Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation
This addresses the issue of unreliable outputs in LLMs for users requiring factual accuracy, though it appears incremental by connecting existing advances.
The paper tackles the problem of hallucinations in large language models by developing a mathematically grounded framework to understand, measure, and mitigate them, resulting in proposed strategies like contrastive decoding and retrieval-augmented grounding for safer and more reliable models.
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.