大型语言模型中幻觉动态的数学分析：不确定性量化、高级解码与原则性缓解
Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation
AI总结：
针对大型语言模型（LLMs）的幻觉问题，本研究提出基于数学的统一框架，结合多学科方法分析错误复合机制、提出改进指标并开发多类缓解策略，连接多领域进展以提升LLMs的安全性与可靠性。
摘要：
大型语言模型（LLMs）是强大的语言引擎，但仍易产生幻觉：即听起来合理但事实错误或无依据的输出。本研究提出一个基于数学的框架，用于理解、测量和缓解这些幻觉。借助概率建模、信息论、三角信号分析和贝叶斯不确定性估计，我们分析了错误如何自回归复合，提出包括语义和相位感知变体在内的改进不确定性指标，并开发对比解码、检索增强基础、事实对齐和弃权（不执行）等原则性缓解策略。这一统一视角连接了校准、检索和对齐领域的最新进展，以支持更安全可靠的LLMs。
英文摘要：
Large Language Models (LLMs) are powerful linguistic engines but remain susceptible to hallucinations: plausible-sounding outputs that are factually incorrect or unsupported. In this work, we present a mathematically grounded framework to understand, measure, and mitigate these hallucinations. Drawing on probabilistic modeling, information theory, trigonometric signal analysis, and Bayesian uncertainty estimation, we analyze how errors compound autoregressively, propose refined uncertainty metrics, including semantic and phase-aware variants, and develop principled mitigation strategies such as contrastive decoding, retrieval-augmented grounding, factual alignment, and abstention. This unified lens connects recent advances in calibration, retrieval, and alignment to support safer and more reliable LLMs.
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