Target-Aware Calibration Data Selection for Preserving Uncertainty in Quantized Language Models

Zhen Yang; Sizai Hou; Kaiwen Zheng; Yaofang Liu; Liang He; Yixuan Chen; Kangning Cui

cs.CLAug 21, 2026

Target-Aware Calibration Data Selection for Preserving Uncertainty in Quantized Language Models

Authors: Zhen Yang, Sizai Hou, Kaiwen Zheng, Yaofang Liu, Liang He, Yixuan Chen, Kangning Cui

Organizations: Yale University · The Hong Kong University of Science and Technology · The Hong Kong University of Science and Technology (Guangzhou) · City University of Hong Kong ·

Abstract

Quantization is widely used to deploy large language models, but its effect on uncertainty behavior, such as confidence, margins, and abstention, is rarely treated as a primary objective. We frame calibration-data selection for quantization as a target-dependent uncertainty-preservation problem. Different deployments emphasize different regions of the input distribution, yet prior work mainly optimizes accuracy-oriented compression metrics or adjusts scores after quantization. We formalize this goal with distributional and boundary preservation risks, and provide a simple mixture-mismatch argument explaining why no single calibration recipe should be expected to fit all targets. We introduce Doubt-Preserving Quantization (DPQ), a lightweight pre-quantization recipe family that uses full-precision predictions to construct target-aligned calibration mixtures of high-doubt examples and generic anchors. Across 8 language models, 9 NLP benchmarks, and 22 comparison methods, the leading fixed recipe changes with the preservation target: DPQ-r75 leads on SQuAD2 answerability-boundary preservation, while milder or single-signal variants, including DPQ-r50, confidence-only, and entropy-only, better preserve broad multiple-choice QA behavior. These results show that calibration data should be selected for the specific full-precision score behavior a deployment needs to preserve, rather than treated as a fixed quantization detail.

Figures & tables

Figure 1: Motivating example of uncertainty drift after quantization. The top-1 answer is unchanged, but the confidence margin shifts substantially, affecting downstream uncertainty-aware decisions.

Method	Worse than FP (%, $\downarrow$ )
Method	Acc.	ECE	NLL	Brier
BNB-NF4	84.7	66.7	84.7	81.9
GPTQ -RandomQA	83.3	61.1	76.4	86.1
GPTQ -WikiText	76.4	58.3	63.9	83.3
GPTQ -C4	83.3	65.3	68.1	77.8
DPQ -s128-r75	80.6	62.5	70.8	83.3

Table 1: Low-bit quantization often worsens accuracy and calibration metrics. Entries show the percentage of model–dataset settings worse than FP ; lower is better. Full results are in Table 11 .

Figure 2: SQuAD2 answerability ECDF area to FP per pre-quantization method, averaged over Qwen2.5-7B, Llama-3.1-8B, and Mistral-7B-v0.3. Numbers denote the mean of the answerable and unanswerable areas. Methods are sorted top-to-bottom by mean area (worst first); DPQ -r75, the best aggregate boundary recipe in Table 2 , is highlighted.

Check	Main finding
Boundary ratio $r$	DPQ -r75 performs best. A high boundary ratio helps, but using only boundary examples over-concentrates the calibration set.
Calibration size $s$	The composition of the calibration set matters more than simply increasing the calibration budget.
Boundary mixing	Mixed calibration outperforms boundary-only variants, suggesting that generic anchors stabilize boundary-focused selection.
Single-signal variants	Confidence-only, entropy-only, and answerability-only variants are useful, but none matches the mixed DPQ -r75 recipe.
Negative controls	HighNLL-QA and LowDoubt-QA underperform DPQ -r75, showing that high doubt is different from ordinary hard- or easy-example selection.

Table 3: Ablation summary for the SQuAD2 boundary target. Full results are in Appendix A.1 .

Figure 4: Target-dependent preservation trade-off: SQuAD2 boundary rank versus extra- MCQA broad-preservation rank. Lower is better on both axes; no calibration recipe dominates both targets.

Method	Rank $\downarrow$	Top-5 $\uparrow$	Agr. $\uparrow$	JSD $\downarrow$
DPQ -confidence-only	8.96	7	0.8357	0.0284
GPTQ -TaskRandom	9.12	11	0.8361	0.0276
HighNLL-QA	9.18	6	0.8327	0.0294
DPQ -entropy-only	9.30	10	0.8324	0.0296
Uncertainty-only	9.31	4	0.8318	0.0297
LowDoubt-QA	9.47	9	0.8328	0.0286

Table 4: Broad MCQA preservation on six answerable datasets. Rank aggregates agreement with FP (Agr.), JSD, margin drift, confidence shift, accuracy deviation, and margin correlation; Top-5 counts model–dataset pairs where the method ranks in the top five. Milder, single-signal, or broad-selection recipes lead, unlike on the SQuAD2 boundary target.

Method	Acc. $\uparrow$	Agr. $\uparrow$	JSD $\downarrow$	Margin $\Delta$ $\downarrow$
Base	0.6833	0.8245	0.0320	0.1533
Adaptive temp.	0.6833	0.8245	0.0445	0.2385
Option bias	0.6985	0.8147	0.0328	0.1591
Vector	0.7029	0.7773	0.0519	0.2344
Matrix	0.6992	0.7723	0.0550	0.2380
Dirichlet	0.6989	0.7740	0.0548	0.2400

Table 5: Post-hoc calibration on extra- MCQA . Flexible calibrators improve accuracy but reduce agreement with FP and increase distributional drift.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Rank $\downarrow$	Agr. $\uparrow$	Acc $\Delta$ $\downarrow$	Rate $\Delta$ $\downarrow$	JSD $\downarrow$
DPQ -s128-r75	6.26	0.9360	0.0331	0.0094	0.0088
DPQ -answerability-only	7.50	0.9250	0.0569	0.0267	0.0100
DPQ -entropy-only	7.66	0.9263	0.0891	0.0446	0.0091
DPQ -boundary-random	8.26	0.9326	0.0411	0.0183	0.0093
DPQ -boundary-only	8.61	0.9316	0.0460	0.0210	0.0099
GPTQ -ActivationKCenter	9.39	0.9294	0.0606	0.0291	0.0105

Appendix

Table 6: SQuAD2 answerability-boundary preservation after removing the Llama-3.2-1B stress case. The main r75 result remains stable.

Figure 5: Additional SQuAD2 answerability ECDFs for Qwen2.5-7B (top) and Mistral-7B-v0.3 (bottom). Lower area-to- FP indicates closer preservation of FP answerability behavior.

Group	Method	Rank $\downarrow$	Agr. $\uparrow$	Acc $\Delta$ $\downarrow$	Rate $\Delta$ $\downarrow$	JSD $\downarrow$
Reference	DPQ -s128-r75	6.20	0.8495	0.2125	0.1000	0.0158
Ratio / size	DPQ -s64-r50	10.18	0.8245	0.2800	0.1382	0.0197
	DPQ -s256-r50	11.18	0.8240	0.2870	0.1425	0.0235
	DPQ -s128-r0	10.31	0.8097	0.3205	0.1598	0.0220
	DPQ -s128-r25	12.06	0.8106	0.3277	0.1639	0.0214
	DPQ -s128-r50	13.12	0.8140	0.3210	0.1602	0.0258

Appendix

Table 7: Boundary-target ablation grid on SQuAD2 answerability. Methods are grouped by ablation axis; columns follow Table 2 . Acc

\Delta

and Rate

\Delta

denote boundary-accuracy and answerability-rate deviation, respectively.

Method	Family	Rank $\downarrow$	Top-5 $\uparrow$	Agr. $\uparrow$	JSD $\downarrow$	Margin $\Delta$ $\downarrow$
DPQ -confidence-only	DPQ component	8.96	7	0.8357	0.0284	0.1447
GPTQ -TaskRandom	Selection baseline	9.12	11	0.8361	0.0276	0.1452
HighNLL-QA	Negative control	9.18	6	0.8327	0.0294	0.1478
DPQ -entropy-only	DPQ component	9.30	10	0.8324	0.0296	0.1473
Uncertainty-only	Selection baseline	9.31	4	0.8318	0.0297	0.1471
LowDoubt-QA	Negative control	9.47	9	0.8328	0.0286	0.1472

Appendix

Table 8: Expanded broad- MCQA preservation on the six answerable datasets. The table adds method family and margin drift to the main broad- MCQA summary in Table 4 .

Suite	Method	Rows	Acc. $\uparrow$	Agr. $\uparrow$	JSD $\downarrow$	Margin $\Delta$ $\downarrow$
Old-core	Base	72	0.6196	0.7906	0.0364	0.1609
	Adaptive temp.	72	0.6196	0.7906	0.0605	0.2892
	Option bias	72	0.5991	0.7811	0.0410	0.1876
	Vector	72	0.7985	0.6875	0.1360	0.3099
	Matrix	72	0.7925	0.6796	0.1404	0.3146
	Dirichlet	72	0.7929	0.6817	0.1403	0.3162

Appendix

Table 9: Post-hoc family summary on old-core and extra- MCQA suites. Flexible calibrators can improve accuracy but often reduce agreement with FP and increase distributional drift.

Dataset	AWQ recipe	$n$	Acc. $\uparrow$	ECE $\downarrow$	NLL $\downarrow$	Brier $\downarrow$	Agr. $\uparrow$
ARC-Challenge	WikiText	8	0.6994	0.1185	0.8645	0.4133	0.8516
	RandomQA	8	0.7082	0.0920	0.8191	0.3974	0.8637
	DPQ-r75	8	0.7153	0.1040	0.8360	0.3952	0.8662
	DPQ-r50	8	0.7174	0.1136	0.8373	0.4008	0.8792
SQuAD2 answerability	WikiText	8	0.6474	0.2122	1.0830	0.5330	0.8483
	RandomQA	8	0.6429	0.2237	1.2086	0.5472	0.8398

Appendix

Table 10: AWQ per-dataset

\times

recipe breakdown averaged over the 8 models. Best values for each dataset and metric are bolded. Agr. denotes agreement with the full-precision model. The preferred recipe varies by dataset and metric, showing that AWQ transfer is target- and metric-dependent rather than fixed to a single calibration recipe.

Method	$n$	Worse than FP (%, $\downarrow$ )				Mean drift ( $\downarrow$ )
Method	$n$	Acc.	ECE	NLL	Brier	Conf. shift	Margin $\Delta$
BNB-NF4	72	84.7	66.7	84.7	81.9	0.0190	0.1376
GPTQ -RandomQA	72	83.3	61.1	76.4	86.1	0.0373	0.1500
GPTQ -WikiText	72	76.4	58.3	63.9	83.3	0.0583	0.1901
GPTQ -C4	72	83.3	65.3	68.1	77.8	0.0493	0.1812
DPQ -s128-r75	72	80.6	62.5	70.8	83.3	0.0363	0.1543

Appendix

Table 11: Calibration-gap prevalence on all nine datasets. The first four metric columns follow Table 1 ; the last two columns report mean confidence shift and margin drift relative to FP .

Suite	Method	Acc.	Conf. correct	Correct gap	Conf. wrong
Old-core	FP	0.6483	0.8358	0.1642	0.7225
	DPQ -s128-r75	0.6136	0.8054	0.1946	0.6953
	DPQ -confidence-only	0.6338	0.8106	0.1894	0.6996
	DPQ -entropy-only	0.6418	0.8153	0.1847	0.7071
	GPTQ -RandomQA	0.6316	0.8089	0.1911	0.7042
	GPTQ -TaskRandom	0.6296	0.8087	0.1913	0.6999

Appendix

Table 12: Correct-vs-wrong confidence decomposition. “Correct gap” is

1-\mathbb{E}[\mathrm{conf}\mid\mathrm{correct}]

; “Conf. wrong” is

\mathbb{E}[\mathrm{conf}\mid\mathrm{wrong}]

, which directly measures overconfidence on errors.

Suite	Method	$n$	ECE $\Delta$ pre $\to$ post	NLL $\Delta$ pre $\to$ post
Old-core	GPTQ -WikiText	24	$-0.009\to-0.091$	$-0.050\to-0.308$
	GPTQ -RandomQA	24	$-0.003\to-0.097$	$+0.013\to-0.314$
	DPQ -r75	24	$+0.002\to-0.102$	$+0.054\to-0.296$
	BNB-NF4	24	$+0.012\to-0.091$	$+0.099\to-0.313$
Extra- MCQA	GPTQ -WikiText	48	$+0.015\to-0.048$	$+0.091\to-0.037$
	GPTQ -RandomQA	48	$+0.002\to-0.055$	$+0.046\to-0.066$

Appendix

Table 13: Effect of fitting one optimal temperature per model–dataset setting. Temperature improves proper-score deltas but does not change accuracy, FP agreement, or boundary decisions.

Scope	AWQ method	Acc. $\uparrow$	ECE $\downarrow$	NLL $\downarrow$	Brier $\downarrow$	Agr. $\uparrow$	JSD $\downarrow$
All 8 models	WikiText	0.6267	0.1891	1.2277	0.5450	0.8346	0.0325
	RandomQA	0.6270	0.1872	1.2712	0.5477	0.8327	0.0336
	DPQ-r75	0.6148	0.2018	1.3011	0.5583	0.8379	0.0320
	DPQ-r50	0.6113	0.2106	1.3488	0.5760	0.8440	0.0332
7B/8B subset	WikiText	0.6987	0.1857	1.2220	0.4784	0.8950	0.0262
	RandomQA	0.7105	0.1795	1.2368	0.4618	0.9116	0.0210

Appendix

Table 14: AWQ metric averages over old-core datasets, split by model scope. The 7B/8B subset is Qwen2.5-7B, Llama-3.1-8B, and Mistral-7B-v0.3. Agr. denotes agreement with the full-precision model.

Scope	AWQ method	Mean rank $\downarrow$	Top-1 freq. $\uparrow$	Top-2 freq. $\uparrow$
All 8 models	DPQ-r75	2.25	29.2%	66.7%
	RandomQA	2.41	8.3%	62.5%
	WikiText	2.66	16.7%	45.8%
	DPQ-r50	2.69	4.2%	50.0%
7B/8B subset	DPQ-r75	1.97	42.9%	73.0%
	RandomQA	2.43	27.0%	47.6%

Appendix

Table 15: Rank-based AWQ summary by model scope.

Group	Purpose	Coverage
Full precision	unquantized reference	all 9 datasets
BNB-NF4	4-bit NF4 quantizer baseline	all 9 datasets
GPTQ -WikiText / GPTQ -C4	generic text calibration	WikiText all 9; C4 extended
GPTQ -RandomQA / TaskRandom	task-formatted random QA	all 9 datasets
DPQ -r0/r25/r50/r75/r100	high-doubt ratio sweep at $s{=}128$	old-core + extra- MCQA
DPQ -s64/s128/s256-r50	calibration-size sweep	old-core + extra- MCQA

Appendix

Table 16: Inventory of experimental groups.

Tag	Nominal scale	Checkpoint
qwen25_05b	0.5B	Qwen/Qwen2.5-0.5B-Instruct
qwen25_1p5b	1.5B	Qwen/Qwen2.5-1.5B-Instruct
qwen25_3b	3B	Qwen/Qwen2.5-3B-Instruct
qwen25_7b	7B	Qwen/Qwen2.5-7B-Instruct
llama32_1b_instruct	1B	meta-llama/Llama-3.2-1B-Instruct
llama32_3b_instruct	3B	meta-llama/Llama-3.2-3B-Instruct

Appendix

Table 17: Model identifiers and nominal parameter scales.

Dataset	Suite	Eval. examples
ARC-Challenge	Old-core	299
SQuAD2 answerability	Old-core	1000
TruthfulQA	Old-core	817
ARC-Easy	Extra- MCQA	570
BoolQ	Extra- MCQA	1000
PIQA	Extra- MCQA	1000

Appendix

Table 18: Evaluation sizes after deterministic filtering and subsampling.

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Mixed-precision quantization (MPQ) has become a key technique for deploying large language models under stringent memory and compute constraints. We first identify a phenomenon that we term the Perplexity Illusion: layers ranked as important by perplexity-based sensitivity show little rank correlation with those that are most influential for complex reasoning performance, with Kendall

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