  With the widespread application of Large Language Models (LLMs) to various
domains, concerns regarding the trustworthiness of LLMs in safety-critical
scenarios have been raised, due to their unpredictable tendency to hallucinate
and generate misinformation. Existing LLMs do not have an inherent
functionality to provide the users with an uncertainty metric for each response
it generates, making it difficult to evaluate trustworthiness. Although a
number of works aim to develop uncertainty quantification methods for LLMs,
they have fundamental limitations, such as being restricted to classification
tasks, requiring additional training and data, considering only lexical instead
of semantic information, and being prompt-wise but not response-wise. A new
framework is proposed in this paper to address these issues. Semantic density
extracts uncertainty information for each response from a probability
distribution perspective in semantic space. It has no restriction on task types
and is "off-the-shelf" for new models and tasks. Experiments on seven
state-of-the-art LLMs, including the latest Llama 3 and Mixtral-8x22B models,
on four free-form question-answering benchmarks demonstrate the superior
performance and robustness of semantic density compared to prior approaches.
