# Why LLMs Hallucinate, and How to Get (Evidential) Closure: Perceptual, Intensional, and Extensional Learning for Faithful Natural Language Generation

arXiv: https://arxiv.org/abs/2310.15355 · HTML: https://mlsanity.com/paper/2310.15355/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 62 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [Reading Wikipedia to Answer Open-Domain Questions](https://mlsanity.com/paper/1704.00051/) (2017)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Data and its (dis)contents: A survey of dataset development and use in machine learning research](https://mlsanity.com/paper/2012.05345/) (2020)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [Sources of Hallucination by Large Language Models on Inference Tasks](https://mlsanity.com/paper/2305.14552/) (2023)
- [Contrastive Behavioral Similarity Embeddings for Generalization in Reinforcement Learning](https://mlsanity.com/paper/2101.05265/) (2021)
- [Domain Robustness in Neural Machine Translation](https://mlsanity.com/paper/1911.03109/) (2019)
- [Pre-Trained Image Encoder for Generalizable Visual Reinforcement Learning](https://mlsanity.com/paper/2212.08860/) (2022)
- [Grounded Language Learning Fast and Slow](https://mlsanity.com/paper/2009.01719/) (2020)
- [Multimodal LLMs for health grounded in individual-specific data](https://mlsanity.com/paper/2307.09018/) (2023)
- [Evidentiality-guided Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2112.08688/) (2021)
- [HalOmi: A Manually Annotated Benchmark for Multilingual Hallucination and Omission Detection in Machine Translation](https://mlsanity.com/paper/2305.11746/) (2023)
- [Fluency Over Adequacy: A Pilot Study in Measuring User Trust in Imperfect MT](https://mlsanity.com/paper/1802.06041/) (2018)
- [Towards Tracing Factual Knowledge in Language Models Back to the Training Data](https://mlsanity.com/paper/2205.11482/) (2022)
- [Robustifying Multi-hop QA through Pseudo-Evidentiality Training](https://mlsanity.com/paper/2107.03242/) (2021)
- [Contrastive Representation Learning for Exemplar-Guided Paraphrase Generation](https://mlsanity.com/paper/2109.01484/) (2021)
- [Principled Paraphrase Generation with Parallel Corpora](https://mlsanity.com/paper/2205.12213/) (2022)

## Built on by (most cited first, 13 of 13)

- [Prompting open-source and commercial language models for grammatical error correction of English learner text](https://mlsanity.com/paper/2401.07702/) (2024)
- [An Audit on the Perspectives and Challenges of Hallucinations in NLP](https://mlsanity.com/paper/2404.07461/) (2024)
- [Look Within, Why LLMs Hallucinate: A Causal Perspective](https://mlsanity.com/paper/2407.10153/) (2024)
- [Loki's Dance of Illusions: A Comprehensive Survey of Hallucination in Large Language Models](https://mlsanity.com/paper/2507.02870/) (2025)
- [HGOT: Hierarchical Graph of Thoughts for Retrieval-Augmented In-Context Learning in Factuality Evaluation](https://mlsanity.com/paper/2402.09390/) (2024)
- [1.5-Pints Technical Report: Pretraining in Days, Not Months -- Your Language Model Thrives on Quality Data](https://mlsanity.com/paper/2408.03506/) (2024)
- [Evaluating and Improving Robustness in Large Language Models: A Survey and Future Directions](https://mlsanity.com/paper/2506.11111/) (2025)
- [Deontological Keyword Bias: The Impact of Modal Expressions on Normative Judgments of Language Models](https://mlsanity.com/paper/2506.11068/) (2025)
- [Triple-Encoders: Representations That Fire Together, Wire Together](https://mlsanity.com/paper/2402.12332/) (2024)
- [Linguistically Conditioned Semantic Textual Similarity](https://mlsanity.com/paper/2406.03673/) (2024)
- [Context Does Matter: Implications for Crowdsourced Evaluation Labels in Task-Oriented Dialogue Systems](https://mlsanity.com/paper/2404.09980/) (2024)
- [Exploring Causal Effect of Social Bias on Faithfulness Hallucinations in Large Language Models](https://mlsanity.com/paper/2508.07753/) (2025)
- [Language Models Can Resolve Reference Compositionally, But It's Not Their Native Strength: The Case of the Personal Relation Task](https://mlsanity.com/paper/2605.31480/) (2026)

## Abstract (arXiv)

We show that LLMs hallucinate because their output is not constrained to be synonymous with claims for which they have evidence: a condition that we call evidential closure. Information about the truth or falsity of sentences is not statistically identified in the standard neural probabilistic language model setup, and so cannot be conditioned on to generate new strings. We then show how to constrain LLMs to produce output that does satisfy evidential closure. A multimodal LLM must learn about the external world (perceptual learning); it must learn a mapping from strings to states of the world (extensional learning); and, to achieve fluency when generalizing beyond a body of evidence, it must learn mappings from strings to their synonyms (intensional learning). The output of a unimodal LLM must be synonymous with strings in a validated evidence set. Finally, we present a heuristic procedure, Learn-Babble-Prune, that yields faithful output from an LLM by rejecting output that is not synonymous with claims for which the LLM has evidence.