D-Score: A Spectral Hidden-State Signal for Hallucination Detection in Large Language Models

2026-07-27

AI Summary

This work addresses the pervasive issue of hallucinations in large language models—where outputs appear fluent yet contain factual inaccuracies or logical inconsistencies—by introducing D-Score, a novel hallucination detection metric derived from spectral statistics of hidden activations. Specifically, D-Score leverages the singular value distribution of the hidden activation matrix obtained from a single forward pass, establishing for the first time a connection between the spectral geometry of internal representations and the presence of hallucinations. Notably, this approach operates without reliance on external verifiers, retrieval augmentation, or multi-round generation, offering both computational efficiency and minimal overhead. Empirical evaluations on the FAVA-Annotation and RAGTruth benchmarks demonstrate that D-Score serves as a robust and effective signal for identifying hallucinated content.

Abstract

Large Language Models can produce fluent text that is false, unsupported by the available evidence, or inconsistent with information that appears to be internally represented by the model. We study hallucination detection from the geometry of hidden activations and introduce the D-Score, a simple spectral statistic computed from a single forward pass. For a fixed model, layer, and tolerance parameter, the D-Score counts how many singular directions of the hidden activation matrix have singular values that remain close to the leading one. We use this quantity as a hallucination score, classifying an input text as hallucinated when its D-Score is larger than a pre-defined quantity. The motivation is that, when a model processes a text that conflicts with information available in its own internal state, the hidden representation may encode both the asserted content and some form of counter-evidence, uncertainty, correction, or lack of support; this can make the hidden trajectory spread across additional singular directions. We formalize this intuition through a lightweight spectral argument and evaluate the resulting detector on FAVA-Annotation and RAGTruth. The experiments indicate that the D-Score is a strong hidden-state signal for hallucination detection, while requiring no external verifier, no retrieval step, and no multiple generations.

Problem

• hallucination detection
• large language models
• hidden-state signal
• spectral analysis
• D-Score

Innovation

• D-Score
• hallucination detection
• spectral analysis
• hidden-state geometry
• singular values