Are Large Language Models More Honest in Their Probabilistic or Verbalized Confidence?

Large language models (LLMs) have been found to produce hallucinations when the question exceeds their internal knowledge boundaries. A reliable model should have a clear perception of its knowledge boundaries, providing correct answers within its scope and refusing to answer when it lacks knowledge. Existing research on LLMs' perception of their knowledge boundaries typically uses either the probability of the generated tokens or the verbalized confidence as the model's confidence in its response. However, these studies overlook the differences and connections between the two. In this paper, we conduct a comprehensive analysis and comparison of LLMs' probabilistic perception and verbalized perception of their factual knowledge boundaries. First, we investigate the pros and cons of these two perceptions. Then, we study how they change under questions of varying frequencies. Finally, we measure the correlation between LLMs' probabilistic confidence and verbalized confidence. Experimental results show that 1) LLMs' probabilistic perception is generally more accurate than verbalized perception but requires an in-domain validation set to adjust the confidence threshold. 2) Both perceptions perform better on less frequent questions. 3) It is challenging for LLMs to accurately express their internal confidence in natural language.