Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914164082999296 |
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| author | Kiprono, Moses |
| author_facet | Kiprono, Moses |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation Kiprono, Moses Computation and Language Artificial Intelligence 68T05, 62F15, 68Q32, 94A12, 62P25 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. |
| title | Mathematical Analysis of Hallucination Dynamics in Large Language Models: Uncertainty Quantification, Advanced Decoding, and Principled Mitigation |
| topic | Computation and Language Artificial Intelligence 68T05, 62F15, 68Q32, 94A12, 62P25 |
| url | https://arxiv.org/abs/2511.15005 |