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

TL;DR

This paper introduces a low-cost, black-box method for detecting hallucinations in LLMs by modeling their responses as dynamical systems and using Koopman operator theory for classification.

Contribution

It presents a novel approach that treats LLM responses as dynamical systems and uses Koopman theory to detect hallucinations efficiently without external knowledge.

Findings

Achieves state-of-the-art hallucination detection performance.

Operates with reduced resource overhead compared to existing methods.

Works effectively across multiple data benchmarks.

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.