从数学角度解析大模型幻觉机制，提出可量化、可抑制的改进方案。
Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation
- 用概率建模与贝叶斯估计分析错误如何逐词累积。
- 设计语义敏感与相位感知的不确定性度量指标。
- 提出对比解码、检索增强等实用方法，适合安全部署者参考。
大型语言模型虽具强大语言生成能力，但易产生看似合理实则错误的幻觉输出。本文构建一个数学基础框架，用于理解、测量和缓解此类幻觉。基于概率建模、信息论、三角信号分析与贝叶斯不确定性估计，我们分析了误差在自回归过程中的累积机制，提出包括语义感知与相位感知在内的改进不确定性度量，并发展出对比解码、检索增强校准、事实对齐及拒绝生成等有原则的缓解策略。该统一视角将校准、检索与对齐等近期进展有机整合，助力更安全可靠的LLM应用。
原文摘要 · Abstract (English)
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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