Innovative Low-Cost Method for Detecting LLM Hallucinations Using Dynamical System Theory

Large Language Models (LLMs) are prone to generating plausible but non-factual content, termed hallucination. Current detection techniques often involve costly sampling-based checks or external knowledge retrieval. Researchers propose a novel approach that treats LLMs as black-box dynamical systems, projecting responses into a high-dimensional manifold through an embedding model. This method utilizes Koopman operator theory to fit transition operators for both factual and hallucinated outputs, establishing a differential residual score from prediction errors. To meet diverse user needs, a preference-aware calibration mechanism optimizes classification thresholds based on limited demonstrations. Testing across three data benchmarks reveals that this method achieves state-of-the-art performance with significantly lower resource requirements.