Identifying Influential N-grams in Confidence Calibration via Regression Analysis

Shintaro Ozaki; Wataru Hashimoto; Hidetaka Kamigaito; Katsuhiko Hayashi; Taro Watanabe

cs.CLApr 7, 2026

Identifying Influential N-grams in Confidence Calibration via Regression Analysis

Authors: Shintaro Ozaki, Wataru Hashimoto, Hidetaka Kamigaito, Katsuhiko Hayashi, Taro Watanabe

Organizations: Nara Institute of Science and Technology (NAIST) · The University of Tokyo

Abstract

While large language models (LLMs) improve performance by explicit reasoning, their responses are often overconfident, even though they include linguistic expressions demonstrating uncertainty. In this work, we identify what linguistic expressions are related to confidence by applying the regression method. Specifically, we predict confidence of those linguistic expressions in the reasoning parts of LLMs as the dependent variables and analyze the relationship between a specific $n$ -gram and confidence. Across multiple models and QA benchmarks, we show that LLMs remain overconfident when reasoning is involved and attribute this behavior to specific linguistic information. Interestingly, several of the extracted expressions coincide with cue phrases intentionally inserted on test-time scaling to improve reasoning performance. Through our test on causality and verification that the extracted linguistic information truly affects confidence, we reveal that confidence calibration is possible by simply suppressing those overconfident expressions without drops in performance.

Figures & tables

Figure 1: Overview of our work that segments the reasoning process into $n$ -grams to identify what $n$ -grams contribute to overconfidence. Moreover, we demonstrate that suppressing the identified $n$ -grams leads to successful confidence calibration.

Figure 2: Our calibration approach, $N$ -gram Suppression and Injection.

Figure 3: Results of the calibration plot. Ideally, the curve matches the diagonal line, meaning that when the x-axis confidence is 70%, the y-axis accuracy should also be 70%.

Model	Baseline Inference					$N$ -gram Suppression					$N$ -gram Injection
Model	ECE $\downarrow$	ACE $\downarrow$	Brier $\downarrow$	Acc. $\uparrow$	AUROC $\uparrow$	ECE $\downarrow$	ACE $\downarrow$	Brier $\downarrow$	Acc. $\uparrow$	AUROC $\uparrow$	ECE $\downarrow$	ACE $\downarrow$	Brier $\downarrow$	Acc. $\uparrow$	AUROC $\uparrow$
Reasoning Models
R1 Qwen	0.334	0.334	0.713	0.627	0.502	0.318	0.316	0.700	0.630	0.510	0.312	0.310	0.704	0.616	0.542
R1 Llama	0.245	0.245	0.615	0.620	0.691	0.079	0.079	0.769	0.251	0.528	0.267	0.267	0.723	0.488	0.728
R1 Qwen3	0.198	0.198	0.450	0.759	0.604	0.166	0.166	0.344	0.826	0.566	0.167	0.166	0.359	0.815	0.566
Nemotron	0.415	0.415	0.896	0.510	0.517	0.334	0.334	0.859	0.553	0.637	0.409	0.409	0.898	0.496	0.544

Table 1: Experimental results. Bold text indicates the best score among the models. AUROC is an abbreviation of AUC-ROC.

1-gram	Conf.	Acc.	Freq.	2-gram	Conf.	Acc.	Freq.	3-gram	Conf.	Acc.	Freq.	4-gram	Conf.	Acc.	Freq.
R1 Qwen
looking	2.16	0.00 †	27776	options answer	2.35	0.00 †	972	options hmm let	1.81	0.14 †	79	correct answer wait let	1.37	0.00 †	139
yes	1.76	0.00 †	4147	options hmm	2.08	0.00 †	1107	answer wait let	1.54	0.14 †	505	trying figure answer question	1.12	0.00 †	203
option	1.75	0.00 †	249743	looking options	1.62	0.00 †	16721	option perhaps answer	1.48	0.14 †	371	figure option correctly describes	1.12	0.00 †	467
answer	1.46	0.00 †	83503	look options	1.48	0.00 †	1035	options answer wait	1.27	0.14 †	159	need figure answer question	1.12	0.00 †	208
bit	1.42	0.00 †	11949	options let	1.34	0.00 †	1894	perhaps problem asking	1.26	0.14 †	361	need figure option correct	1.11	0.00 †	151

Table 2: Results of confidence analysis using Lasso and accuracy analysis using logistic for R1 Llama and R1 Qwen. We apply Z-score standardization to the

n

-gram scores across all features. † indicates results where the original feature value was 0 before standardization. Blue bold text indicates features for which confidence decreased, and accuracy increased.

1-gram	Conf.	Acc.	Freq.	2-gram	Conf.	Acc.	Freq.	3-gram	Conf.	Acc.	Freq.	4-gram	Conf.	Acc.	Freq.
Nemotron
final	2.00	0.31	12122	answer final	1.46	0.85	3828	final correct answer	1.10	0.95 †	265	answer finalthink final answer	1.02	0.00 †	119
answer	1.46	-0.08	95521	howthe answer	1.38	0.45 †	49	answer finalthink final	1.06	0.95 †	121	answer answer final answer	0.98	0.00 †	463
correct	1.09	0.03 †	41395	final answer	1.30	0.45 †	9325	answer final answer	1.05	1.37	3082	correct answer final answer	0.91	0.00 †	1028
thethe	0.95	2.28	2627	sure option	1.17	0.45 †	256	correct final answer	0.89	0.95 †	384	answer final final answer	0.89	0.00 †	239
mention	0.87	0.03 †	6166	option answer	1.17	0.45 †	1669	thethe correct answer	0.85	0.95 †	180	final answer final answer	0.71	0.00 †	291

Table 3: Results of models other than those in Table 2 . Red underlined text shows features where confidence improves and accuracy decreases.

Figure 4: Changes in $n$ -gram frequencies.

Figure 5: Results of extracting

n

-grams common to the models.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

QA	Data	HuggingFace	Citation
HellaSwag	10,042	Rowan/hellaswag	Zellers et al. (2019)
MathQA	2,985	allenai/math_qa	Amini et al. (2019)
MMLU (STEM)	1,990	cais/mmlu	Hendrycks et al. (2021a)
RACE	2,985	EleutherAI/race	Lai et al. (2017)
CosmosQA	3,498	allenai/cosmos_qa	Huang et al. (2019)
Overall	21,500

Appendix

Table 5: Datasets used and their sizes.

Model	Parameter	Detailed Name on HuggingFace	Citation
R1 Qwen	7B	deepseek-ai/DeepSeek-R1-Distill-Qwen-7B	Guo et al. (2025)
R1 Llama	8B	deepseek-ai/DeepSeek-R1-Distill-Llama-8B	Guo et al. (2025)
Nemotron	8B	nvidia/Llama-3.1-Nemotron-Nano-8B-v1	Bercovich et al. (2025)
R1 Qwen3	8B	deepseek-ai/DeepSeek-R1-0528-Qwen3-8B	Guo et al. (2025)
Phi-4	15B	microsoft/Phi-4-reasoning	Abdin et al. (2025)
GPT-oss	20B	openai/gpt-oss-20b	Agarwal et al. (2025)

Appendix

Table 6: Detailed model names used in the experiments.

Model	$N$	Acc.			Confidence
		Acc.	ROC AUC	Log Loss	Generation			Forced-Decoding
		Acc.	ROC AUC	Log Loss	$\lambda$	MAE	MRE	$\lambda$	MAE	MRE
	1	0.6150	0.5000	0.7541	0.0000	0.1913	0.4531	0.0000	0.0880	0.1336
	2	0.6150	0.5000	0.7540	0.0000	0.1871	0.4396	0.0046	0.1900	0.3991
	3	0.6150	0.5000	0.7540	0.0000	0.2191	0.5117	0.0029	0.1866	0.3922
	4	0.6150	0.5000	0.7540	0.0000	0.2467	0.5733	0.0018	0.1900	0.3991

Appendix

Table 7: Evaluation results of the regression analysis. We use accuracy, ROC-AUC, and log loss to evaluate logistic regression, and MAE and MRE to evaluate Lasso regression.

\lambda

denotes the regularization coefficient of Lasso regression.

Model	$N$	Acc.			Confidence
		Acc.	ROC AUC	Log Loss	Generation			Forced-Decoding
		Acc.	ROC AUC	Log Loss	$\lambda$	MAE	MRE	$\lambda$	MAE	MRE
	1	0.7604	0.6407	0.5419	0.0001	0.2514	0.5519	0.0006	0.1434	0.2723
	2	0.7656	0.6509	0.5346	0.0001	0.2514	0.5531	0.0000	0.1202	0.2259
	3	0.7642	0.6387	0.5375	0.0000	0.2509	0.5528	0.0000	0.1225	0.2307
	4	0.7893	0.7439	0.4852	0.0001	0.2564	0.5672	0.0000	0.1307	0.2464

Appendix

Table 8: Evaluation results of the regression analysis. We use accuracy, ROC-AUC, and log loss to evaluate logistic regression, and MAE and MRE to evaluate Lasso regression.

\lambda

denotes the regularization coefficient of Lasso regression.

Model	Baseline Inference						$N$ -gram Suppression						$N$ -gram Injection
Model	M	H	Ma	R	C	Avg.	M	H	Ma	R	C	Avg.	M	H	Ma	R	C	Avg.
Reasoning Models
R1 Qwen	86.5	52.4	77.2	71.6	57.6	62.67	87.3	54.0	77.3	69.6	56.1	63.04	85.7	52.3	75.5	69.9	54.2	61.64
R1 Llama	79.5	62.2	68.2	77.9	25.2	61.97	29.1	26.5	21.0	22.1	25.2	25.10	26.1	60.9	44.5	47.4	28.7	48.77
Nemotron	74.0	40.6	72.4	67.9	46.6	51.04	62.8	37.8	51.0	55.0	58.9	55.25	63.3	41.5	54.3	62.7	51.1	49.56
R1 Qwen3	95.3	70.5	84.8	89.2	70.1	75.89	94.4	62.6	100.0	86.8	71.5	82.61	94.2	65.6	93.5	86.6	70.9	81.50

Appendix

Table 9: Accuracy results and their average for solving five QA tasks. M, H, Ma, R, and C indicate MMLU, HellaSwag, MathQA, RACE, and CosmosQA, respectively.

Figure 6: Calibration curve obtained using the generation-based method.

Figure 7: Correlation between TF-IDF-based and count-based methods.

Model	Baseline Inference					$N$ -gram Suppression					Suppression w/o $N$ -gram
Model	ECE $\downarrow$	ACE $\downarrow$	Brier $\downarrow$	Acc. $\uparrow$	AUROC $\uparrow$	ECE $\downarrow$	ACE $\downarrow$	Brier $\downarrow$	Acc. $\uparrow$	AUROC $\uparrow$	ECE $\downarrow$	ACE $\downarrow$	Brier $\downarrow$	Acc. $\uparrow$	AUROC $\uparrow$
R1 Qwen	0.334	0.334	0.713	0.627	0.502	0.318	0.316	0.700	0.630	0.510	0.323	0.323	0.708	0.625	0.516
R1 Llama	0.245	0.245	0.615	0.620	0.691	0.079	0.079	0.769	0.251	0.528	0.088	0.088	0.759	0.287	0.604
R1 Qwen3	0.198	0.198	0.450	0.759	0.604	0.166	0.166	0.344	0.826	0.566	0.169	0.170	0.361	0.820	0.566
Nemotron	0.415	0.415	0.896	0.510	0.517	0.334	0.334	0.859	0.553	0.637	0.404	0.404	0.907	0.476	0.551
Phi-4	0.199	0.199	0.405	0.795	0.562	0.194	0.194	0.448	0.734	0.689	0.201	0.200	0.408	0.794	0.567

Appendix

Table 10: Experimental results. Bold indicates the best score across the models. AUROC is an abbreviation of AUC-ROC.

1-gram	Conf.	Acc.	Freq.	2-gram	Conf.	Acc.	Freq.	3-gram	Conf.	Acc.	Freq.	4-gram	Conf.	Acc.	Freq.
R1 Qwen3
directly	1.32	0.00 †	96965	decision select	3.23	0.00 †	1167	final decision select	2.55	0.15 †	1164	choice final decision select	1.80	0.00 †	158
yes	1.22	0.00 †	8209	add explanation	2.79	0.00 †	2258	user asking answer	1.58	0.15 †	2044	perhaps need output thought	1.60	0.00 †	351
output	0.94	0.00 †	156404	asking answer	2.11	0.00 †	2046	says add explanation	1.57	0.15 †	723	asking answer question selecting	1.54	0.00 †	1666
context	0.90	0.00 †	153054	let verify	1.80	0.00 †	2916	perhaps need output	1.55	0.15 †	2010	guidelines include having thought	1.42	0.00 †	1300
probably	0.90	0.00 †	27043	need infer	1.57	0.00 †	7288	exactly option question	1.45	0.15 †	2660	explanation output required format	1.42	0.00 †	738

Appendix

Table 11: Results of models other than those in Tables 2 and 3 .

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Wired for Overconfidence: A Mechanistic Perspective on Inflated Verbalized Confidence in LLMs

Tianyi Zhao, Yinhan He, Wendy Zheng, Yujie Zhang+1

University of Virginia

Confidence Estimation in Language Models Language Model Calibration LLM Interpretability Causal Interventions in Language Models

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Large language models are often not just wrong, but confidently wrong: when they produce factually incorrect answers, they tend to verbalize overly high confidence rather than signal uncertainty. Such verbalized overconfidence can mislead users and weaken confidence scores as a reliable uncertainty signal, yet its internal mechanisms remain poorly understood. We present a circuit-level mechanistic analysis of this inflated verbalized confidence in LLMs, organized around three axes: capturing verbalized confidence as a differentiable internal signal, identifying the circuits that causally inflate it, and leveraging these insights for targeted inference-time recalibration. Across two instruction-tuned LLMs on three datasets, we find that a compact set of MLP blocks and attention heads, concentrated in middle-to-late layers, consistently writes the confidence-inflation signal at the final token position. We further show that targeted inference-time interventions on these circuits substantially improve calibration. Together, our results suggest that verbalized overconfidence in LLMs is driven by identifiable internal circuits and can be mitigated through targeted intervention.

Abstract

Language Model Calibration

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