Large Language Models (LLMs) have shown impressive capabilities but also a concerning tendency to hallucinate. This paper presents RefChecker, a framework that introduces claim-triplets to represent claims in LLM responses, aiming to detect fine-grained hallucinations. In RefChecker, an extractor generates claim-triplets from a response, which are then evaluated by a checker against a reference. We delineate three task settings: Zero, Noisy and Accurate Context, to reflect various real-world use cases. We curated a benchmark spanning various NLP tasks and annotated 11k claim-triplets from 2.1k responses by seven LLMs. RefChecker supports both proprietary and open-source models as the extractor and checker. Experiments demonstrate that claim-triplets enable superior hallucination detection, compared to other granularities such as response, sentence and sub-sentence level claims. RefChecker outperforms prior methods by 6.8 to 26.1 points on our benchmark and the checking results of RefChecker are strongly aligned with human judgments. This work is open sourced at https://github.com/amazon-science/RefChecker
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