  Large language models (LLMs) can suffer from hallucinations when generating
text. These hallucinations impede various applications in society and industry
by making LLMs untrustworthy. Current LLMs generate text in an autoregressive
fashion by predicting and appending text tokens. When an LLM is uncertain about
the semantic meaning of the next tokens to generate, it is likely to start
hallucinating. Thus, it has been suggested that hallucinations stem from
predictive uncertainty. We introduce Semantically Diverse Language Generation
(SDLG) to quantify predictive uncertainty in LLMs. SDLG steers the LLM to
generate semantically diverse yet likely alternatives for an initially
generated text. This approach provides a precise measure of aleatoric semantic
uncertainty, detecting whether the initial text is likely to be hallucinated.
Experiments on question-answering tasks demonstrate that SDLG consistently
outperforms existing methods while being the most computationally efficient,
setting a new standard for uncertainty estimation in LLMs.
