# Embedding Graph Kernel Entropy (EGKE): Fine-grained Hallucination Detection for LLMs from Embeddings

arXiv: https://arxiv.org/abs/2610.14214 · HTML: https://mlsanity.com/paper/2610.14214/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 18 of 18)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization](https://mlsanity.com/paper/2111.09525/) (2021)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Detecting Hallucinations in Large Language Model Generation: A Token Probability Approach](https://mlsanity.com/paper/2405.19648/) (2024)
- [Chain of Natural Language Inference for Reducing Large Language Model Ungrounded Hallucinations](https://mlsanity.com/paper/2310.03951/) (2023)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)
- [CLATTER: Comprehensive Entailment Reasoning for Hallucination Detection](https://mlsanity.com/paper/2506.05243/) (2025)
- [Semantic Uncertainty Quantification of Hallucinations in LLMs: A Quantum Tensor Network Based Method](https://mlsanity.com/paper/2601.20026/) (2026)

## Abstract (arXiv)

Hallucination detection is critical for ensuring the reliability of Large Language Models (LLMs) in real-world deployments. While recent works, such as Semantic Entropy (SE) and Kernel Language Entropy (KLE), identify hallucinations by measuring semantic disagreement across multiple generated responses using Natural Language Inference (NLI) models, these methods depend on separately loaded NLI classifiers to estimate pairwise semantic similarity, introducing significant computational overhead. We propose Embedding Graph Kernel Entropy (EGKE), a variant of Kernel Language Entropy (KLE) that replaces its NLI-derived semantic graph with a Radial Basis Function (RBF) kernel applied to dense sentence embeddings generated by a BGE embedding model, while retaining KLE's graph Laplacian, heat kernel, and von Neumann entropy formulation unchanged. By computing similarities directly in a continuous embedding space, the proposed method provides a symmetric and computationally efficient alternative to NLI-based semantic comparison. We evaluate our approach across 30 experimental setups (covering multiple question-answer datasets and open-weight LLM families) using both AUROC and AUARC, and demonstrate that this RBF-based method achieves competitive hallucination detection performance against state-of-the-art methods.