I-CALM: Incentivizing Confidence-Aware Abstention for LLM Selective Answering

Haotian Zong; Binze Li; Yufei Long; Sinyin Chang; Jialong Wu; Gillian K. Hadfield

cs.CLApr 5, 2026

I-CALM: Incentivizing Confidence-Aware Abstention for LLM Selective Answering

Authors: Haotian Zong, Binze Li, Yufei Long, Sinyin Chang, Jialong Wu, Gillian K. Hadfield

Organizations: Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA · Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, USA · School of Government and Policy, Johns Hopkins University, Washington, D.C. 20001, USA · Vector Institute for Artificial Intelligence, Toronto, ON, Canada

Abstract

Large language models (LLMs) often produce confident but incorrect answers, in part because standard evaluation incentives reward guessing over expressing uncertainty. We study epistemic abstention for factual questions with verifiable answers, where the goal is to improve selective answering, making LLMs abstain when they are likely to be wrong while preserving correct answers. Inspired by human behavioral decisions in question answering, we introduce I-CALM, a prompt-level framework for black-box LLMs. I-CALM combines elicited verbal confidence, announced answer/abstain payoffs, and normative guidance emphasizing truthfulness, humility, evidential support, and responsibility. To distinguish targeted abstention from indiscriminate refusal, we use a two-stage evaluation protocol, in which LLMs first choose whether to answer or abstain, and are then forced to provide a best guess for the abstained ones. Across models and factual QA datasets, I-CALM improves selective answering by reducing false-answer rate among surfaced responses and improving abstention quality, shifting error-prone cases into abstention while retaining answers the model would have answered correctly. Overall, I-CALM offers a lightweight way to improve inference-time selective answering without retraining or access to model's internal states. Code is available at https://github.com/FayLONG03/hallucinationControl.

Figures & tables

Human Decision Question	Functional Role	Conceptual Grounding	I-CALM Component
Do I know enough?	Epistemic assessment	Metacognitive monitoring and control; strategic regulation of memory accuracy [ 49 , 34 ]	Verbal confidence
What happens if I am wrong or abstain?	Consequence-sensitive action selection	Expected utility theory; behavioral decision theory; deterrence theory [ 62 , 31 , 4 ]	Announced answer/abstain payoffs
Should I assert this as fact?	Norm-governed factual assertion	Epistemic norms of assertion; knowledge as a condition for warranted assertion [ 72 ]	Normative guidance

Table 1: Functional motivation for the three I-CALM components. Each component corresponds to a distinct role in deciding whether to surface a factual answer.

Figure 2: Two-stage evaluation. Stage 1 allows answering/abstention; after abstention, Stage 2 elicits a forced best guess.

	C	FAR	$\boldsymbol{J}_{\mathrm{abs}}$	$\widehat{\textbf{ECE}}$		Brier Score
	C	FAR	$\boldsymbol{J}_{\mathrm{abs}}$	A	O	A	O
I-CALM	0.56	0.36	0.44	0.15	0.10	0.21	0.19
w/o Payoffs	0.76	0.43	0.33	0.21	0.17	0.25	0.24
w/o Confidence	0.25	0.26	0.30	Not applicable
w/o Norms	0.68	0.42	0.38	0.15	0.12	0.21	0.19

Table 3: Component ablations relative to the full I-CALM configuration

(+1,-1,+0.4)

for GPT-5 mini on PopQA. C: coverage; FAR:

\mathrm{FAR}_{\mathrm{answered}}

; A and O: answered and overall, respectively.

Figure 3: Evaluation on PopQA as I-CALM’s components are added incrementally.

Panel of Figure 4 — Figure 4: Confidence distributions for GPT-5 mini under representative schemes on PopQA. Left: Stage 1 surfaced answers. Right: Stage 2 best guesses.

Figure 5: The abstention–FAR curve for GPT-5 mini on PopQA across all experimented configurations.

Announced Payoff			C	FAR	ECR	CAR
Correct	Wrong	Abstain	C	FAR	ECR	CAR
+1	-1	+0.4	0.564	0.418 (0.01)	0.481	0.900
+100	-1	+0.4	0.752	0.445 (0.01)	0.400	0.942
+1	-100	+0.4	0.694	0.425 (0.01)	0.474	0.906
+1	-1	+40	0.429	0.285 (0.11)	0.776	0.677

Table 4: Sensitivity to extreme payoffs; GPT-5 mini on PopQA. C: coverage; FAR:

\mathrm{FAR}_{\mathrm{answered}}

Appendix figures & tables39 assets

Supplementary material from the paper’s appendix.

Appendix

Prompt	FAR	Pearson’s $r$	Brier Score		$\widehat{\textbf{ECE}}$
Prompt	FAR	Pearson’s $r$	$\tau^{self}$	$\tau_{avg}^{token}$	$\tau^{self}$	$\tau_{avg}^{token}$
①	0.63 (0.008)	0.54 (0.012)	0.34 (0.006)	0.36 (0.006)	0.38	0.42
②	0.62 (0.008)	0.54 (0.012)	0.34 (0.006)	0.35 (0.005)	0.39	0.41
③	0.62 (0.008)	0.52 (0.012)	0.35 (0.006)	0.34 (0.005)	0.38	0.41
④	0.62 (0.008)	0.55 (0.011)	0.34 (0.006)	0.35 (0.006)	0.37	0.41

Appendix

Table 5: Comparison of self-reported and token-probability-based confidence metrics across paraphrased abstention-conditioned prompt templates for GPT-4o mini on PopQA. Values in parentheses denote 95% confidence-interval half-widths.

Confidence Format	FAR	Pearson’s $r$	Brier Score		$\widehat{\textbf{ECE}}$
Confidence Format	FAR	Pearson’s $r$	$\tau^{self}$	$\tau_{avg}^{token}$	$\tau^{self}$	$\tau_{avg}^{token}$
$[0,1]$	0.63	0.54	0.34	0.36	0.38	0.42
$[0,20]$	0.62	0.59	0.35	0.35	0.41	0.42
$[0,100]$	0.62	0.55	0.36	0.35	0.41	0.42
$[0\%,100\%]$	0.62	0.54	0.36	0.35	0.41	0.42

Appendix

Table 6: Comparison of self-reported confidence formats under prompt ① for GPT-4o mini on PopQA.

GPT-5 mini
Method	Coverage	$\mathbf{FAR}_{\mathrm{answered}}\downarrow$	ECR	CAR	$\boldsymbol{J}_{\mathrm{abs}}\uparrow$
Pure Eval	1.000	0.873 (0.020)	0.000	1.000	0.000
IDK	0.157	0.822 (0.060)	0.854	0.243	0.097
Verbal Conf.	0.736	0.846 (0.026)	0.291	0.934	0.225
Token Prob.	Not supported
I-CALM	0.736	0.871 (0.023)	0.276	0.832	0.108

Appendix

Table 8: Selective-answering and abstention-quality comparisons for three models on SimpleQA-Verified. Values in parentheses denote 95% confidence-interval half-widths. Gray-shaded rows indicate I-CALM, while red-shaded cells indicate unsupported metrics or results with very low coverage.

GPT-5 mini
Method	$\widehat{\textbf{ECE}}\downarrow$		Brier Score $\downarrow$
Method	Answered	Overall	Answered	Overall
Pure Eval	Not supported
IDK	Not supported
Verbal Conf.	0.583	0.491	0.473 (0.017)	0.375 (0.017)
Token Prob.	Not supported

Appendix

Table 9: Calibration comparisons for three models on SimpleQA-Verified. Values in parentheses denote 95% confidence-interval half-widths. ECE and Brier scores are not provided for Pure Eval and IDK, which do not output confidence scores. Gray-shaded rows indicate I-CALM, while red-shaded cells indicate unsupported metrics.

Payoff	Scheme	FAR	Coverage	ECR	CAR	$J_{\mathrm{abs}}$
–	Pure Eval	0.523 (0.008)	0.965	–	–	–
(1, 0, -)	A	0.496 (0.009)	0.878	0.197	0.967	0.164
(1, 0, 0.2)	B	0.449 (0.009)	0.767	0.373	0.937	0.310
(1, 0, 0.2)	I-CALM	0.408 (0.010)	0.660	0.510	0.868	0.378
(1, 0, 0.4)	B	0.451 (0.009)	0.764	0.370	0.926	0.296
(1, 0, 0.4)	I-CALM	0.414 (0.010)	0.677	0.493	0.888	0.381

Appendix

Table 10: PopQA (

N_{\mathrm{total}}=14{,}267

) evaluation across the full set of reward configurations for GPT-5 mini, including Pure Eval and all tested Scheme A, Scheme B, and I-CALM configurations. FAR denotes

\mathrm{FAR}_{\mathrm{answered}}

Payoff	Scheme	FAR	Coverage	ECR	CAR	$J_{\mathrm{abs}}$
–	Pure Eval	0.593 (0.008)	0.996	–	–	–
(1, 0, -)	A	0.502 (0.010)	0.698	0.436	0.914	0.349
(1, 0, 0.2)	B	0.456 (0.010)	0.613	0.552	0.882	0.434
(1, 0, 0.2)	I-CALM	0.437 (0.011)	0.566	0.607	0.853	0.460
(1, 0, 0.4)	B	0.478 (0.010)	0.648	0.507	0.899	0.406
(1, 0, 0.4)	I-CALM	0.428 (0.011)	0.545	0.632	0.843	0.475

Appendix

Table 11: PopQA (

N_{\mathrm{total}}=14{,}267

) evaluation across the full set of reward configurations for GPT-4o mini, including Pure Eval and all tested Scheme A, Scheme B, and I-CALM configurations. FAR denotes

\mathrm{FAR}_{\mathrm{answered}}

Payoff	Scheme	$\widehat{\textbf{ECE}}$		Brier Score ( $\pm$ 95% CI)
Payoff	Scheme	Answered	Overall	Answered	Overall
(1, 0, -)	A	0.142	0.133	0.204 (0.007)	0.197 (0.007)
(1, 0, 0.2)	B	0.152	0.128	0.212 (0.008)	0.199 (0.007)
(1, 0, 0.2)	I-CALM	0.180	0.143	0.226 (0.009)	0.202 (0.007)
(1, 0, 0.4)	B	0.171	0.144	0.221 (0.008)	0.206 (0.007)
(1, 0, 0.4)	I-CALM	0.189	0.156	0.231 (0.009)	0.205 (0.007)

Appendix

Table 12: PopQA evaluation across the full set of reward configurations: calibration metrics for GPT-5 mini across all tested Scheme A, Scheme B, and I-CALM configurations.

Payoff	Scheme	$\widehat{\textbf{ECE}}$		Brier Score ( $\pm$ 95% CI)
Payoff	Scheme	Answered	Overall	Answered	Overall
(1, 0, -)	A	0.429	0.386	0.422 (0.010)	0.350 (0.008)
(1, 0, 0.2)	B	0.386	0.341	0.382 (0.010)	0.304 (0.008)
(1, 0, 0.2)	I-CALM	0.373	0.321	0.371 (0.011)	0.287 (0.007)
(1, 0, 0.4)	B	0.405	0.353	0.399 (0.010)	0.317 (0.008)
(1, 0, 0.4)	I-CALM	0.359	0.330	0.360 (0.011)	0.287 (0.007)

Appendix

Table 13: PopQA evaluation across the full set of reward configurations: calibration metrics for GPT-4o mini across all tested Scheme A, Scheme B, and I-CALM configurations.

Panel of Figure 16 — (a) GPT-5 mini: incorrect answer penalty = 0

(a) GPT-5 mini: incorrect answer penalty = -1

Panel of Figure 18 — (a) GPT-4o mini: incorrect answer penalty = 0

Panel of Figure 9 — Figure 9: Confidence distributions on PopQA under matched reward settings. For each model, rows correspond to Scheme A, Scheme B, and I-CALM (Scheme B with norms). Figures (a) and (c) use zero penalty for incorrect answers for GPT-5 mini and GPT-4o mini, respectively, while (b) and (d) use a $-1$ penalty. Within each small panel, the left histogram shows first-round answered cases and the right histogram shows second-round best guesses after an initial “I don’t know.”

Payoff	Scheme	FAR	Coverage	ECR	CAR
(1, -1, -)	A	0.486 (0.009)	0.848	0.248	0.964
(1, -1, 0.4)	B	0.418 (0.010)	0.689	0.481	0.900
(1, -1, 0.4)	I-CALM	0.355 (0.011)	0.564	0.636	0.808
(10, -10, -)	A	0.479 (0.009)	0.831	0.271	0.954
(10, -10, 4)	B	0.391 (0.010)	0.640	0.561	0.907
(10, -10, 4)	I-CALM	0.361 (0.011)	0.549	0.648	0.803

Appendix

Table 14: GPT-5 mini on PopQA (

N_{\mathrm{total}}=14{,}267

): performance metrics when the entire reward scheme is scaled by factors of

10

100

, and

1000

. FAR denotes

\mathrm{FAR}_{\mathrm{answered}}

. Parentheses report 95% CI half-widths.

Payoff	Scheme	$\widehat{\textbf{ECE}}$		Brier Score
Payoff	Scheme	Answered	Overall	Answered	Overall
(1, -1, -)	A	0.144	0.131	0.200	0.193
(1, -1, 0.4)	B	0.149	0.121	0.210	0.193
(1, -1, 0.4)	I-CALM	0.147	0.104	0.206	0.186
(10, -10, -)	A	0.177	0.158	0.220	0.210
(10, -10, 4)	B	0.151	0.109	0.210	0.198

Appendix

Table 15: GPT-5 mini on PopQA: calibration metrics when the entire reward scheme is scaled by factors of

10

100

, and

1000

Kept Norms	FAR		Total Reward	Brier Score (Answered)
Kept Norms	Answered	Overall	Total Reward	Brier Score (Answered)
Full-norm	0.355 (0.011)	0.550 (0.008)	4822.6	0.2061 (0.0090)
No-norm	0.418 (0.010)	0.555 (0.008)	3382.6	0.2102 (0.0082)
{1}	0.379 (0.010)	0.562 (0.008)	4384.2	0.2256 (0.0090)
{2}	0.379 (0.010)	0.565 (0.008)	4368.4	0.2190 (0.0089)
{3}	0.365 (0.011)	0.614 (0.008)	4659	0.2069 (0.0091)

Appendix

Table 16: Norm performance metrics for GPT-5 mini under I-CALM

(+1,-1,+0.4)

. The first two rows compare the full-norm and no-norm variants; subsequent rows report ablations over retained norm subsets. Brier stands for the Brier score for the first-round answered questions. Parentheses report 95% CI half-widths.

GPT-5 mini
Scheme	Category	Total Reward	ECR	CAR	FAR
Scheme	Category	Total Reward	ECR	CAR	Answered	Overall
Scheme A	Common	687	0.267	0.959	0.341 (0.015)	0.403 (0.014)
Scheme A	Rare	-1995	0.222	0.965	0.652 (0.015)	0.699 (0.013)
Scheme B	Common	2083.8	0.494	0.903	0.274 (0.015)	0.403 (0.014)
Scheme B	Rare	130.20	0.471	0.911	0.592 (0.017)	0.714 (0.013)

Appendix

Table 17: PopQA (

\mathrm{N}_{\mathrm{total}}=14{,}267

) common-versus-rare fact split: performance metrics for GPT-5 mini and GPT-4o mini under Scheme A

(+1,-1)

, Scheme B

(+1,-1,+0.4)

, and I-CALM

(+1,-1,+0.4)

. Parentheses report 95% CI half-widths.

GPT-5 mini
Scheme	Category	$\widehat{\mathbf{ECE}}$		Brier Score
Scheme	Category	Answered	Overall	Answered	Overall
Scheme A	Common	0.081	0.073	0.172 (0.012)	0.174 (0.011)
Scheme A	Rare	0.222	0.201	0.229 (0.013)	0.214 (0.012)
Scheme B	Common	0.073	0.057	0.163 (0.012)	0.170 (0.011)
Scheme B	Rare	0.242	0.196	0.264 (0.016)	0.214 (0.012)

Appendix

Table 18: PopQA common-versus-rare fact split: calibration metrics for GPT-5 mini and GPT-4o mini under Scheme A

(+1,-1)

, Scheme B

(+1,-1,+0.4)

, and I-CALM

(+1,-1,+0.4)

. Parentheses report 95% CI half-widths.

Model	Scheme	C	FAR	ECR	CAR	$J_{\mathrm{abs}}$
Meta-Llama-3- 8B-Instruct	Pure Eval	0.963	0.683 (0.008)	–	–	–
	A	0.931	0.691 (0.008)	0.093	0.989	0.082
	B	0.775	0.650 (0.009)	0.294	0.944	0.238
	I-CALM	0.447	0.515 (0.012)	0.685	0.805	0.49
Gemini-3.1- Flash-Lite	Pure Eval	0.999	0.444 (0.008)	–	–	–
	A	0.850	0.388 (0.009)	0.268	0.948	0.216

Appendix

Table 19: PopQA results (

N_{\mathrm{total}}=14{,}267

): selective answering performance metrics for Meta-Llama-3-8B-Instruct, Gemini-3.1-Flash-Lite, and Qwen3-4B-Instruct-2507 under Pure Eval, Scheme A, Scheme B, and I-CALM. C stands for coverage; FAR stands for

\mathrm{FAR}_{\mathrm{answered}}

. Parentheses report 95% CI half-widths.

Model	Scheme	$\widehat{\textbf{ECE}}$		Brier Score
Model	Scheme	Answered	Overall	Answered	Overall
Meta-Llama-3- 8B-Instruct	A	0.666	0.646	0.663 (0.008)	0.637 (0.008)
	B	0.630	0.563	0.625 (0.009)	0.553 (0.008)
	I-CALM	0.497	0.446	0.496 (0.012)	0.423 (0.009)
Gemini-3.1- Flash-Lite	A	0.370	0.367	0.367 (0.009)	0.362 (0.008)
	B	0.374	0.359	0.371 (0.009)	0.354 (0.008)

Appendix

Table 20: PopQA results: calibration metrics for Meta-Llama-3-8B-Instruct, Gemini-3.1-Flash-Lite, and Qwen3-4B-Instruct-2507 under Scheme A

(+1,-1)

, Scheme B

(+1,-1,+0.4)

, and I-CALM

(+1,-1,+0.4)

. Parentheses report 95% CI half-widths.

Panel of Figure 27 — (a) Meta-Llama-3-8B-Instruct

Panel of Figure 28 — (a) Gemini-3.1-Flash-Lite

Panel of Figure 12 — Figure 12: PopQA confidence distributions under Scheme A (+1,-1), Scheme B (+1,-1,+0.4), and I-CALM (+1,-1,+0.4) (Scheme B with norms is equivalent to I-CALM.). Within each panel, the left histogram shows first-round answered cases and the right histogram shows second-round best guesses after an initial “I don’t know.”

Model	Scheme	C	FAR	ECR	CAR	$J_{\mathrm{abs}}$
GPT-5 mini	Pure Eval	0.998	0.145 (0.005)	–	–	–
	A	0.982	0.140 (0.005)	0.087	0.994	0.081
	B	0.963	0.139 (0.005)	0.157	0.986	0.143
	I-CALM	0.950	0.136 (0.005)	0.191	0.976	0.167
GPT-4o mini	Pure Eval	1.000	0.148 (0.005)	–	–	–
	A	0.983	0.156 (0.005)	0.066	0.994	0.060

Appendix

Table 21: TriviaQA results (

N_{\mathrm{total}}=14{,}267

): selective answering performance metrics for GPT-5 mini, GPT-4o mini, Meta-Llama-3-8B-Instruct, Gemini-3.1-Flash-Lite, Qwen3-4B-Instruct-2507 under Pure Eval, Scheme A, Scheme B, and I-CALM. C stands for coverage; FAR stands for

\mathrm{FAR}_{\mathrm{answered}}

. Parentheses report 95% CI half-widths.

Model	Scheme	$\widehat{\textbf{ECE}}$		Brier Score
Model	Scheme	Answered	Overall	Answered	Overall
GPT-5 mini	A	0.026	0.026	0.086 (0.004)	0.088 (0.004)
	B	0.037	0.034	0.087 (0.004)	0.090 (0.004)
	I-CALM	0.041	0.040	0.087 (0.004)	0.092 (0.004)
GPT-4o mini	A	0.118	0.118	0.132 (0.005)	0.131 (0.005)
	B	0.112	0.113	0.128 (0.005)	0.130 (0.005)

Appendix

Table 22: TriviaQA results: calibration metrics for GPT-5 mini, GPT-4o mini, Meta-Llama-3-8B-Instruct, Gemini-3.1-Flash-Lite, and Qwen3-4B-Instruct-2507 under Scheme A

(+1,-1)

, Scheme B

(+1,-1,+0.4)

, and I-CALM

(+1,-1,+0.4)

. Parentheses report 95% CI half-widths.

Panel of Figure 34 — (a) Meta-Llama-3-8B-Instruct

Panel of Figure 35 — (a) Gemini-3.1-Flash-Lite

Panel of Figure 17 — Figure 17: TriviaQA confidence distributions under Scheme A (+1,-1), Scheme B (+1,-1,+0.4), and I-CALM (+1,-1,+0.4) (Scheme B with norms is equivalent to I-CALM.). Within each panel, the left histogram shows first-round answered cases and the right histogram shows second-round best guesses after an initial “I don’t know.”

Model	Scheme	C	FAR	ECR	CAR	$J_{\mathrm{abs}}$
GPT-5 mini	Pure Eval	0.999	0.873 (0.020)	–	–	–
	A	0.882	0.889 (0.020)	0.126	0.951	0.077
	B	0.805	0.871 (0.022)	0.207	0.897	0.104
	I-CALM	0.736	0.871 (0.023)	0.276	0.832	0.108
GPT-4o mini	Pure Eval	1.000	0.917 (0.017)	–	–	–
	A	0.752	0.902 (0.021)	0.260	0.881	0.141

Appendix

Table 23: SimpleQA Verified results (

N_{\mathrm{total}}=14{,}267

\mathrm{FAR}_{\mathrm{answered}}

. Parentheses report 95% CI half-widths.

Model	Scheme	$\widehat{\textbf{ECE}}$		Brier Score
Model	Scheme	Answered	Overall	Answered	Overall
GPT-5 mini	A	0.483	0.438	0.374 (0.032)	0.349 (0.030)
	B	0.484	0.404	0.379 (0.033)	0.345 (0.031)
	I-CALM	0.520	0.414	0.416 (0.036)	0.345 (0.030)
GPT-4o mini	A	0.792	0.664	0.723 (0.032)	0.575 (0.031)
	B	0.777	0.620	0.707 (0.034)	0.521 (0.031)

Appendix

Table 24: SimpleQA Verified results: calibration metrics for GPT-5 mini, GPT-4o mini, Meta-Llama-3-8B-Instruct, Gemini-3.1-Flash-Lite, and Qwen3-4B-Instruct-2507 under Scheme A

(+1,-1)

, Scheme B

(+1,-1,+0.4)

, and I-CALM

(+1,-1,+0.4)

. Parentheses report 95% CI half-widths.

Panel of Figure 41 — (a) Meta-Llama-3-8B-Instruct

Panel of Figure 42 — (a) Gemini-3.1-Flash-Lite

Panel of Figure 22 — Figure 22: SimpleQA Verified confidence distributions under Scheme A (+1,-1), Scheme B (+1,-1,+0.4), and I-CALM (+1,-1,+0.4) (Scheme B with norms is equivalent to I-CALM.). Within each panel, the left histogram shows first-round answered cases and the right histogram shows second-round best guesses after an initial “I don’t know.”

Figure 23: Empirical CFAR as a function of reported uncertainty $u=1-\tau^{\mathrm{self}}$ for GPT-5 mini on the full PopQA dataset under Scheme A, Scheme B, and I-CALM. Shaded bands show pointwise 95% confidence intervals.

Risk Target	Calibrated Uncertainty Threshold	Calibration Acceptance Rate	Validation Acceptance Rate	Validation $\widehat{\textbf{CFAR}}$
Scheme A (+1, -1)
0.1	reject-all	0.00	0.00 (0.00)	–
0.2	0.08	0.21	0.20 (0.01)	0.13 (0.01)
0.3	0.24	0.44	0.43 (0.01)	0.24 (0.01)
0.4	0.48	0.62	0.60 (0.01)	0.34 (0.01)
Scheme B (+1, -1, +0.4)

Appendix

Table 25: Bonferroni CP-UCB threshold selection for GPT-5 mini on PopQA using a 20%/80% calibration–validation split. Validation FAR is computed among answers accepted by the threshold selected on the calibration split.

Risk Target	Calibrated Uncertainty Threshold	Calibration Acceptance Rate	Validation Acceptance Rate	Validation $\widehat{\textbf{CFAR}}$
Scheme A (+1, -1)
0.1	reject-all	0.00	0.00 (0.00)	–
0.2	0.11	0.24	0.23 (0.01)	0.15 (0.01)
0.3	0.25	0.45	0.44 (0.01)	0.25 (0.01)
0.4	0.56	0.63	0.62 (0.01)	0.35 (0.01)
Scheme B (+1, -1, +0.4)

Appendix

Table 26: Multistart fixed-sequence CP threshold selection with

L=10

for GPT-5 mini on PopQA using a 20%/80% calibration–validation split. Validation FAR is computed among answers accepted by the threshold selected on the calibration split.

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Zhangjiang University · Ibaraki University

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Uncertainty-Aware Abstention in Large Language Models with Provable Alignment Guarantees

Sijin Dong, Hiroyuki Shinnou

1Ibaraki University, Japan.

Selective Prediction Confidence Estimation in Language Models Question Answering LLM Reliability LLM Uncertainty Estimation Uncertainty Calibration

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Large language models (LLMs) are increasingly deployed in question answering (QA) systems, yet they may generate hallucinated or misaligned responses without reliable confidence estimates. Uncertainty quantification (UQ) offers a natural basis for selective answering, where a system answers only when its prediction is deemed reliable and abstains otherwise. However, existing uncertainty scores for LLMs are often heuristic: a threshold chosen on such scores does not, by itself, provide statistical guarantees on the error rate among accepted answers. We propose CIC, a confidence-interval-based calibration framework that converts arbitrary uncertainty scores into risk-controlled selective answering rules. Given a held-out calibration set, CIC evaluates each generated response using an application-specific alignment criterion and associates it with an uncertainty score and a binary error label. For each candidate uncertainty threshold, CIC estimates the acceptance-conditioned error rate and constructs a high-probability upper confidence bound using either Hoeffding-style or Clopper-Pearson confidence intervals. It then selects the largest threshold whose upper bound is below a user-specified risk level

α

, thereby maximizing the answering rate subject to a finite-sample reliability constraint. Under exchangeability, CIC guarantees with probability at least

1-δ

that the selected threshold, if non-null, controls the error rate among accepted answers at level

α

. We evaluate CIC on both closed-ended and open-ended QA benchmarks across seven LLMs and multiple uncertainty estimators. Experimental results show that CIC consistently achieves valid risk control while retaining strong answering efficiency, providing a practical and statistically grounded mechanism for deploying LLMs in reliability-sensitive QA workflows.

Abstract

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