Epistemic Uncertainty Quantification

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.

Large language models (LLMs) have achieved great success, but their occasional content fabrication, or hallucination, limits their practical application. Hallucination arises because LLMs struggle to admit ignorance due to inadequate training on knowledge boundaries. We call it a limitation of LLMs that they can not accurately express their knowledge boundary, answering questions they know while admitting ignorance to questions they do not know. In this paper, we aim to teach LLMs to recognize and express their knowledge boundary, so they can reduce hallucinations caused by fabricating when they do not know. We propose CoKE, which first probes LLMs' knowledge boundary via internal confidence given a set of questions, and then leverages the probing results to elicit the expression of the knowledge boundary. Extensive experiments show CoKE helps LLMs express knowledge boundaries, answering known questions while declining unknown ones, significantly improving in-domain and out-of-domain performance.

In recent years, substantial advancements have been made in the development of large language models, achieving remarkable performance across diverse tasks. To evaluate the knowledge ability of language models, previous studies have proposed lots of benchmarks based on question-answering pairs. We argue that it is not reliable and comprehensive to evaluate language models with a fixed question or limited paraphrases as the query, since language models are sensitive to prompt. Therefore, we introduce a novel concept named knowledge boundary to encompass both prompt-agnostic and prompt-sensitive knowledge within language models. Knowledge boundary avoids prompt sensitivity in language model evaluations, rendering them more dependable and robust. To explore the knowledge boundary for a given model, we propose projected gradient descent method with semantic constraints, a new algorithm designed to identify the optimal prompt for each piece of knowledge. Experiments demonstrate a superior performance of our algorithm in computing the knowledge boundary compared to existing methods. Furthermore, we evaluate the ability of multiple language models in several domains with knowledge boundary.

Large language models (LLMs) have shown impressive prowess in solving a wide range of tasks with world knowledge. However, it remains unclear how well LLMs are able to perceive their factual knowledge boundaries, particularly under retrieval augmentation settings. In this study, we present the first analysis on the factual knowledge boundaries of LLMs and how retrieval augmentation affects LLMs on open-domain question answering (QA), with a bunch of important findings. Specifically, we focus on three research questions and analyze them by examining QA, priori judgement and posteriori judgement capabilities of LLMs. We show evidence that LLMs possess unwavering confidence in their knowledge and cannot handle the conflict between internal and external knowledge well. Furthermore, retrieval augmentation proves to be an effective approach in enhancing LLMs' awareness of knowledge boundaries. We further conduct thorough experiments to examine how different factors affect LLMs and propose a simple method to dynamically utilize supporting documents with our judgement strategy. Additionally, we find that the relevance between the supporting documents and the questions significantly impacts LLMs' QA and judgemental capabilities.

[arXiv 2025] "CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought"