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

• URL: http://arxiv.org/abs/2605.05134v1
• Date: Wed, 06 May 2026 17:07:29 GMT
• Title: Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Prediction
• Abstract summary: Large Language Models (LLMs) frequently generate plausible but non-factual content, a phenomenon known as hallucination.<n>We propose a new method that treats the LLM as a black-box dynamical system.<n>Our method achieves state-of-the-art performance with reduced resource overhead.
• Score: 3.6209977238182276
• License: http://creativecommons.org/licenses/by/4.0/
• 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. To accommodate varying user requirements and domain-specific sensitivities, we introduce a preference-aware calibration mechanism that optimizes the classification threshold based on a small set of demonstrations. 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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