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

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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BibTeX RIS

BibTeX

@misc{wilson2026lowcost,
  title = {{Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Prediction}},
  author = {Dan Wilson and Mohamed Akrout},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.05134},
  eprint = {2605.05134},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.05134},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Prediction
AU  - Dan Wilson
AU  - Mohamed Akrout
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.05134
UR  - https://arxiv.org/abs/2605.05134
AB  - 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.
ER  -

Abstract

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