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

How can we detect hallucinations in Large Language Models (LLMs) without relying on external retrieval, multiple generation passes, or additional verifier models? The authors investigate whether the internal geometric structure of a model's hidden states—specifically the spectral properties of its activation trajectory—contains sufficient information to identify unsupported or false claims.

To address this, the authors introduce the D-Score, a metric based on the Singular Value Decomposition (SVD) of the hidden activation matrix. The intuition is that a well-supported, truthful text produces a coherent hidden trajectory concentrated in a few dominant singular directions. Conversely, when a model generates an unsupported claim that conflicts with its internal knowledge, the hidden representation must encode both the assertion and the underlying uncertainty or counter-evidence. This conflict causes the hidden trajectory to spread across additional singular directions. The D-Score quantifies this by counting how many singular values remain above a specific relative threshold compared to the leading singular value.

The study demonstrates that the D-Score serves as a robust signal for hallucination detection across several open-weight models, including Llama-2-7B, Llama-3-8B, and Vicuna-7B. By evaluating the method on the FAVA-Annotation and RAGTruth benchmarks, the authors show that the D-Score outperforms existing internal-state detection methods. Because the score relies on the relative ratio of singular values, it is invariant to global scaling of activations and can be computed efficiently using partial eigensolvers, making it a lightweight diagnostic tool for real-time monitoring.

Most current hallucination detection techniques are computationally expensive, requiring multiple model inferences (e.g., self-consistency checks) or external knowledge retrieval. The D-Score offers a path toward "zero-shot" internal monitoring, allowing developers to assess the reliability of a model's output using only the internal states generated during the primary inference pass. This provides a scalable, model-agnostic way to flag potential hallucinations without increasing latency or requiring external infrastructure.