# Geometry-Aware Hallucination Detection in Large Language Models

arXiv: https://arxiv.org/abs/2601.06196 · HTML: https://mlsanity.com/paper/2601.06196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 44 references that are in the map.
- First posted on arXiv 8 Jan 2026.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [What Makes Good In-Context Examples for GPT-3?](https://mlsanity.com/paper/2101.06804/) (2021)
- [A Survey on In-context Learning](https://mlsanity.com/paper/2301.00234/) (2022)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [FacTool: Factuality Detection in Generative AI -- A Tool Augmented Framework for Multi-Task and Multi-Domain Scenarios](https://mlsanity.com/paper/2307.13528/) (2023)
- [Demystifying Prompts in Language Models via Perplexity Estimation](https://mlsanity.com/paper/2212.04037/) (2022)
- [A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation](https://mlsanity.com/paper/2307.03987/) (2023)
- [Active Example Selection for In-Context Learning](https://mlsanity.com/paper/2211.04486/) (2022)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [Self-Adaptive In-Context Learning: An Information Compression Perspective for In-Context Example Selection and Ordering](https://mlsanity.com/paper/2212.10375/) (2022)
- [Large Language Models Are Latent Variable Models: Explaining and Finding Good Demonstrations for In-Context Learning](https://mlsanity.com/paper/2301.11916/) (2023)
- [Compositional Exemplars for In-context Learning](https://mlsanity.com/paper/2302.05698/) (2023)
- [Unified Demonstration Retriever for In-Context Learning](https://mlsanity.com/paper/2305.04320/) (2023)
- [Generating Benchmarks for Factuality Evaluation of Language Models](https://mlsanity.com/paper/2307.06908/) (2023)
- [A Comprehensive Survey of Hallucination in Large Language, Image, Video and Audio Foundation Models](https://mlsanity.com/paper/2405.09589/) (2024)
- [An Information-theoretic Approach to Prompt Engineering Without Ground Truth Labels](https://mlsanity.com/paper/2203.11364/) (2022)
- [In-Context Learning with Iterative Demonstration Selection](https://mlsanity.com/paper/2310.09881/) (2023)
- [Multilingual LLMs are Better Cross-lingual In-context Learners with Alignment](https://mlsanity.com/paper/2305.05940/) (2023)
- [Revisiting Demonstration Selection Strategies in In-Context Learning](https://mlsanity.com/paper/2401.12087/) (2024)
- [Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTS](https://mlsanity.com/paper/2411.18478/) (2024)
- [PURR: Efficiently Editing Language Model Hallucinations by Denoising Language Model Corruptions](https://mlsanity.com/paper/2305.14908/) (2023)
- [Large Language Model-Aware In-Context Learning for Code Generation](https://mlsanity.com/paper/2310.09748/) (2023)
- [Which Examples to Annotate for In-Context Learning? Towards Effective and Efficient Selection](https://mlsanity.com/paper/2310.20046/) (2023)
- [Zero-Resource Hallucination Prevention for Large Language Models](https://mlsanity.com/paper/2309.02654/) (2023)
- [MMHQA-ICL: Multimodal In-context Learning for Hybrid Question Answering over Text, Tables and Images](https://mlsanity.com/paper/2309.04790/) (2023)
- [FACTOID: FACtual enTailment fOr hallucInation Detection](https://mlsanity.com/paper/2403.19113/) (2024)
- [Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era](https://mlsanity.com/paper/2310.15816/) (2023)

## Abstract (arXiv)

Large language models (LLMs) frequently generate factually incorrect or unsupported content, commonly referred to as hallucinations. Prior work has explored decoding strategies, retrieval augmentation, and supervised fine-tuning for hallucination detection, while recent studies show that in-context learning (ICL) can substantially influence factual reliability. However, existing ICL demonstration selection methods often rely on surface-level similarity heuristics and exhibit limited robustness across tasks and models. We propose GA-ICL, a geometry-aware demonstration sampling framework for selecting in-context demonstrations that leverages latent representations extracted from frozen LLMs. By jointly modeling local manifold structure and class-aware prototype geometry, GA-ICL selects demonstrations based on their proximity to learned prototypes rather than lexical or embedding similarity alone. Across factual verification (FEVER) and hallucination detection (HaluEval) benchmarks, GA-ICL outperforms standard ICL selection baselines in the majority of evaluated settings, with particularly strong gains on dialogue and summarization tasks. The method remains robust under temperature perturbations and model variation, indicating improved stability compared to heuristic retrieval strategies. While lexical retrieval can remain competitive in certain question-answering regimes at smaller model scales, our results demonstrate that geometry-aware prototype selection provides a reliable and training-light approach for hallucination detection without modifying LLM parameters. Extended evaluations on Phi-14B and Qwen3-32B confirm that GA-ICL scales effectively to larger models, outperforming all compared baselines including on QA tasks where smaller models show boundary-condition limitations, offering a principled direction for improved ICL demonstration selection.