Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation

2025/11/19 by Kiprono, Moses
Computer Science · Neuroscience · #62F15 #62P25 #68Q32 #68T05 #94A12 #Artificial Intelligence (cs.AI) #Computation and Language (cs.CL) #FOS: Computer and information sciences #Natural Language Processing Techniques #Neurobiology of Language and Bilingualism #Topic Modeling

paper · doi:10.48550/arxiv.2511.15005

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Hybrid Retrieval for Hallucination Mitigation in Large Language Models: A Comparative Analysis
• REFIND at SemEval-2025 Task 3: Retrieval-Augmented Factuality Hallucination Detection in Large Language Models
• RAC: Efficient LLM Factuality Correction with Retrieval Augmentation
• FactAlign: Long-form Factuality Alignment of Large Language Models
• Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities
• FLAME: Factuality-Aware Alignment for Large Language Models
• Learning to Trust Your Feelings: Leveraging Self-awareness in LLMs for Hallucination Mitigation
• Ever: Mitigating Hallucination in Large Language Models through Real-Time Verification and Rectification
• BTR: Binary Token Representations for Efficient Retrieval Augmented Language Models
• Sources of Hallucination by Large Language Models on Inference Tasks
• Rowen: Adaptive Retrieval-Augmented Generation for Hallucination Mitigation in LLMs

Related

• Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions
• Theoretical Foundations and Mitigation of Hallucination in Large Language Models
• Improving Uncertainty Estimation through Semantically Diverse Language Generation
• Revisiting Hallucination Detection with Effective Rank-based Uncertainty
• Uncertainty Quantification for Language Models: A Suite of Black-Box, White-Box, LLM Judge, and Ensemble Scorers