# Theoretical Foundations and Mitigation of Hallucination in Large Language Models

arXiv: https://arxiv.org/abs/2507.22915 · HTML: https://mlsanity.com/paper/2507.22915/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 20 Jul 2025.

## Builds on (most cited first, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Get To The Point: Summarization with Pointer-Generator Networks](https://mlsanity.com/paper/1704.04368/) (2017)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Evaluating the Factual Consistency of Abstractive Text Summarization](https://mlsanity.com/paper/1910.12840/) (2019)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Asking and Answering Questions to Evaluate the Factual Consistency of Summaries](https://mlsanity.com/paper/2004.04228/) (2020)
- [Six Challenges for Neural Machine Translation](https://mlsanity.com/paper/1706.03872/) (2017)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Understanding Factuality in Abstractive Summarization with FRANK: A Benchmark for Factuality Metrics](https://mlsanity.com/paper/2104.13346/) (2021)
- [Selective Question Answering under Domain Shift](https://mlsanity.com/paper/2006.09462/) (2020)
- [A Neural Conversational Model](https://mlsanity.com/paper/1506.05869/) (2015)
- [The Curious Case of Hallucinations in Neural Machine Translation](https://mlsanity.com/paper/2104.06683/) (2021)

## Built on by (most cited first, 3 of 3)

- [Explainable Knowledge Graph Retrieval-Augmented Generation (KG-RAG) with KG-SMILE](https://mlsanity.com/paper/2509.03626/) (2025)
- [Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing](https://mlsanity.com/paper/2602.00906/) (2026)
- [Do No Harm? Hallucination and Actor-Level Abuse in Web-Deployed Medical Large Language Models](https://mlsanity.com/paper/2605.20591/) (2026)

## Abstract (arXiv)

Hallucination in Large Language Models (LLMs) refers to the generation of content that is not faithful to the input or the real-world facts. This paper provides a rigorous treatment of hallucination in LLMs, including formal definitions and theoretical analyses. We distinguish between intrinsic and extrinsic hallucinations, and define a textithallucination risk for models. We derive bounds on this risk using learning-theoretic frameworks (PAC-Bayes and Rademacher complexity). We then survey detection strategies for hallucinations, such as token-level uncertainty estimation, confidence calibration, and attention alignment checks. On the mitigation side, we discuss approaches including retrieval-augmented generation, hallucination-aware fine-tuning, logit calibration, and the incorporation of fact-verification modules. We propose a unified detection and mitigation workflow, illustrated with a diagram, to integrate these strategies. Finally, we outline evaluation protocols for hallucination, recommending datasets, metrics, and experimental setups to quantify and reduce hallucinations. Our work lays a theoretical foundation and practical guidelines for addressing the crucial challenge of hallucination in LLMs.