Large Language Models (LLMs) often generate overconfident yet factually incorrect hallucinations. Current detection paradigms suffer from a trade-off between the high accuracy of computationally expensive black-box methods and the inability of white-box methods to detect stubborn hallucinations. To bridge this gap, we propose GHOST (Geometric Hidden-state Observation for Semantic Truthfulness), an efficient white-box framework for hallucination detection in LLMs. We primarily target confused hallucinations marked by internal reasoning instability, while also capturing stubborn hallucinations characterized by premature layer-wise convergence as a complementary signal. By integrating internal geometric dynamics with output probability distributions, GHOST constructs a high-dimensional feature space for non-linear truthfulness classification. Extensive evaluations on FinanceBench, RAGTruth, HaluEval, and PopQA show that GHOST outperforms white-box baselines and achieves competitive black-box performance while reducing computational overhead by over 90%, offering a robust solution for real-time detection.

Large language models (LLMs) demonstrate exceptional instruct-following ability to complete various downstream tasks. Although this impressive ability makes LLMs flexible task solvers, their performance in solving tasks also heavily relies on instructions. In this paper, we reveal that LLMs are over-sensitive to lexical variations in task instructions, even when the variations are imperceptible to humans. By providing models with neighborhood instructions, which are closely situated in the latent representation space and differ by only one semantically similar word, the performance on downstream tasks can be vastly different. Following this property, we propose a black-box Combinatorial Optimization framework for Prompt Lexical Enhancement (COPLE). COPLE performs iterative lexical optimization according to the feedback from a batch of proxy tasks, using a search strategy related to word influence. Experiments show that even widely-used human-crafted prompts for current benchmarks suffer from the lexical sensitivity of models, and COPLE recovers the declined model ability in both instruct-following and solving downstream tasks.