Adaptive Conformal Prediction for Improving Factuality of Generations by Large Language Models

Aleksandr Rubashevskii; Dzianis Piatrashyn; Preslav Nakov; Maxim Panov

cs.CLApr 15, 2026

Adaptive Conformal Prediction for Improving Factuality of Generations by Large Language Models

Authors: Aleksandr Rubashevskii, Dzianis Piatrashyn, Preslav Nakov, Maxim Panov

Organizations: Mohamed bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, UAE

Abstract

Large language models (LLMs) are prone to generating factually incorrect outputs. Recent work has applied conformal prediction to provide uncertainty estimates and statistical guarantees for the factuality of LLM generations. However, existing approaches are typically not prompt-adaptive, limiting their ability to capture input-dependent variability. As a result, they may filter out too few items (leading to over-coverage) or too many (under-coverage) for a given task or prompt. We propose an adaptive conformal prediction approach that extends conformal score transformation methods to LLMs, with applications to long-form generation and multiple-choice question answering. This enables prompt-dependent calibration, retaining marginal coverage guarantees while improving conditional coverage. In addition, the approach naturally supports selective prediction, allowing unreliable claims or answer choices to be filtered out in downstream applications. We evaluate our approach on multiple white-box models across diverse domains and show that it significantly outperforms existing baselines in terms of conditional coverage.

Figures & tables

Panel of Figure 1 — Figure 1: Long-form QA target vs. empirical coverage for (a) Conformal Factuality and (b) Adaptive Conformal (ours). The conformal procedure is calibrated jointly on two categories (“Inventions” and “Persons”). While both methods achieve the target coverage marginally, only the adaptive approach closely approximates conditional coverage.

Panel of Figure 2 — Figure 2: Multi-choice QA experimental results: target vs. empirical coverage for (a) Conformal Factuality and (b) Adaptive Conformal method (ours). Results are shown for two prompt categories, with coverage reported for each category individually as well as jointly. The conformal threshold is calibrated jointly across both categories.

Claim Scoring Method	Mistral 7B	Llama3 8B	Gemma3 12B
Random Baseline	0.189	0.166	0.138
Maximum Probability	0.273	0.281	0.180
Perplexity	0.255	0.257	0.162
Max Token Entropy	0.313	0.324	0.189
Pointwise Mutual Information	0.189	0.158	0.136
Claim Conditioned Probability	0.360	0.367	0.238

Table 1: PR-AUC for long-form QA claim scoring functions on Mistral 7B, Llama3 8B and Gemma3 12B. Higher is better, best method per column is colored.

	Coverage		% Removed
Category	Original	Adaptive	Original	Adaptive
inventions	84.59 $\pm$ 2.98	82.47 $\pm$ 4.26	87.71 $\pm$ 0.47	83.33 $\pm$ 3.30
persons	81.37 $\pm$ 2.87	78.97 $\pm$ 5.88	82.41 $\pm$ 1.02	81.12 $\pm$ 5.43
artworks	77.39 $\pm$ 3.46	79.29 $\pm$ 3.22	90.12 $\pm$ 0.53	82.40 $\pm$ 2.23
books	82.02 $\pm$ 3.33	81.23 $\pm$ 4.03	84.83 $\pm$ 0.76	81.47 $\pm$ 3.87
cities	78.31 $\pm$ 3.37	79.08 $\pm$ 4.63	82.11 $\pm$ 0.89	80.47 $\pm$ 4.32

Table 2: Mistral 7B results (mean

\pm

std over seeds) at

\alpha=0.20

. Coverage target is

0.80

. Adaptive conformal prediction improves category-wise coverage alignment while typically reducing the fraction of removed items.

Panel of Figure 3 — Figure 3: Dolan-Moré profiles for calibration error for (a) Mistral 7B, (b) Llama3 8B. Problems are defined by (category, seed, $\alpha$ ) with $\alpha\in\{0.5,0.55,\dots,0.8\}$ , 20 seeds and 16 categories. Calibration error is defined as $|\text{empirical coverage}-(1-\alpha)|$ , normalized per problem. The x-axis ( $\delta$ ) is plotted on a logarithmic scale. Curves show the fraction of problems within a factor $\delta$ of the best (higher is better).

	Coverage		% Removed
Category	Original	Adaptive	Original	Adaptive
inventions	85.12 $\pm$ 2.69	80.33 $\pm$ 4.93	88.18 $\pm$ 0.92	81.52 $\pm$ 3.44
persons	73.91 $\pm$ 2.32	79.82 $\pm$ 3.62	79.45 $\pm$ 0.73	81.80 $\pm$ 4.02
artworks	68.00 $\pm$ 4.98	76.90 $\pm$ 5.02	80.99 $\pm$ 0.89	81.04 $\pm$ 3.87
books	85.73 $\pm$ 3.75	82.20 $\pm$ 3.60	83.82 $\pm$ 1.30	80.66 $\pm$ 3.50
cities	86.35 $\pm$ 2.04	77.21 $\pm$ 4.10	86.54 $\pm$ 0.47	80.79 $\pm$ 3.61

Table 3: Gemma-3 12B results (mean

\pm

std over seeds) at

\alpha=0.20

with target coverage

0.80

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

	Coverage		% Removed
Category	Original	Adaptive	Original	Adaptive
inventions	85.66 $\pm$ 3.38	81.81 $\pm$ 3.86	87.56 $\pm$ 1.35	82.25 $\pm$ 3.14
persons	78.59 $\pm$ 3.75	81.29 $\pm$ 4.84	86.87 $\pm$ 1.31	84.35 $\pm$ 3.24
artworks	79.90 $\pm$ 4.25	80.44 $\pm$ 4.03	88.39 $\pm$ 1.13	83.83 $\pm$ 3.75
books	78.07 $\pm$ 5.93	78.51 $\pm$ 4.16	78.18 $\pm$ 1.12	78.98 $\pm$ 2.95
cities	82.98 $\pm$ 6.15	77.65 $\pm$ 3.64	85.01 $\pm$ 1.00	81.89 $\pm$ 2.30

Appendix

Table 4: LLaMA-3.1 8B results (mean

\pm

std over seeds) at

\alpha=0.20

with target coverage

0.80

Panel of Figure 4 — Figure 4: Multi-choice QA target vs. empirical coverage for (a) Conformal Factuality and (b) Our adaptive conformal method. The conformal procedure is calibrated on all 16 categories. While both methods achieve the target coverage marginally, only the adaptive approach closely approximates conditional coverage.

Figure 5: T-SNE visualization of PCA clustering of long-form QA prompts.

Category	Size
Marketing	259
Professional Accounting	313
College Computer Science	111
Formal Logic	140
High School Computer Science	109
Computer Security	111

Appendix

Table 5: Category indices and corresponding dataset sizes.

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Conditional Factuality Controlled LLMs with Generalization Certificates via Conformal Sampling

Kai Ye, Qingtao Pan, Shuo Li

Case Western Reserve University

LLM Reliability LLM Hallucination Mitigation Group-Conditional Conformal Prediction

Open paper AskPDF arXiv

Large language models (LLMs) need reliable test-time control of hallucinations. Existing conformal methods for LLMs typically provide only marginal guarantees and rely on a single global threshold, which can under-cover hard prompts, over-cover easy ones, and produce oversized prediction sets. We propose Conditional Factuality Control (CFC), a post-hoc conformal framework that returns set-valued outputs with conditional coverage guarantees. CFC defines a continuous, feature-conditional acceptance threshold through augmented quantile regression on a latent ``success'' score, and deploys it through a fixed-point threshold rule at inference time. Theoretically, we show that CFC satisfies a conditional coverage guarantee under exchangeability and analyze its efficiency, proving that, under mild assumptions on the score distributions, the conditional rule is strictly more sample-efficient than marginal conformal prediction at the same target coverage. We further derive a PAC-style variant, CFC-PAC, which shrinks the nominal risk level based on a stability bound, yielding a finite-sample certificate that the conditional miscoverage deviates from the target by at most

O(\sqrt{\log(1/δ)/N})

. Empirically, on synthetic data, real-world reasoning and QA benchmarks, and a Flickr8k VLM setting, CFC and CFC-PAC consistently attain near-target coverage across difficulty groups while using smaller prediction sets than CP and non-CP baselines.

Abstract

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