Although large language models (LLMs) store vast amount of knowledge in their parameters, they still have limitations in the memorization and utilization of certain knowledge, leading to undesired behaviors such as generating untruthful and inaccurate responses. This highlights the critical need to understand the knowledge boundary of LLMs, a concept that remains inadequately defined in existing research. In this survey, we propose a comprehensive definition of the LLM knowledge boundary and introduce a formalized taxonomy categorizing knowledge into four distinct types. Using this foundation, we systematically review the field through three key lenses: the motivation for studying LLM knowledge boundaries, methods for identifying these boundaries, and strategies for mitigating the challenges they present. Finally, we discuss open challenges and potential research directions in this area. We aim for this survey to offer the community a comprehensive overview, facilitate access to key issues, and inspire further advancements in LLM knowledge research.

Despite the remarkable abilities of Large Language Models (LLMs) to answer questions, they often display a considerable level of overconfidence even when the question does not have a definitive answer. To avoid providing hallucinated answers to these unknown questions, existing studies typically investigate approaches to refusing to answer these questions. In this work, we propose a novel and scalable self-alignment method to utilize the LLM itself to enhance its response-ability to different types of unknown questions, being capable of not just refusing to answer but further proactively providing explanations to the unanswerability of unknown questions. Specifically, the Self-Align method first employ a two-stage class-aware self-augmentation approach to generate a large amount of unknown question-response data. Then we conduct disparity-driven self-curation to select qualified data for fine-tuning the LLM itself for aligning the responses to unknown questions as desired. Experimental results on two datasets across four types of unknown questions validate the superiority of the Self-Aligned method over existing baselines in terms of three types of task formulation.