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

arXiv: https://arxiv.org/abs/2511.15005 · HTML: https://mlsanity.com/paper/2511.15005/

## 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.

## Builds on (most cited first, 12 of 12)

- [Sources of Hallucination by Large Language Models on Inference Tasks](https://mlsanity.com/paper/2305.14552/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Self-Alignment for Factuality: Mitigating Hallucinations in LLMs via Self-Evaluation](https://mlsanity.com/paper/2402.09267/) (2024)
- [FLAME: Factuality-Aware Alignment for Large Language Models](https://mlsanity.com/paper/2405.01525/) (2024)
- [Learning to Trust Your Feelings: Leveraging Self-awareness in LLMs for Hallucination Mitigation](https://mlsanity.com/paper/2401.15449/) (2024)
- [Ever: Mitigating Hallucination in Large Language Models through Real-Time Verification and Rectification](https://mlsanity.com/paper/2311.09114/) (2023)
- [FactAlign: Long-form Factuality Alignment of Large Language Models](https://mlsanity.com/paper/2410.01691/) (2024)
- [Honest AI: Fine-Tuning "Small" Language Models to Say "I Don't Know", and Reducing Hallucination in RAG](https://mlsanity.com/paper/2410.09699/) (2024)
- [BTR: Binary Token Representations for Efficient Retrieval Augmented Language Models](https://mlsanity.com/paper/2310.01329/) (2023)
- [RAC: Efficient LLM Factuality Correction with Retrieval Augmentation](https://mlsanity.com/paper/2410.15667/) (2024)
- [Hybrid Retrieval for Hallucination Mitigation in Large Language Models: A Comparative Analysis](https://mlsanity.com/paper/2504.05324/) (2025)
- [REFIND at SemEval-2025 Task 3: Retrieval-Augmented Factuality Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2502.13622/) (2025)

## 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.