The paper introduces Kernel Language Entropy (KLE), a novel method for uncertainty estimation in Large Language Models (LLMs). KLE addresses the challenge of capturing semantic uncertainty, which is crucial for improving the reliability and trustworthiness of LLMs by detecting factually incorrect responses, known as hallucinations. Unlike previous methods that focus on lexical or syntactic variations, KLE uses positive semidefinite unit trace kernels to encode semantic similarities between LLM outputs and quantifies uncertainty using von Neumann entropy. This approach allows KLE to consider pairwise semantic dependencies between answers or semantic clusters, providing more fine-grained uncertainty estimates compared to methods based on hard clustering of answers. The authors theoretically prove that KLE generalizes the previous state-of-the-art method, semantic entropy (SE), and empirically demonstrate its superior performance across multiple natural language generation datasets and LLM architectures. KLE is designed to work both in white-box and black-box settings, making it applicable to a wide range of practical scenarios. The paper also discusses the design choices for KLE, including the use of graph kernels and weight functions, and provides a detailed comparison with existing methods, showing that KLE outperforms them in terms of uncertainty estimation accuracy. - **Kernel Language Entropy (KLE)**: A novel method for uncertainty estimation in LLMs that captures semantic similarities between outputs. - **Theoretical Proofs**: KLE generalizes semantic entropy and is more expressive in certain cases. - **Empirical Results**: KLE achieves state-of-the-art performance across various datasets and LLM architectures. - **Design Choices**: Practical approaches for constructing semantic kernels and selecting hyperparameters. - **Comparative Analysis**: KLE outperforms existing methods in uncertainty estimation and model accuracy. - **Safety and Reliability**: KLE can improve the safety and reliability of LLMs by detecting hallucinations. - **Practical Applications**: KLE is applicable to a wide range of practical scenarios, including high-stakes applications. - **Future Work**: Further research could explore other types of semantic kernels and their applications in diverse LLM tasks.The paper introduces Kernel Language Entropy (KLE), a novel method for uncertainty estimation in Large Language Models (LLMs). KLE addresses the challenge of capturing semantic uncertainty, which is crucial for improving the reliability and trustworthiness of LLMs by detecting factually incorrect responses, known as hallucinations. Unlike previous methods that focus on lexical or syntactic variations, KLE uses positive semidefinite unit trace kernels to encode semantic similarities between LLM outputs and quantifies uncertainty using von Neumann entropy. This approach allows KLE to consider pairwise semantic dependencies between answers or semantic clusters, providing more fine-grained uncertainty estimates compared to methods based on hard clustering of answers. The authors theoretically prove that KLE generalizes the previous state-of-the-art method, semantic entropy (SE), and empirically demonstrate its superior performance across multiple natural language generation datasets and LLM architectures. KLE is designed to work both in white-box and black-box settings, making it applicable to a wide range of practical scenarios. The paper also discusses the design choices for KLE, including the use of graph kernels and weight functions, and provides a detailed comparison with existing methods, showing that KLE outperforms them in terms of uncertainty estimation accuracy. - **Kernel Language Entropy (KLE)**: A novel method for uncertainty estimation in LLMs that captures semantic similarities between outputs. - **Theoretical Proofs**: KLE generalizes semantic entropy and is more expressive in certain cases. - **Empirical Results**: KLE achieves state-of-the-art performance across various datasets and LLM architectures. - **Design Choices**: Practical approaches for constructing semantic kernels and selecting hyperparameters. - **Comparative Analysis**: KLE outperforms existing methods in uncertainty estimation and model accuracy. - **Safety and Reliability**: KLE can improve the safety and reliability of LLMs by detecting hallucinations. - **Practical Applications**: KLE is applicable to a wide range of practical scenarios, including high-stakes applications. - **Future Work**: Further research could explore other types of semantic kernels and their applications in diverse LLM tasks.