Conditional Factuality Controlled LLMs with Generalization Certificates via Conformal Sampling

• URL: http://arxiv.org/abs/2603.27403v1
• Date: Sat, 28 Mar 2026 20:48:13 GMT
• Title: Conditional Factuality Controlled LLMs with Generalization Certificates via Conformal Sampling
• Abstract summary: We propose emphConditional Factuality Control (CFC) for large language models (LLMs)<n>CFC defines a continuous, feature-conditional acceptance threshold through augmented quantile regression on a latent success'' score.<n>We show that CFC satisfies a conditional coverage guarantee under exchangeability and analyze its emphefficiency<n>We derive a PAC-style variant, CFC-PAC, which shrinks the nominal risk level based on a stability bound.
• Score: 7.974834731988445
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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