  This paper investigates the capabilities of Large Language Models (LLMs) in
the context of understanding their knowledge and uncertainty over questions.
Specifically, we focus on addressing known-unknown questions, characterized by
high uncertainty due to the absence of definitive answers. To facilitate our
study, we collect a new dataset with Known-Unknown Questions (KUQ) and
establish a categorization framework to clarify the origins of uncertainty in
such queries. Subsequently, we examine the performance of open-source LLMs,
fine-tuned using this dataset, in distinguishing between known and unknown
queries within open-ended question-answering scenarios. The fine-tuned models
demonstrated a significant improvement, achieving a considerable increase in
F1-score relative to their pre-fine-tuning state. Through a comprehensive
analysis, we reveal insights into the models' improved uncertainty articulation
and their consequent efficacy in multi-agent debates. These findings help us
understand how LLMs can be trained to identify and express uncertainty,
improving our knowledge of how they understand and express complex or unclear
information.
