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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.27403 |
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| _version_ | 1866915897328795648 |
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| author | Ye, Kai Pan, Qingtao Li, Shuo |
| author_facet | Ye, Kai Pan, Qingtao Li, Shuo |
| contents | Large language models (LLMs) need reliable test-time control of hallucinations. Existing conformal methods for LLMs typically provide only \emph{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 \emph{Conditional Factuality Control} (CFC), a post-hoc conformal framework that returns \emph{set-valued} outputs with \emph{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 \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27403 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conditional Factuality Controlled LLMs with Generalization Certificates via Conformal Sampling Ye, Kai Pan, Qingtao Li, Shuo Machine Learning Artificial Intelligence Large language models (LLMs) need reliable test-time control of hallucinations. Existing conformal methods for LLMs typically provide only \emph{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 \emph{Conditional Factuality Control} (CFC), a post-hoc conformal framework that returns \emph{set-valued} outputs with \emph{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 \emph{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. |
| title | Conditional Factuality Controlled LLMs with Generalization Certificates via Conformal Sampling |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.27403 |