# HARP: Hallucination Detection via Reasoning Subspace Projection

arXiv: https://arxiv.org/abs/2509.11536 · HTML: https://mlsanity.com/paper/2509.11536/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Hallucination detection and mitigation, one of 17 directions in LLM reasoning.
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Placed in

- LLM reasoning / [Hallucination detection and mitigation](https://mlsanity.com/lr/hallucination-detection-and-mitigation/)

## Builds on (most cited first, 23 of 23)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [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)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [TyDi QA: A Benchmark for Information-Seeking Question Answering in Typologically Diverse Languages](https://mlsanity.com/paper/2003.05002/) (2020)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [Truth is Universal: Robust Detection of Lies in LLMs](https://mlsanity.com/paper/2407.12831/) (2024)
- [How Large Language Models Encode Context Knowledge? A Layer-Wise Probing Study](https://mlsanity.com/paper/2402.16061/) (2024)
- [Steer LLM Latents for Hallucination Detection](https://mlsanity.com/paper/2503.01917/) (2025)
- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Interpreting Key Mechanisms of Factual Recall in Transformer-Based Language Models](https://mlsanity.com/paper/2403.19521/) (2024)
- [Decoding Probing: Revealing Internal Linguistic Structures in Neural Language Models using Minimal Pairs](https://mlsanity.com/paper/2403.17299/) (2024)

## Built on by (most cited first, 5 of 5)

- [HalluSAE: Detecting Hallucinations in Large Language Models via Sparse Auto-Encoders](https://mlsanity.com/paper/2604.16430/) (2026)
- [Sparse Reward Subsystem in Large Language Models](https://mlsanity.com/paper/2602.00986/) (2026)
- [AURORA: Asymmetry and Update-Induced Rotation for Robust Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2606.29545/) (2026)
- [ProjAgent: Procedural Similarity Retrieval for Repository-Level Code Generation](https://mlsanity.com/paper/2607.08691/) (2026)
- [Hallucination Across the Reasoning Lifecycle: Interface Visibility, Causal Evidence, and Release Control in Large Reasoning Models](https://mlsanity.com/paper/2610.05472/) (2026)

## Abstract (arXiv)

Hallucinations in Large Language Models (LLMs) pose a major barrier to their reliable use in critical decision-making. Although existing hallucination detection methods have improved accuracy, they still struggle with disentangling semantic and reasoning information and maintaining robustness. To address these challenges, we propose HARP (Hallucination detection via reasoning subspace projection), a novel hallucination detection framework. HARP establishes that the hidden state space of LLMs can be decomposed into a direct sum of a semantic subspace and a reasoning subspace, where the former encodes linguistic expression and the latter captures internal reasoning processes. Moreover, we demonstrate that the Unembedding layer can disentangle these subspaces, and by applying Singular Value Decomposition (SVD) to its parameters, the basis vectors spanning the semantic and reasoning subspaces are obtained. Finally, HARP projects hidden states onto the basis vectors of the reasoning subspace, and the resulting projections are then used as input features for hallucination detection in LLMs. By using these projections, HARP reduces the dimension of the feature to approximately 5% of the original, filters out most noise, and achieves enhanced robustness. Experiments across multiple datasets show that HARP achieves state-of-the-art hallucination detection performance; in particular, it achieves an AUROC of 92.8% on TriviaQA, outperforming the previous best method by 7.5%.