Large Language Models (LLMs) enhanced with retrieval, an approach known as Retrieval-Augmented Generation (RAG), have achieved strong performance in open-domain question answering. However, RAG remains prone to hallucinations: factually incorrect outputs may arise from inaccuracies in the model's internal knowledge and the retrieved context. Existing approaches to mitigating hallucinations often conflate factuality with faithfulness to the retrieved evidence, incorrectly labeling factually correct statements as hallucinations if they are not explicitly supported by the retrieval. In this paper, we introduce FRANQ, a new method for hallucination detection in RAG outputs. FRANQ applies distinct uncertainty quantification (UQ) techniques to estimate factuality, conditioning on whether a statement is faithful to the retrieved context. To evaluate FRANQ and competing UQ methods, we construct a new long-form question answering dataset annotated for both factuality and faithfulness, combining automated labeling with manual validation of challenging cases. Extensive experiments across multiple datasets, tasks, and LLMs show that FRANQ achieves more accurate detection of factual errors in RAG-generated responses compared to existing approaches.

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