# Relational Linearity is a Predictor of Hallucinations

arXiv: https://arxiv.org/abs/2601.11429 · HTML: https://mlsanity.com/paper/2601.11429/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 16 Jan 2026.

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

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Do I Know This Entity? Knowledge Awareness and Hallucinations in Language Models](https://mlsanity.com/paper/2411.14257/) (2024)
- [On Linear Representations and Pretraining Data Frequency in Language Models](https://mlsanity.com/paper/2504.12459/) (2025)
- [Truth-value judgment in language models: 'truth directions' are context sensitive](https://mlsanity.com/paper/2404.18865/) (2024)
- [The Structure of Relation Decoding Linear Operators in Large Language Models](https://mlsanity.com/paper/2510.26543/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Survey on the Linear Representation Hypothesis](https://mlsanity.com/paper/2609.22695/) (2026)

## Abstract (arXiv)

Hallucination is a central failure mode of language models (LMs). We focus on hallucinations in response to questions like: "Which instrument did Glenn Gould play?", but we ask these questions for synthetic entities designed to be unknown to the model. We find that LMs like Gemma-7B-IT frequently hallucinate, i.e., they have difficulty recognizing that the hallucinated fact is not part of their knowledge. Based on the idea of linear relational embeddings, we put forward the following hypothesis. (i) Due to the abstract scheme that is used to represent them, LMs can easily produce plausible objects for non-existing subjects of linear relations, which can lead to hallucinations. (ii) For nonlinear relations, this mechanism for producing an object is not available and so a hallucination is easier to avoid. To test this hypothesis, we create SynthHal, a synthetic unknown-entity benchmark for 15 relations. We find that across four instruction-tuned models, relational linearity is a strong predictor of models hallucinating an object for an unknown subject vs refusing to give an answer, with correlations r ∈ [.58, .84]. While this is not direct evidence for the hypothesized causal mechanism, it is suggestive and opens up a new line of inquiry into understanding LM hallucinations.