# Strong hallucinations from negation and how to fix them

arXiv: https://arxiv.org/abs/2402.10543 · HTML: https://mlsanity.com/paper/2402.10543/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Hallucination detection and mitigation, one of 17 directions in LLM reasoning.
- Builds on 39 of its 92 references that are in the map.
- First posted on arXiv 16 Feb 2024.

## Placed in

- LLM reasoning / [Hallucination detection and mitigation](https://mlsanity.com/lr/hallucination-detection-and-mitigation/)

## Builds on (most cited first, 30 of 39)

- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [PaLM-E: An Embodied Multimodal Language Model](https://mlsanity.com/paper/2303.03378/) (2023)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [VisualBERT: A Simple and Performant Baseline for Vision and Language](https://mlsanity.com/paper/1908.03557/) (2019)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [Cross-Task Generalization via Natural Language Crowdsourcing Instructions](https://mlsanity.com/paper/2104.08773/) (2021)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [What do you learn from context? Probing for sentence structure in contextualized word representations](https://mlsanity.com/paper/1905.06316/) (2019)
- [Entity-Based Knowledge Conflicts in Question Answering](https://mlsanity.com/paper/2109.05052/) (2021)
- [ToTTo: A Controlled Table-To-Text Generation Dataset](https://mlsanity.com/paper/2004.14373/) (2020)
- [Negated and Misprimed Probes for Pretrained Language Models: Birds Can Talk, But Cannot Fly](https://mlsanity.com/paper/1911.03343/) (2019)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [oLMpics -- On what Language Model Pre-training Captures](https://mlsanity.com/paper/1912.13283/) (2019)
- [Faithful to the Original: Fact Aware Neural Abstractive Summarization](https://mlsanity.com/paper/1711.04434/) (2017)
- [Evaluating Factuality in Generation with Dependency-level Entailment](https://mlsanity.com/paper/2010.05478/) (2020)
- [Handling Divergent Reference Texts when Evaluating Table-to-Text Generation](https://mlsanity.com/paper/1906.01081/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [Controlled Hallucinations: Learning to Generate Faithfully from Noisy Data](https://mlsanity.com/paper/2010.05873/) (2020)
- [The Factual Inconsistency Problem in Abstractive Text Summarization: A Survey](https://mlsanity.com/paper/2104.14839/) (2021)
- [Language models are not naysayers: An analysis of language models on negation benchmarks](https://mlsanity.com/paper/2306.08189/) (2023)
- [Understanding by Understanding Not: Modeling Negation in Language Models](https://mlsanity.com/paper/2105.03519/) (2021)
- [Knowledge Graph-Augmented Abstractive Summarization with Semantic-Driven Cloze Reward](https://mlsanity.com/paper/2005.01159/) (2020)
- [Tighter Bounds on the Expressivity of Transformer Encoders](https://mlsanity.com/paper/2301.10743/) (2023)

## Built on by (most cited first, 6 of 6)

- [Hallucination Detection in Large Language Models with Metamorphic Relations](https://mlsanity.com/paper/2502.15844/) (2025)
- [Investigating Symbolic Triggers of Hallucination in Gemma Models Across HaluEval and TruthfulQA](https://mlsanity.com/paper/2509.09715/) (2025)
- [On the Thinking-Language Modeling Gap in Large Language Models](https://mlsanity.com/paper/2505.12896/) (2025)
- [The Impact of Negated Text on Hallucination with Large Language Models](https://mlsanity.com/paper/2510.20375/) (2025)
- [Walking on the DARKSIDE](https://mlsanity.com/paper/2608.23370/) (2026)
- [Understanding as No-Arbitrage: Bounded Dutch Books as a Definition and Training Objective for Language Models](https://mlsanity.com/paper/2609.39341/) (2026)

## Abstract (arXiv)

Despite great performance on many tasks, language models (LMs) still struggle with reasoning, sometimes providing responses that cannot possibly be true because they stem from logical incoherence. We call such responses textitstrong hallucinations and prove that they follow from an LM's computation of its internal representations for logical operators and outputs from those representations. Focusing on negation, we provide a novel solution in which negation is treated not as another element of a latent representation, but as textitan operation over an LM's latent representations that constrains how they may evolve. We show that our approach improves model performance in cloze prompting and natural language inference tasks with negation without requiring training on sparse negative data.