# A Geometric Analysis of Small-sized Language Model Hallucinations

arXiv: https://arxiv.org/abs/2602.14778 · HTML: https://mlsanity.com/paper/2602.14778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical and scientific domain agents, one of 16 directions in LLM agents and tool use.
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Placed in

- LLM agents and tool use / [Medical and scientific domain agents](https://mlsanity.com/agents/medical-and-scientific-domain-agents/)

## Builds on (most cited first, 30 of 31)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [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)
- [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)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [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)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Hallucination is Inevitable: An Innate Limitation of Large Language Models](https://mlsanity.com/paper/2401.11817/) (2024)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [TrustLLM: Trustworthiness in Large Language Models](https://mlsanity.com/paper/2401.05561/) (2024)
- [Small Language Models are the Future of Agentic AI](https://mlsanity.com/paper/2506.02153/) (2025)
- [A Comprehensive Survey of Hallucination Mitigation Techniques in Large Language Models](https://mlsanity.com/paper/2401.01313/) (2024)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [A Survey on LLM-Generated Text Detection: Necessity, Methods, and Future Directions](https://mlsanity.com/paper/2310.14724/) (2023)
- [A Comprehensive Survey of Hallucination in Large Language, Image, Video and Audio Foundation Models](https://mlsanity.com/paper/2405.09589/) (2024)
- [Unsupervised Real-Time Hallucination Detection based on the Internal States of Large Language Models](https://mlsanity.com/paper/2403.06448/) (2024)
- [The FACTS Grounding Leaderboard: Benchmarking LLMs' Ability to Ground Responses to Long-Form Input](https://mlsanity.com/paper/2501.03200/) (2025)
- [Uncertainty Quantification for In-Context Learning of Large Language Models](https://mlsanity.com/paper/2402.10189/) (2024)
- [Hallucination Detection: Robustly Discerning Reliable Answers in Large Language Models](https://mlsanity.com/paper/2407.04121/) (2024)
- [FactBench: A Dynamic Benchmark for In-the-Wild Language Model Factuality Evaluation](https://mlsanity.com/paper/2410.22257/) (2024)
- [HEMM: Holistic Evaluation of Multimodal Foundation Models](https://mlsanity.com/paper/2407.03418/) (2024)
- [Robust Hallucination Detection in LLMs via Adaptive Token Selection](https://mlsanity.com/paper/2504.07863/) (2025)

## Built on by (most cited first, 2 of 2)

- [Contextualized Counterspeech Can Be More Persuasive Than Generic Counterspeech](https://mlsanity.com/paper/2607.26236/) (2026)
- [RAIM: Robust Aggregation of Inexpensive Models for Hallucination Detection](https://mlsanity.com/paper/2609.39229/) (2026)

## Abstract (arXiv)

Hallucinations -- plausible but factually incorrect responses -- pose a major challenge to the reliability of Large Language Models (LLMs), especially in multi-step or agentic settings. Existing work largely frames hallucinations as a consequence of missing knowledge; we show instead that, even when the relevant factual knowledge is present, models still produce hallucinated answers, pointing to retrieval instability rather than knowledge gaps. Building on this observation, we introduce APORIA (Aggregate Prompt-wise Observation Retrieving Instability via Asymmetry -- the state of puzzlement-in-contradiction that hallucinations embody), a geometric framework that studies repeated responses to the same prompt in sentence-embedding space. Our central hypothesis is that genuine responses cluster more tightly than hallucinated ones; we empirically validate this and show that, after Fisher projection, the two response classes become consistently separable. We leverage this asymmetry in geometry via APORIA-LP, an efficient label-propagation method that classifies large collections of responses from as few as 30--50 annotations, achieving F1 scores above 90% across ten small-sized LLMs. To support further research, we release SOCRATES-300K, a fully labelled dataset of 300,000 responses, together with the code for both dataset generation and result reproduction. Our key finding -- framing hallucinations from a geometric perspective in the embedding space -- complements traditional knowledge-centric and single-response evaluation paradigms, paving the way for further research.