  Large language models (LLMs) are notorious for hallucinating, i.e., producing
erroneous claims in their output. Such hallucinations can be dangerous, as
occasional factual inaccuracies in the generated text might be obscured by the
rest of the output being generally factually correct, making it extremely hard
for the users to spot them. Current services that leverage LLMs usually do not
provide any means for detecting unreliable generations. Here, we aim to bridge
this gap. In particular, we propose a novel fact-checking and hallucination
detection pipeline based on token-level uncertainty quantification. Uncertainty
scores leverage information encapsulated in the output of a neural network or
its layers to detect unreliable predictions, and we show that they can be used
to fact-check the atomic claims in the LLM output. Moreover, we present a novel
token-level uncertainty quantification method that removes the impact of
uncertainty about what claim to generate on the current step and what surface
form to use. Our method Claim Conditioned Probability (CCP) measures only the
uncertainty of a particular claim value expressed by the model. Experiments on
the task of biography generation demonstrate strong improvements for CCP
compared to the baselines for seven LLMs and four languages. Human evaluation
reveals that the fact-checking pipeline based on uncertainty quantification is
competitive with a fact-checking tool that leverages external knowledge.
