Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Prediction

arXiv:2605.05134 · cs.LG, math.DS · Submitted 2026-05-06 · Read on arXiv

cs.LG, math.DS

Submitted: 2026-05-06

Updated: 2026-09-25

License: http://creativecommons.org/licenses/by/4.0/

The gist: Large Language Models (LLMs) frequently generate plausible but non-factual content, a phenomenon known as hallucination.

Terminology

Abstract

Large Language Models (LLMs) frequently generate plausible but non-factual content, a phenomenon known as hallucination. While existing detection methods typically rely on computationally expensive sampling-based consistency checks or external knowledge retrieval, we propose a new method that treats the LLM as a black-box dynamical system. By projecting LLM responses into a high-dimensional manifold via an embedding model, we characterize the resulting vector sequences as observable realizations of the model's latent state-space dynamics. Leveraging Koopman operator theory, we fit the transition operators for both factual and hallucinated regimes and define a differential residual score based on their respective prediction errors. This approach enables low-cost hallucination detection in a single-sample pass, avoiding the need for secondary sampling or external grounding. Extensive testing across three data benchmarks demonstrates that our method achieves state-of-the-art performance with reduced resource overhead.

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