# D2HScore: Reasoning-Aware Hallucination Detection via Semantic Breadth and Depth Analysis in LLMs

arXiv: https://arxiv.org/abs/2509.11569 · HTML: https://mlsanity.com/paper/2509.11569/

## 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 21 of its 31 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, 21 of 21)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (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)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [The Belebele Benchmark: a Parallel Reading Comprehension Dataset in 122 Language Variants](https://mlsanity.com/paper/2308.16884/) (2023)
- [Prompting GPT-3 To Be Reliable](https://mlsanity.com/paper/2210.09150/) (2022)
- [WritingBench: A Comprehensive Benchmark for Generative Writing](https://mlsanity.com/paper/2503.05244/) (2025)
- [SAC3: Reliable Hallucination Detection in Black-Box Language Models via Semantic-aware Cross-check Consistency](https://mlsanity.com/paper/2311.01740/) (2023)
- [Unsupervised Real-Time Hallucination Detection based on the Internal States of Large Language Models](https://mlsanity.com/paper/2403.06448/) (2024)
- [Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation](https://mlsanity.com/paper/2410.13640/) (2024)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [Small Agent Can Also Rock! Empowering Small Language Models as Hallucination Detector](https://mlsanity.com/paper/2406.11277/) (2024)

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

- [Seeing but Not Thinking: Routing Distraction in Multimodal Mixture-of-Experts](https://mlsanity.com/paper/2604.08541/) (2026)
- [HalluGuard: Demystifying Data-Driven and Reasoning-Driven Hallucinations in LLMs](https://mlsanity.com/paper/2601.18753/) (2026)
- [Does Bielik Know What It Doesn't Know? Activation Dispersion Separates Entity Familiarity from Factual Reliability Across Model Scale](https://mlsanity.com/paper/2607.07670/) (2026)
- [Useful Features, Backward Scores: OOD in Language-Model Trajectories](https://mlsanity.com/paper/2605.00269/) (2026)
- [Graded Entity-Familiarity Readouts in Language Models: Polish Adaptation, Cross-Language Robustness, and Refusal Steering](https://mlsanity.com/paper/2607.13568/) (2026)

## Abstract (arXiv)

Although large Language Models (LLMs) have achieved remarkable success, their practical application is often hindered by the generation of non-factual content, which is called "hallucination". Ensuring the reliability of LLMs' outputs is a critical challenge, particularly in high-stakes domains such as finance, security, and healthcare. In this work, we revisit hallucination detection from the perspective of model architecture and generation dynamics. Leveraging the multi-layer structure and autoregressive decoding process of LLMs, we decompose hallucination signals into two complementary dimensions: the semantic breadth of token representations within each layer, and the semantic depth of core concepts as they evolve across layers. Based on this insight, we propose D2HScore (Dispersion and Drift-based Hallucination Score), a training-free and label-free framework that jointly measures: (1) Intra-Layer Dispersion, which quantifies the semantic diversity of token representations within each layer; and (2) Inter-Layer Drift, which tracks the progressive transformation of key token representations across layers. To ensure drift reflects the evolution of meaningful semantics rather than noisy or redundant tokens, we guide token selection using attention signals. By capturing both the horizontal and vertical dynamics of representation during inference, D2HScore provides an interpretable and lightweight proxy for hallucination detection. Extensive experiments across five open-source LLMs and five widely used benchmarks demonstrate that D2HScore consistently outperforms existing training-free baselines.