# Purging the Gray Zone: Latent-Geometric Denoising for Precise Knowledge Boundary Awareness

arXiv: https://arxiv.org/abs/2604.14324 · HTML: https://mlsanity.com/paper/2604.14324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Learning to Trust Your Feelings: Leveraging Self-awareness in LLMs for Hallucination Mitigation](https://mlsanity.com/paper/2401.15449/) (2024)
- [From Directions to Cones: Exploring Multidimensional Representations of Propositional Facts in LLMs](https://mlsanity.com/paper/2505.21800/) (2025)
- [The Curious Case of Factuality Finetuning: Models' Internal Beliefs Can Improve Factuality](https://mlsanity.com/paper/2507.08371/) (2025)
- [Teaching LLMs to Abstain via Fine-Grained Semantic Confidence Reward](https://mlsanity.com/paper/2510.24020/) (2025)

## Abstract (arXiv)

Large language models (LLMs) often exhibit hallucinations due to their inability to accurately perceive their own knowledge boundaries. Existing abstention fine-tuning methods typically partition datasets directly based on response accuracy, causing models to suffer from severe label noise near the decision boundaries and consequently exhibit high rates of abstentions or hallucinations. This paper adopts a latent space representation perspective, revealing a "gray zone" near the decision hyperplane where internal belief ambiguity constitutes the core performance bottleneck. Based on this insight, we propose the **GeoDe** (**Geo**metric **De**noising) framework for abstention fine-tuning. This method constructs a truth hyperplane using linear probes and performs "geometric denoising" by employing geometric distance as a confidence signal for abstention decisions. This approach filters out ambiguous boundary samples while retaining high-fidelity signals for fine-tuning. Experiments across multiple models (Llama3, Qwen3) and benchmark datasets (TriviaQA, NQ, SciQ, SimpleQA) demonstrate that GeoDe significantly enhances model truthfulness and demonstrates strong generalization in out-of-distribution (OOD) scenarios. Code is available at https://github.com/Notbesidemoon/GeoDe.