# What do Geometric Hallucination Detection Metrics Actually Measure?

arXiv: https://arxiv.org/abs/2602.09158 · HTML: https://mlsanity.com/paper/2602.09158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 18 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [The FACTS Grounding Leaderboard: Benchmarking LLMs' Ability to Ground Responses to Long-Form Input](https://mlsanity.com/paper/2501.03200/) (2025)
- [Characterizing Truthfulness in Large Language Model Generations with Local Intrinsic Dimension](https://mlsanity.com/paper/2402.18048/) (2024)
- [On the Universal Truthfulness Hyperplane Inside LLMs](https://mlsanity.com/paper/2407.08582/) (2024)

## Abstract (arXiv)

Hallucination remains a barrier to deploying generative models in high-consequence applications. This is especially true in cases where external ground truth is not readily available to validate model outputs. This situation has motivated the study of geometric signals in the internal state of an LLM that are predictive of hallucination and require limited external knowledge. Given that there are a range of factors that can lead model output to be called a hallucination (e.g., irrelevance vs incoherence), in this paper we ask what specific properties of a hallucination these geometric statistics actually capture. To assess this, we generate a synthetic dataset which varies distinct properties of output associated with hallucination. This includes output correctness, confidence, relevance, coherence, and completeness. We find that different geometric statistics capture different types of hallucinations. Along the way we show that many existing geometric detection methods have substantial sensitivity to shifts in task domain (e.g., math questions vs. history questions). Motivated by this, we introduce a simple normalization method to mitigate the effect of domain shift on geometric statistics, leading to AUROC gains of +34 points in multi-domain settings.