The Detectability Gap: Hidden Heterogeneity in Hallucination Detection Across Language Models

Pranav Darshan, Pranav A, Sravan Karthick T, Minal Moharir, Ivan P. Yamshchikov

Sampling based consistency is widely used for hallucination detection, yet aggregate performance can conceal systematic differences in which errors are detectable. This work studies that heterogeneity across four language models and three factual question answering datasets. Partitioning hallucinations by answer agreement reveals high agreement (Ghost) and low agreement (Flickering) regimes with an apparent detectability gap of $0.35$ to $0.46$ AUC. Because the statistics used to define the regimes and measure this gap are strongly coupled ($|ρ|\approx0.94$ to $1.00$), the raw result is treated as a property of agreement based detection rather than independent evidence. After freezing regime assignments, lexical and semantic response dispersion preserve the asymmetry, with bootstrap $95\%$ intervals excluding zero in all $12$ model and dataset settings. A stricter test using individual diffusion trajectories and no cross seed information preserves the asymmetry across all three LLaDA datasets ($p<0.005$) and directionally across all three Dream datasets, with one reaching significance. The hard regime varies substantially in prevalence across models ($16\%$ to $77\%$), and…