Prompt-Response Semantic Divergence Metrics for Faithfulness Hallucination and Misalignment Detection in Large Language Models

• URL: http://arxiv.org/abs/2508.10192v1
• Date: Wed, 13 Aug 2025 20:55:26 GMT
• Title: Prompt-Response Semantic Divergence Metrics for Faithfulness Hallucination and Misalignment Detection in Large Language Models
• Authors: Igor Halperin,
• Abstract summary: This paper introduces Semantic Divergence Metrics (SDM), a novel framework for detecting Faithfulness Hallucinations.<n>A heatmap of topic co-occurances between prompts and responses can be viewed as a quantified two-dimensional visualization of the user-machine dialogue.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The proliferation of Large Language Models (LLMs) is challenged by hallucinations, critical failure modes where models generate non-factual, nonsensical or unfaithful text. This paper introduces Semantic Divergence Metrics (SDM), a novel lightweight framework for detecting Faithfulness Hallucinations -- events of severe deviations of LLMs responses from input contexts. We focus on a specific implementation of these LLM errors, {confabulations, defined as responses that are arbitrary and semantically misaligned with the user's query. Existing methods like Semantic Entropy test for arbitrariness by measuring the diversity of answers to a single, fixed prompt. Our SDM framework improves upon this by being more prompt-aware: we test for a deeper form of arbitrariness by measuring response consistency not only across multiple answers but also across multiple, semantically-equivalent paraphrases of the original prompt. Methodologically, our approach uses joint clustering on sentence embeddings to create a shared topic space for prompts and answers. A heatmap of topic co-occurances between prompts and responses can be viewed as a quantified two-dimensional visualization of the user-machine dialogue. We then compute a suite of information-theoretic metrics to measure the semantic divergence between prompts and responses. Our practical score, $\mathcal{S}_H$, combines the Jensen-Shannon divergence and Wasserstein distance to quantify this divergence, with a high score indicating a Faithfulness hallucination. Furthermore, we identify the KL divergence KL(Answer $||$ Prompt) as a powerful indicator of \textbf{Semantic Exploration}, a key signal for distinguishing different generative behaviors. These metrics are further combined into the Semantic Box, a diagnostic framework for classifying LLM response types, including the dangerous, confident confabulation.

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