  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.
