, without sacrificing accuracy, as evidenced in Appendix B.8 .

	NQ		Bamboogle		Average			NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct							DeepSeek-R1-Distill-Llama-8B
Vanilla	0.371	0.645	0.212	0.633	0.292	0.639	Vanilla	0.376	0.625	0.154	0.671	0.265	0.648
CoT	0.352	0.670	0.199	0.579	0.276	0.625	CoT	0.373	0.621	0.203	0.633	0.288	0.627
Noise-aware	0.289	0.667	0.140	0.806	0.215	0.737	Noise-aware	0.290	0.605	0.153	0.658	0.222	0.632
Ensemble	0.334	0.693	0.173	0.680	0.254	0.687	Ensemble	0.351	0.590	0.143	0.711	0.247	0.651

Table 3: Out-of-Distribution (OOD) results with 5 passage per query on the NQ and Bamboogle datasets, demonstrating that NOVA maintains robust calibration performance and consistently outperforms several strong baselines even when facing varying amounts of retrieved context in unseen scenarios. More generalization test is in Appendix B.1 .

	Average			Average
Method	ECE $\downarrow$	AUROC $\uparrow$	Method	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct			DeepSeek-R1-Distill-Llama-8B
Vanilla	0.472	0.616	Vanilla	0.429	0.684
CoT	0.423	0.552	CoT	0.454	0.672
Noise-aware	0.318	0.655	Noise-aware	0.409	0.633
Ensemble	0.354	0.620	Ensemble	0.505	0.672

Table 4: Average calibration performance of four models across four datasets with Contriever. Full results are in Appendix B.4 . Bold and underline mark the best and second-best scores within each model.

Appendix figures & tables30 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	# Questions	Confidence Interval
HotpotQA	800	$\pm$ 0.0347
StrategyQA	800	$\pm$ 0.0347
NQ	800	$\pm$ 0.0347
Bamboogle	150	$\pm$ 0.0800

Appendix

Table 5: Dataset statistics and 95% confidence intervals of ECE and AUROC.

Hyperparameter	BM25	Contriever
Top- $K$ Retrieval	5	5
Reranker	No	No
Model Specifics
Architecture	Sparse (Probabilistic)	Dense (Bi-Encoder)
Embedding Model	N/A	facebook/ contriever
Max Input Length	N/A	256 tokens

Appendix

Table 6: Retrieval Hyperparameters.

Category	Sub-category	Definition
Counterfactual	—	Passages that are semantically relevant to the question but directly contradict the ground truth answer. They provide specific, plausible-sounding information that supports an incorrect alternative answer.
	Entity-relevant	Passages that mention the correct entities in the question but only provide partial, tangential, or incomplete factual information, without containing the evidence needed to answer the question.
Relevant Noise	Relation-relevant	Passages that capture the type of relations required by the question but do not involve the queried entities, thereby providing misleading or insufficient evidence.
	Theme-relevant	Passages that are topically aligned with the question and provide high-level background or contextual information, but do not contain entity-level or relation-level facts necessary for answering.
Irrelevant Noise	—	Passages that have little to no semantic relation to the question. They are from unrelated topics or domains and provide no useful information for answering.

Appendix

Table 7: Definitions of noise passages for retrieval-augmented question answering. Relevant noise is further categorized into entity-level, relation-level, and theme-level noise to better simulate real-world conditions.

Model	Total	Kept Responses
		(1) Format	(2) Passage	(3) Rule	(4) Alignment	(5) Common	(6) Balance
			Judgment	Following		IDs
DS-R1-Llama	96000	85723	39008	34403	5211	2801	1945
DS-R1-Qwen	96000	88201	28481	24586	4611	2801	1945
Llama-3.1	96000	78200	35255	28790	4895	2801	1945
Qwen-2.5	96000	94898	31065	26221	3609	2801	1945

Appendix

Table 8: Training data statistics: This table shows the number of training data left after each filtering step. (1) Format: retains only samples from which a valid answer, a confidence score, and intermediate passage judgments can be successfully extracted. (2) Passage judgment: filters out samples containing incorrect assessments of the retrieved passages. (3) Rule following: filters for samples that have a explicit reasoning process for rule following. (4) Alignment: for each query, selects the final response that minimizes the instance-level Brier Score. (5) Common IDs: retains only samples with question IDs common across all models. (6) Balance: balances the 3 groups (counterfactual, consistent, irrelevant) by downsampling consistent to match irrelevant. Model name abbreviations: DS-R1-Llama : DeepSeek-R1-Distill-Llama-8B; DS-R1-Qwen : DeepSeek-R1-Distill-Qwen-7B; Llama-3.1 : Llama-3.1-8B-Instruct; Qwen-2.5 : Qwen2.5-7B-Instruct.

Figure 4: Reliability Diagram for HotpotQA: comparison of CoT prompt with base model (upper row) and SFT models (lower row). Each subplot displays accuracy v.s. confidence, with the diagonal dashed line representing perfect calibration.

Retriever	Prompt Type	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Retriever	Prompt Type	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
BM25	Vanilla	0.266	0.550	0.515	0.626	0.446	0.696	0.755	0.554	0.495	0.607
	CoT	0.217	0.480	0.538	0.548	0.416	0.648	0.613	0.452	0.446	0.532
	Multi-Step	0.250	0.482	0.452	0.486	0.394	0.503	0.603	0.530	0.425	0.500
Contriever	Vanilla	0.284	0.563	0.614	0.576	0.490	0.638	0.735	0.619	0.531	0.599

Appendix

Table 9: Evaluation of verbal confidence calibration performance (ECE and AUROC) on four datasets across varying retrievers and prompting strategies. Results show that the model consistently exhibits an average ECE greater than 0.4, indicating poor calibration performance.

	HotpotQA		NQ			HotpotQA		NQ
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct					Qwen2.5-7B-Instruct
Vanilla	0.358	0.630	0.389	0.655	Vanilla	0.333	0.692	0.363	0.707
CoT	0.340	0.672	0.370	0.679	CoT	0.327	0.712	0.349	0.685
Noise-aware	0.263	0.693	0.315	0.661	Noise-aware	0.285	0.673	0.316	0.650
Ensemble	0.316	0.648	0.364	0.683	Ensemble	0.318	0.718	0.363	0.707

Appendix

Table 10: Four passages OOD results. Lower ECE and higher AUROC indicate better calibration performance.

Setting	Pos	Bamboogle		HotpotQA		NQ		StrategyQA		Average
		ECE	AUROC	ECE	AUROC	ECE	AUROC	ECE	AUROC	ECE	AUROC
gt_only	N/A	0.071	0.675	0.117	0.693	0.139	0.688	0.046	0.679	0.093	0.684
gt_with_noise/counterfactual	pos1	0.475	0.474	0.500	0.475	0.477	0.483	0.648	0.290	0.525	0.431
	pos2	0.416	0.581	0.514	0.504	0.490	0.557	0.609	0.291	0.507	0.483
	pos3	0.365	0.671	0.452	0.613	0.472	0.714	0.492	0.397	0.445	0.599
gt_with_noise/relevant	pos1	0.126	0.579	0.199	0.538	0.196	0.612	0.058	0.572	0.145	0.575

Appendix

Table 11: The table evaluate the impact of passage ordering on Llama-3.1-8B-Instruct ’s calibration performance. The “Setting” column defines the context structure, where gt_only refers to a noise-free baseline containing only the ground truth passage, while the gt_with_noise categories involve mixing the ground truth with specific types of noise (counterfactual, relevant, or irrelevant). The “Pos” column specifies the exact position (1st, 2nd, or 3rd) of the ground truth passage within the sequence of retrieved passages, designed to assess the model’s sensitivity to positional bias when processing mixed-quality contexts. The results indicate that calibration performance steadily declines as noise passages are added.

	ECE					AUROC
Model	Baseline	NOVA	$\Delta$	$p$	Sig.	Baseline	NOVA	$\Delta$	$p$	Sig.
DeepSeek-R1-Distill-Llama-8B	0.407	0.311	+0.096	0.0001		0.657	0.679	+0.022	0.0425	**
DeepSeek-R1-Distill-Qwen-7B	0.437	0.344	+0.093	0.0001		0.654	0.723	+0.069	0.0001
Llama-3.1-8B-Instruct	0.411	0.266	+0.145	0.0001		0.605	0.751	+0.146	0.0001
Qwen2.5-7B-Instruct	0.366	0.264	+0.102	0.0001		0.730	0.768	+0.038	0.0052

Appendix

Table 12: Significance analysis comparing NOVA with Vanilla. Here, significance codes are defined as follows: ***

p\leq 0.01

, **

p\leq 0.05

, *

p\leq 0.10

, and ns indicates not significant.

	ECE					AUROC
Model	Baseline	NOVA	$\Delta$	$p$	Sig.	Baseline	NOVA	$\Delta$	$p$	Sig.
DeepSeek-R1-Distill-Llama-8B	0.436	0.311	+0.125	0.0001		0.650	0.679	+0.029	0.0143	**
DeepSeek-R1-Distill-Qwen-7B	0.474	0.344	+0.130	0.0001		0.655	0.723	+0.068	0.0001
Llama-3.1-8B-Instruct	0.377	0.266	+0.111	0.0001		0.591	0.751	+0.160	0.0001
Qwen2.5-7B-Instruct	0.335	0.264	+0.071	0.0001		0.726	0.768	+0.042	0.0030

Appendix

Table 13: Significance analysis comparing NOVA with CoT. The significance codes are defined the same in Table 12

Setting	Pos	Bamboogle		HotpotQA		NQ		StrategyQA		Average
		ECE	AUROC	ECE	AUROC	ECE	AUROC	ECE	AUROC	ECE	AUROC
gt_only	N/A	0.079	0.750	0.144	0.567	0.144	0.576	0.063	0.719	0.108	0.653
gt_with_noise/counterfactual	pos1	0.395	0.502	0.450	0.508	0.519	0.524	0.670	0.380	0.509	0.479
	pos2	0.340	0.527	0.519	0.525	0.527	0.538	0.623	0.404	0.502	0.499
	pos3	0.290	0.573	0.475	0.534	0.482	0.540	0.600	0.371	0.462	0.505
gt_with_noise/relevant	pos1	0.093	0.572	0.168	0.546	0.166	0.602	0.082	0.708	0.127	0.607

Appendix

Table 14: The table evaluate the impact of passage ordering on DeepSeek-R1-Distill-Llama-8B ’s calibration performance. The “Setting” column defines the context structure, where gt_only refers to a noise-free baseline containing only the ground truth passage, while the gt_with_noise categories involve mixing the ground truth with specific types of noise (counterfactual, relevant, or irrelevant). The “Pos” column specifies the exact position (1st, 2nd, or 3rd) of the ground truth passage within the sequence of retrieved passages, designed to assess the model’s sensitivity to positional bias when processing mixed-quality contexts. The results indicate that calibration performance steadily declines as noise passages are added.

Setting	bamboogle		hotpotqa		nq		strategyqa		Average
Setting	ECE	AUROC	ECE	AUROC	ECE	AUROC	ECE	AUROC	ECE	AUROC
noise_only / counterfactual	0.822	0.397	0.860	0.339	0.775	0.448	0.649	0.478	0.777	0.416
noise_only / irrelevant	0.225	0.851	0.227	0.772	0.293	0.776	0.345	0.554	0.273	0.738
noise_only / relevant	0.331	0.766	0.304	0.717	0.267	0.733	0.128	0.543	0.258	0.690

Appendix

Table 15: Llama3.1-8B performance in noise only settings.

Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Qwen2.5-7B-Instruct
Vanilla	0.398	0.689	0.391	0.712	0.438	0.710	0.236	0.809	0.366	0.730
A $\rightarrow$ NOVA	0.399	0.698	0.344	0.668	0.391	0.713	0.165	0.822	0.325	0.725
B $\rightarrow$ NOVA	0.371	0.702	0.376	0.742	0.417	0.732	0.219	0.855	0.346	0.758
C $\rightarrow$ NOVA	0.351	0.679	0.349	0.773	0.370	0.731	0.145	0.793	0.304	0.744

Appendix

Table 16: Comparison results across four datasets on Qwen2.5-7B-Instruct and Llama-3.1-8B-Instruct. Lower ECE and higher AUROC indicate better calibration and discrimination performance.

Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
Vanilla	0.238	0.573	0.497	0.642	0.414	0.725	0.670	0.625	0.455	0.641
CoT	0.205	0.485	0.496	0.552	0.369	0.688	0.566	0.557	0.409	0.571
Noise-aware	0.229	0.546	0.329	0.671	0.360	0.679	0.495	0.680	0.353	0.644
Ensemble	0.130	0.551	0.391	0.665	0.376	0.720	0.515	0.616	0.353	0.638

Appendix

Table 17: Calibration performance of various models on four datasets with bm25-facts retriever. Scores in bold indicate the best performance, while underlined scores denote the second-best.

Model	UQ Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Model	UQ Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
Base	Ensemble(3)	0.370	0.609	0.397	0.650	0.428	0.619	0.214	0.713	0.352	0.648
	Self-freq	0.436	0.513	0.338	0.686	0.325	0.665	0.267	0.777	0.342	0.660
	LexicSim	0.421	0.504	0.318	0.694	0.338	0.679	0.245	0.796	0.331	0.668
	EigValLap	0.367	0.506	0.333	0.693	0.373	0.698	0.283	0.796	0.339	0.673

Appendix

Table 18: Performance evaluation of four specific sampling-based UQ methods (Ensemble, Self-freq, LexicSim, and Eig ValLap) on the Base and fine-tuned models. Bold indicates better performance across all tested post-hoc calibration strategies.

Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
Vanilla	0.296	0.569	0.519	0.614	0.415	0.673	0.656	0.607	0.472	0.616
CoT	0.167	0.550	0.585	0.476	0.347	0.649	0.592	0.535	0.423	0.552
Noise-aware	0.218	0.566	0.261	0.711	0.314	0.652	0.478	0.693	0.318	0.655
Ensemble	0.110	0.595	0.416	0.631	0.364	0.633	0.525	0.620	0.354	0.620

Appendix

Table 19: Calibration performance of various models on four datasets with Contriever-facts retriever. Scores in bold indicate the best performance, while underlined scores denote the second-best.

Method	StrategyQA		HotpotQA		NQ		Bamboogle		Average
Method	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$	ECE $\downarrow$	AUROC $\uparrow$
Llama-3.1-8B-Instruct
Vanilla QA	0.200	0.524	0.640	0.636	0.515	0.666	0.796	0.523	0.538	0.587
RAG+Vanilla (BM25)	0.238	0.573	0.497	0.642	0.414	0.725	0.670	0.625	0.455	0.641
RAG+CoT (BM25)	0.205	0.485	0.496	0.552	0.369	0.688	0.566	0.557	0.409	0.571
RAG+Vanilla (Contriever)	0.296	0.569	0.519	0.614	0.415	0.673	0.656	0.607	0.472	0.616

Appendix

Table 20: ECE and AUROC comparison between Vanilla QA (no retrieval) and RAG settings (BM25 / Contriever retrievers, Vanilla / CoT prompts).

Panel of Figure 5 — Figure 5: A comprehensive evaluation of the baselines and NOVA (R1: Vanilla, R2: CoT, R3: Noise-aware, R4: Label-only SFT, R5: NOVA ). (a) The spider plot illustrates the multi-dimensional performance across 5 evaluation criteria, highlighting the overall balance. (b) The bar plot provides a detailed mean and variance of the evaluation criteria breakdown.

Figure 6: Screenshot of an example query in our human annotation interface. For each query, annotators answer five questions. For each question, they are presented with five candidate responses and asked to rate each response on a scale from 1 to 5.

Panel of Figure 7 — Figure 7: Case study setup illustrating a high-conflict retrieval scenario. The input consists of a query and three retrieved passages: the Ground Truth passage (Passage 1) is mixed with two Counterfactual passages (Passages 2 and 3) that support mutually exclusive incorrect answers (“Blargon-7” and “Omicron Persei 8”), testing the model’s ability to handle contradictory evidence.

Panel of Figure 8 — Figure 8: Comparison of model responses under counterfactual noise. The Vanilla model (top) fails to resolve the conflict, hallucinating an incorrect answer with high confidence (80%). In contrast, NOVA (bottom) employs step-by-step reasoning to explicitly identify the contradictions among retrieved passages. By adhering to the Conflict Independence rule, it falls back to internal knowledge and assigns an appropriately low confidence score (10%), demonstrating superior calibration.

Panel of Figure 9 — Figure 9: Prompt templates for the baseline methods. We employ three prompting strategies: Vanilla, Chain-of-Thought (CoT), and Multi-step. The specific instructions requiring step-by-step reasoning and step-level confidence estimation are highlighted in red. The placeholders {question} and {retrieved passages} represent the specific question and passages for one prompt.

Panel of Figure 10 — Figure 10: The noise-aware prompt used in Table 2 . The placeholders {question} and {retrieved passages} represent the specific question and passages for one prompt.

Panel of Figure 11 — Figure 11: The NOVA prompt used in Table 2 . The placeholders {question} and {retrieved passages} represent the specific question and passages for one prompt.

Panel of Figure 12 — Figure 12: Noise generation prompt (for counterfactual noise ) used in Section § 5.1 . The placeholders {sentence_length} and {word_length} are calculated based on the length of the ground truth passage of each question, to make sure that our generated noise length is approximately the same with the ground truth passage. The concrete example represented by "[Example]" are presented in Figure 13 .

Panel of Figure 13 — Figure 13: The Example partof the noise generation prompt for counterfactual noise . The placeholders {query} and {gt_answer} represent the specific question and answer pair to generate noise passages.

Panel of Figure 14 — Figure 14: Noise generation prompt (for relevant noise ) used in Section § 5.1 . An example of this prompt is shown in Figure 15 . The placeholders {sentence_length} and {word_length} are calculated based on the length of the ground truth passage of each question, to make sure that our generated noise length is approximately the same with the ground truth passage. The placeholders {query} and {gt_answer} represent the specific question and answer pair to generate noise passages.

Panel of Figure 15 — Figure 15: The Example part of the noise generation prompt for relevant noise . The placeholders {query} and {gt_answer} represent the specific question and answer pair to generate noise passages.

Panel of Figure 16 — Figure 16: Noise generation prompt (for irrelevant noise ) used in Section § 5.1 . An example of this prompt is shown in Figure 17 . The placeholders {sentence_length} and {word_length} are calculated based on the length of the ground truth passage of each question, to make sure that our generated noise length is approximately the same with the ground truth passage. The placeholders {query} and {gt_answer} represent the specific question and answer pair to generate noise passages.

Panel of Figure 17 — Figure 17: The Example part of the noise generation prompt for irrelevant noise . The placeholders {query}, {gt_answer} and {gt_passage} represent the specific question, answer and passage to generate noise passages.

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May 12, 2026, cs.LGJ/K move · Enter open · S save

ORCE: Order-Aware Alignment of Verbalized Confidence in Large Language Models

Chen Li, Xiaoling Hu, Songzhu Zheng, Jiawei Zhou+1

Stony Brook University, NY, USA · Massachusetts General Hospital and Harvard Medical School, MA, USA · Morgan Stanley, NY, USA

Confidence Estimation Feature Alignment

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Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.

Abstract

Explore similar work

ORCE: Order-Aware Alignment of Verbalized Confidence in Large Language Models

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