Are You Sure Your LLM Is Sure? Repairing and Auditing Confidence

Arijit Dey; Bhartendu Kumar; Ramya Hebbalaguppe; Khuushi Maheshwari

cs.AIOct 15, 2026

Are You Sure Your LLM Is Sure? Repairing and Auditing Confidence

Authors: Arijit Dey, Bhartendu Kumar, Ramya Hebbalaguppe, Khuushi Maheshwari

Organizations: MBZUAI · TCS Research Labs, India · IIT Delhi

Abstract

Confidence scores determine whether an LLM answer is accepted, reviewed, or regenerated, yet scalar recalibration can only correct errors visible through the score itself. We introduce RADAR (Repair, Adopt, and Diagnose After Recalibration), a reliability framework that separates confidence repair from deciding whether to deploy the repair and auditing the errors that remain. Under squared loss, we decompose prediction risk into outcome noise, information hidden by the score, and mapping error; restricting repair to order-preserving maps additionally introduces a pooling gap. For repair, we propose Probe-Anchored Isotonic Calibration (PAIC), which learns a monotone map from correctness-probe predictions on unlabeled target prompts. PAIC's excess risk depends on the probe's score-conditional bias and fitting error rather than its overall accuracy. For adoption, we derive a paired procedure with finite-sample control of false improvements. For auditing, we develop a prompt-clustered kernel test that detects feature-aligned residual errors while accounting for dependent answers from the same prompt. Across multiple LLM checkpoints, benchmarks, and distribution shifts, richer predictors can improve confidence estimation, but projecting their information back to a scalar score can lose these gains, and lower prediction risk need not yield better review decisions. Across 47,400 replayed raw-score allocations, paired betting adopts candidates with lower held-out test risk in 42.95% of allocations, versus 15.09% for one-sided empirical Bernstein. RADAR thus provides a principled workflow to repair what a scalar score can express, adopt a repair only when supported by evidence, and diagnose systematic errors that recalibration leaves behind. Code and data will be released upon acceptance.

Figures & tables

Panel of Figure 1 — Figure 1: RADAR uses separate prompt sets to fit a confidence repair, compare candidate risks, and test residual errors. All stages use the same outcome definition and weight prompts equally. PAIC fits the repair from probe predictions; comparison and auditing use held-out labels.

Correction	Supervision	Serving inputs
Source scalar maps	Source labels fit the map	$P$
Importance-weighted isotonic	Source labels, reweighted toward unlabeled target prompts	$P$
Source-distilled isotonic	$g$ from source labels; isotonic fit to $g$ on source prompts	$P$
Target-probe Platt, beta	$g$ from source labels; parametric fit to $g$ on target prompts	$P$
PAIC	$g$ from source labels; isotonic fit to $g$ on target prompts	$P$
Target isotonic (yardstick)	Target labels fit the map	$P$

Table 1: Supervision and serving inputs in the raw-score shift experiments, with the base scorer fixed. Source scalar maps are label-isotonic, positive Platt, monotone beta, and a flexible nonmonotone regressor; the four rows from importance weighting to PAIC share 500 unlabeled target and 500 unlabeled source prompts, and target isotonic is a yardstick, not a competitor (Appendix A.10 ).

Figure 2: Direct and projected confidence predictors on BoolQ and ARC. The fourth column measures the risk change from projecting each rich predictor onto a monotone function of

P

Figure 3: Controlled changes in presentation. All six primary risk contrasts; negative favors the first method. PAIC uses target projection;

\mathrm{aug}

fits transformed views with the same unique labels;

P

marks a score-only teacher. Approximate stratified finite-population Welch-

t

intervals allocate

0.05/6

per contrast, conditional on fixed fits and grades.

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

Stage	Inputs and label access
Fit the probe	Train $g$ on its feature inputs and $Y$ . Count these labels even when later stages use only its predictions.
Fit scalar repairs	Label-fitted maps use $(P,Y)$ ; PAIC uses $(P,g(Z))$ on repair prompts independent of probe training, without their labels.
Compare candidates	Evaluate the frozen candidates and $g$ on disjoint $\mathcal{L}$ and $\mathcal{U}$ ; use $Y$ only on $\mathcal{L}$ . Both pools are independent of fitting.
Serve the score	PAIC uses $P$ ; group calibration also needs a feature-based group; direct $g$ needs its feature inputs. None uses $Y$ .
Audit the score	Use $Z$ , $Y$ , and the chosen score on new independent prompts, with a kernel fixed before the audit.

Appendix

Table 2: Information use with the representation and base scorer frozen. Reference-free serving still incurs the cost of

P

; fitting and evaluation use labels. Risk comparisons share one outcome and population weighting.

$C$	$g_{-}$	$g_{\rm offset}$	$g_{+}$
20	$0.04347\;(0.00095)$	$7.6023\;(0.0874)$	$3.5208\;(0.0767)$
50	$0.01649\;(0.00036)$	$6.8077\;(0.0535)$	$1.3354\;(0.0294)$
100	$0.00791\;(0.00017)$	$6.6049\;(0.0366)$	$0.64096\;(0.01358)$
500	$0.001527\;(0.000035)$	$6.4237\;(0.0157)$	$0.12366\;(0.00287)$
2000	$0.000390\;(0.000009)$	$6.4011\;(0.0079)$	$0.03156\;(0.00073)$
Population limit	$0$	$6.4$	$0$

Appendix

Table 3: PAIC excess risk above the scalar optimum

0.2275

. Entries are mean (Monte Carlo standard error), both multiplied by

10^{3}

, over 2,000 repetitions. Standard errors are the empirical standard deviation divided by

\sqrt{2000}

and are pointwise, not simultaneous intervals. The unchanged score’s excess is

0.4

in these units.

Shift	Model	Original	Source iso.	Platt	Beta	Non- mono.	PAIC ridge	PAIC trees	Group	Direct trees	Target
Difficulty	Llama	.296066	.251714	.251608	.251833	.253394	.237544	.238951	.249526	.193440	.236763
	Qwen	.229475	.210177	.209458	.209722	.211439	.194298	.196389	.206683	.138683	.194654
Task	Llama	.247051	.238183	.237836	.236746	.238634	.234934	.218722	.246771	.199584	.219169
	Qwen	.175655	.185457	.185327	.182487	.182422	.166735	.165191	.184328	.148355	.159922
Subject	Llama	.325099	.099458	.103151	.102349	.099871	.083310	.083183	.099059	.054461	.082144
	Qwen	.253062	.122240	.129469	.128146	.120107	.117090	.116237	.125438	.074457	.112542

Appendix

Table 4: Primary shift risks at

F=U=500

, averaged over three overlapping refits (lower is better). “Group” is the adapted group calibrator of Chen et al. (2024) , which serves

P

and group features; direct trees serve the probe’s features. “Target” is the isotonic diagnostic with 250 target labels and no source labels; every other fitted method uses 500 source labels, and PAIC also uses 500 unlabeled target prompts.

Dataset	Model	Original	Label iso.	Flexible scalar	Platt	PAIC	Direct $g$
GSM8K	Llama	.104379	.105213	.104840	.104688	.104812	.106254
	Qwen	.085551	.085418	.085300	.085266	.085281	.086493
10K	Llama	.049106	.048715	.048548	.048779	.048607	.048427
	Qwen	.054499	.054428	.054160	.054534	.054235	.054067

Appendix

Table 5: Archived learned score at the full downstream fitting budget. Entries average 15 overlapping seed/fold blocks per cell.

Shift	Model	PAIC	CE	SQ	CE	SQ	distilled	IW iso.
			Target-probe Platt		Target-probe beta		Source-
Difficulty	Llama	.238951	.240000	.240173	.239466	.239557	.251711	.237170
	Qwen	.196389	.198206	.198034	.196995	.196972	.207772	.197005
Task	Llama	.218722	.219675	.219552	.219042	.218932	.236728	.235725
	Qwen	.165191	.167125	.166397	.165519	.165316	.180906	.184300
Subject	Llama	.083183	.084982	.084411	.084557	.084132	.099035	.092045

Appendix

Table 6: Equally informed adaptation: target risks averaged over three overlapping refits (lower is better). CE and SQ denote cross-entropy and squared-loss fitting of the target-probe maps; the SQ maps are a posthoc sensitivity with its own contrast family.

Comparator	Lower PAIC estimate	Pointwise interval favors PAIC	Global interval favors PAIC
Target-probe Platt (CE)	18	15	10
Target-probe beta (CE)	16	10	8
Source-distilled isotonic	18	18	18
Importance-weighted isotonic	15	12	11
Total	67/72	55/72	47/72
Target-probe Platt (SQ)	18	13	9

Appendix

Table 7: Counts of the 18 refit-level contrasts per comparator in which PAIC has the lower estimate, and in which pointwise or globally adjusted intervals favor PAIC. The squared-loss rows form a separate 36-contrast family.

Shift	Model	Domain AUC	Raw ESS	Clipped ESS	Lower-clipped fraction
Difficulty	Llama	.643	210.0	225.3	.026
	Qwen	.672	195.3	229.7	.023
Task	Llama	.999	46.0	347.8	.956
	Qwen	.998	26.8	137.2	.902
Subject	Llama	.994	24.6	56.3	.808
	Qwen	.993	7.9	43.3	.798

Appendix

Table 8: Top: overlap diagnostics for importance weighting, averaged over three refits; ESS counts source prompts out of 500. Bottom: target risks in the randomized-overlap GSM8K controls.

Model	Candidate	Squared risk	Probe disagreement
Llama	Unchanged score	$0.30109\;[0.29077,0.31163]$	$0.10114\;[0.09632,0.10616]$
Llama	Source label-isotonic	$0.23767\;[0.23206,0.24340]$	$0.01821\;[0.01730,0.01913]$
Llama	Source PAIC	$0.23848\;[0.23284,0.24424]$	$0.01858\;[0.01764,0.01954]$
Llama	Target PAIC	$0.23215\;[0.22695,0.23740]$	$0.01725\;[0.01636,0.01816]$
Llama	Direct probe	$0.21456\;[0.20900,0.22012]$	$0.00000\;[0.00000,0.00000]$
Qwen	Unchanged score	$0.16308\;[0.15296,0.17326]$	$0.01505\;[0.01397,0.01618]$

Appendix

Table 9: A learned GSM8K-trained score on MATH level 3: squared risk and squared disagreement with the fixed probe on the common 1,842-prompt evaluation set (eight answers per prompt), with pointwise 95% intervals.

Candidate	Llama 3.2 3B	Qwen 2.5 3B
Original $P$	0.295817	0.377312
Canonical label-isotonic	0.247903	0.241805
Source PAIC	0.246479	0.244422
Target PAIC	0.250821	0.247072
Direct rich teacher	0.243782	0.231066
Direct score-only teacher	0.244477	0.242851

Appendix

Table 10: Controlled presentation changes: target Brier risk for all twelve candidates, averaging the three transformed views and two instances within each family with fixed stratum weights. All fitted candidates share 2,400 unique fitting labels per model; the six primary paired contrasts are in Figure 3 .

Candidate	MSE	$\Delta$	95% interval for $\Delta$
Original score	0.21274	$-0.01556$	$[-0.02088,\,-0.01031]$
Source isotonic	0.19748	$-0.00030$	$[-0.00863,\,0.00767]$
Source Platt	0.19622	$0.00096$	$[-0.00351,\,0.00574]$
Raw verifier	0.19672	$0.00046$	$[-0.02123,\,0.02271]$
Calibrated verifier	0.15506	$0.04212$	$[0.02548,\,0.05914]$
PAIC	0.19718	$0.00000$	$[0.00000,\,0.00000]$

Appendix

Table 11: Offline verifier as teacher: squared risk and paired differences on the 598 test prompts.

\Delta=L(\mathrm{PAIC})-L(\mathrm{candidate})

; negative values favor PAIC. Intervals are pointwise 95% paired prompt-bootstrap intervals (1,999 draws), conditional on the fitted maps.

	$c=0.10$		$c=0.25$		$c=0.50$
Candidate	Loss	$A$	Loss	$A$	Loss	$A$
Original score	0.14732	58.03	0.25962	97.83	0.26756	100.00
Source isotonic	0.14448	49.16	0.24582	95.32	0.26505	97.83
Source Platt	0.12659	33.61	0.22952	88.46	0.26672	99.50
Raw verifier	0.18846	88.80	0.20778	89.80	0.23495	90.47
Calibrated verifier	0.11488	55.35	0.19064	84.62	0.23328	89.80

Appendix

Table 12: Offline verifier as teacher: review policies at three review costs. Each pair reports mean decision loss and automated acceptance (

A

, percent) under perfect review; scoring latency is not included.

Population	Two-sided EB	One-sided EB	Betting	Assisted EB	Assisted betting	PPI++
Binary constant gain	2,000	2,000	1,000	2,000	1,000	500
Graded constant gain	500	500	250	1,000	250	25
Binary heterogeneous gain	–	2,000	1,000	–	1,000	1,000
Graded heterogeneous gain	1,000	1,000	250	2,000	250	25

Appendix

Table 13: First tested label count at which beneficial adoption has Wilson lower bound at least

80\%

and false improvement Wilson upper bound at most

5\%

(oracle probe,

r=4

; “–”: no crossing through 2,000). The middle four columns share one-sided hypotheses, certified ranges, candidate family, and error budget; PPI++ is asymptotic.

Procedure	Beneficial adoption	PAIC certified	PAIC selected	Richer selected
One-sided EB	7,155 (15.09%)	5,794 (12.22%)	47	7,108
Betting	20,356 (42.95%)	15,635 (32.99%)	125	20,212
Assisted EB	6,610 (13.95%)	5,440 (11.48%)	35	6,575
Assisted betting	19,012 (40.11%)	14,598 (30.80%)	183	18,815
Two-sided EB	6,358 (13.41%)	5,207 (10.99%)	130	6,228

Appendix

Table 14: Matched procedures on 47,400 raw-score allocations per method (learned probes, 16 candidates). “PAIC certified” counts allocations in which at least one PAIC map is certified; false adoption is estimated on a separate test set.

Test	Feature map $\Phi$	Null hypothesis under the prompt-weighted law
Feature	$e_{(S,H)}$	$\mathbb{E}[Y-s\mid S,H]=0$ in every joint state.
Score-only	$e_{S}$	$\mathbb{E}[Y-s\mid S]=0$ at each score level.
Subgroup	$H$	$\mathbb{E}[(Y-s)H]=0$ .
Learned auditor	$h(S,H)$	$\mathbb{E}[(Y-s)h(S,H)]=0$ , conditional on the fitted $h$ .

Appendix

Table 15: An audit’s null depends on its features. Hidden-only error satisfies the score-only null; scalar-only error satisfies the subgroup null. Their non-rejection in these cases is not failure to detect an alternative to their own null.

Configuration	Feature	Score only	Subgroup	Auditor
Identity score $s=S$ , binary outcomes, $K=1$ ; configuration: $(J,\delta)$
$(100,\ 0)$	0.0590 ∘	0.0540 ∘	0.0570 ∘	0.0510 ∘
$(100,\ 0.05)$	0.1265	0.0490 ∘	0.1940	0.1475
$(100,\ 0.1)$	0.3625	0.0510 ∘	0.5950	0.5500
$(100,\ 0.2)$	0.9475	0.0505 ∘	0.9930	0.9915
$(100,\ 0.35)$	1.0000	0.0515 ∘	1.0000	1.0000

Appendix

Table 16: All 37 controlled audit configurations: rejection rates from 2,000 repetitions per configuration at nominal level 0.05. Pointwise 95% Wilson half-widths are about 0.01 near 0.05 and at most 0.022. A superscript

\circ

marks a method-specific population null by construction; for the learned auditor this applies under full calibration.

Partition	Prompts	Learned answers	Mechanical answers	Jaccard	Learned-group error	Mechanical- group error
Discovery	572	200	196	98.00%	97.00%	98.98%
Audit	572	243	238	97.94%	99.59%	100.00%
Final evaluation	1,435	510	498	97.65%	98.82%	99.20%

Appendix

Table 17: Learned audit rule (length

>1{,}018

tokens) versus a mechanical screen (exactly 1,024 tokens) over all eight siblings per prompt.

Dataset	Model	$c=.05$	$.10$	$.20$	$.30$	$.40$	$.50$
GSM8K	Llama	$-.000539$	$-.000410$	$+.000367$	$-.000301$	$+.000067$	$-.000320$
	Qwen	$+.000101$	$+.000415$	$-.000634$	$-.000034$	$+.000359$	$-.000267$
10K	Llama	$+.000100$	$-.000110$	$-.000308$	$-.000318$	$-.000056$	$-.000207$
	Qwen	$+.000027$	$+.000120$	$-.000282$	$+.000055$	$-.000179$	$+.000308$

Appendix

Table 18: Archived learned score, full fitting budget: mean PAIC value-policy loss minus the original-score threshold fitted directly on the same

F

labels. Negative favors PAIC. Each entry averages 15 overlapping blocks and is descriptive, not an independent-refit interval.

Benchmark	$D$	$F$	$C$	$U$	$S$	$T$
BoolQ	400	4,393	1,597	1,598	—	3,270
ARC	112	2,126	570	1,410	2,375	1,172

Appendix

Table 19: Question counts after outcome-blind overlap filtering, shared by all models. BoolQ has no separate source-evaluation role.

Benchmark	Contrast	Effect	Lower	Upper	Direction
BoolQ	Rich $-$ score	$-0.00297949$	$-0.00637632$	$0.00041735$	unresolved
BoolQ	PAIC-R- $U$ $-$ scalar	$0.00010225$	$-0.00079915$	$0.00100366$	unresolved
BoolQ	PAIC-R- $U$ $-$ PAIC-S- $U$	$-0.00032620$	$-0.00092227$	$0.00026986$	unresolved
BoolQ	PAIC-R- $U$ $-$ rich	$0.01234145$	$0.00720879$	$0.01747412$	first higher risk
ARC	Rich $-$ score	$0.00257319$	$-0.00239375$	$0.00754012$	unresolved
ARC	PAIC-R- $U$ $-$ scalar	$0.00109614$	$-0.00309369$	$0.00528598$	unresolved

Appendix

Table 20: Qwen2.5-32B primary contrasts. Approximate joint 95% intervals from 19,999 question-weighted dependency-component draws, conditional on the fitted candidates and the

F

-based control selection. R/S abbreviate rich/score teachers.

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