Directional Consistency (DC)

A geometric metric measuring alignment between query-response displacement vectors and learned domain patterns. DC detects hallucinations by identifying when responses deviate from expected directional behavior in embedding space.

Displacement Geometry

Instead of analyzing absolute positions, DC examines the geometric structure of query-to-response displacement vectors. This relative approach captures semantic transformations independent of specific content, enabling reference-free detection.

Domain Calibration

Grounding geometry is domain-local. Legal Q&A has different displacement structure than medical triage. Cross-domain transfer fails completely (AUROC ≈ 0.50). Proper calibration with domain-specific reference sets is essential for high performance.

Reference-Free Detection

Unlike methods requiring ground truth or external knowledge bases, DC operates purely on geometric consistency. Once calibrated, it detects hallucinations without needing reference answers, making it ideal for open-domain applications.