What do Geometric Hallucination Detection Metrics Actually Measure?
Existing geometric hallucination detection metrics struggle to distinguish specific hallucination types in the absence of ground truth and are highly sensitive to domain shifts. This work addresses these limitations by constructing a synthetic dataset to systematically evaluate the capacity of various geometric statistics to capture key hallucination attributes—such as output correctness, relevance, and coherence—and reveals that different metrics align with distinct hallucination types. Furthermore, the study proposes a simple yet effective normalization strategy that substantially mitigates the impact of domain shift. Experimental results demonstrate that, under multi-domain settings, the proposed approach improves AUROC by 34 percentage points, significantly enhancing the cross-domain robustness of geometric hallucination detection metrics.