From Prerequisites to Predictions: Validating a Geometric Hallucination Taxonomy Through Controlled Induction

TL;DR

This study validates a geometric hallucination taxonomy in GPT-2, showing coverage gaps as the most distinctive failure mode through controlled experiments and statistical analysis.

Contribution

It introduces a controlled induction method to distinguish hallucination types in language models, confirming coverage gaps as a key failure mode.

Findings

Coverage-gap hallucinations are the most geometrically distinctive failure mode.

Type~3 norm separation is robust in static embeddings.

Types~1 and~2 do not separate in either embedding space.

Abstract

We test whether a geometric hallucination taxonomy -- classifying failures as center-drift (Type~1), wrong-well convergence (Type~2), or coverage gaps (Type~3) -- can distinguish hallucination types through controlled induction in GPT-2. Using a two-level statistical design with prompts ($N = 15$/group) as the unit of inference, we run each experiment 20 times with different generation seeds to quantify result stability. In static embeddings, Type~3 norm separation is robust (significant in 18/20 runs, Holm-corrected in 14/20, median $r = +0.61$). In contextual hidden states, the Type~3 norm effect direction is stable (19/20 runs) but underpowered at $N = 15$ (significant in 4/20, median $r = -0.28$). Types~1 and~2 do not separate in either space (${\leq}\,3/20$ runs). Token-level tests inflate significance by 4--16$\times$ through pseudoreplication -- a finding replicated across all 20 runs. The results establish coverage-gap hallucinations as the most geometrically distinctive failure mode, carried by magnitude rather than direction, and confirm the Type~1/2 non-separation as genuine at 124M parameters.