Automatic factuality verification of large language model (LLM) generations is becoming more and more widely used to combat hallucinations. A major point of tension in the literature is the granularity of this fact-checking: larger chunks of text are hard to fact-check, but more atomic facts like propositions may lack context to interpret correctly. In this work, we assess the role of context in these atomic facts. We argue that fully atomic facts are not the right representation, and define two criteria for molecular facts: decontextuality, or how well they can stand alone, and minimality, or how little extra information is added to achieve decontexuality. We quantify the impact of decontextualization on minimality, then present a baseline methodology for generating molecular facts automatically, aiming to add the right amount of information. We compare against various methods of decontextualization and find that molecular facts balance minimality with fact verification accuracy in ambiguous settings.
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