# A Geometric Taxonomy of Hallucinations in LLMs

arXiv: https://arxiv.org/abs/2602.13224 · HTML: https://mlsanity.com/paper/2602.13224/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 64 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 30 of 41)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Towards General Text Embeddings with Multi-stage Contrastive Learning](https://mlsanity.com/paper/2308.03281/) (2023)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Evaluating the Factual Consistency of Abstractive Text Summarization](https://mlsanity.com/paper/1910.12840/) (2019)
- [C-Pack: Packed Resources For General Chinese Embeddings](https://mlsanity.com/paper/2309.07597/) (2023)
- [Sentence-T5: Scalable Sentence Encoders from Pre-trained Text-to-Text Models](https://mlsanity.com/paper/2108.08877/) (2021)
- [SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization](https://mlsanity.com/paper/2111.09525/) (2021)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [RAGTruth: A Hallucination Corpus for Developing Trustworthy Retrieval-Augmented Language Models](https://mlsanity.com/paper/2401.00396/) (2023)
- [QAFactEval: Improved QA-Based Factual Consistency Evaluation for Summarization](https://mlsanity.com/paper/2112.08542/) (2021)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Emergent Misalignment: Narrow finetuning can produce broadly misaligned LLMs](https://mlsanity.com/paper/2502.17424/) (2025)
- [The Curious Case of Hallucinations in Neural Machine Translation](https://mlsanity.com/paper/2104.06683/) (2021)

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

- [Text Corpora as Concept Fields: Black-Box Hallucination and Novelty Measurement](https://mlsanity.com/paper/2605.05103/) (2026)

## Abstract (arXiv)

Hallucinations in deployed language models can have real consequences for downstream decisions in domains such as healthcare, legal, and financial services. In production, detection has to run on what the deployed system can see: the query, the response, and often a source document. White-box access to model internals and multi-sample querying are not generally available behind a third-party API. Within this setting - black-box, single-pass, only question/answer available - the dominant baseline is NLI, which returns a value but no diagnosis when it fails. We argue that operating directly on the geometry of the embedding space provides detection methods whose successes and failures are interpretable as structural properties of contrastive sentence-encoder training citepwang2020understanding. The contribution is: given an operationally-motivated taxonomy, geometry predicts which types of hallucination are detectable and which are not - and the predictions hold. We propose three operational types organized by the relation of the response embedding to the plausibility region of grounded responses on the unit hypersphere, and derive from the alignment objective a prediction for each: (1)query-proximate unfaithfulness is detectable by an angular ratio; (2)confabulation outside the plausibility region produces a directional signature that outperforms NLI on expert-annotated error; (3)factual errors sharing vocabulary and frame with correct answers are not separable by angular geometry. To validate on content resembling deployment, we built a 212-pair human-confabulated dataset across nine domains using provoked confabulation.