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

arXiv 2511.15005 ↗First posted 19 Nov 2025cs.CL cs.AIcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 12 of its 21 references that are in the map. First posted on arXiv 19 Nov 2025.

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12 of 21 references.

References · 12

  1. 2023Sources of Hallucination by Large Language Models on Inference Taskscited by 169
  2. 2024Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similaritiescited by 159
  3. 2024Self-Alignment for Factuality: Mitigating Hallucinations in LLMs via Self-Evaluationcited by 80
  4. 2024FLAME: Factuality-Aware Alignment for Large Language Modelscited by 47
  5. 2024Learning to Trust Your Feelings: Leveraging Self-awareness in LLMs for Hallucination Mitigationcited by 44
  6. 2023Ever: Mitigating Hallucination in Large Language Models through Real-Time Verification and Rectificationcited by 38
  7. 2024FactAlign: Long-form Factuality Alignment of Large Language Modelscited by 12
  8. 2024Honest AI: Fine-Tuning "Small" Language Models to Say "I Don't Know", and Reducing Hallucination in RAGcited by 6
  9. 2023BTR: Binary Token Representations for Efficient Retrieval Augmented Language Modelscited by 5
  10. 2024RAC: Efficient LLM Factuality Correction with Retrieval Augmentationcited by 5
  11. 2025Hybrid Retrieval for Hallucination Mitigation in Large Language Models: A Comparative Analysiscited by 5
  12. 2025REFIND at SemEval-2025 Task 3: Retrieval-Augmented Factuality Hallucination Detection in Large Language Modelscited by 3

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  1. 2025Theoretical Foundations and Mitigation of Hallucination in Large Language Models
  2. 2025Revisiting Hallucination Detection with Effective Rank-based Uncertainty
  3. 2025Confidence-Aware Routing for Large Language Model Reliability Enhancement: A Multi-Signal Approach to Pre-Generation Hallucination Mitigation
  4. 2023A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions
  5. 2025OnionEval: An Unified Evaluation of Fact-conflicting Hallucination for Small-Large Language Models
  6. 2025HAVE: Head-Adaptive Gating and ValuE Calibration for Hallucination Mitigation in Large Language Models
  7. 2024VL-Uncertainty: Detecting Hallucination in Large Vision-Language Model via Uncertainty Estimation
  8. 2026Lyapunov Probes for Hallucination Detection in Large Foundation Models