Whitening Reveals Cluster Commitment as the Geometric Separator of Hallucination Types

TL;DR

This paper introduces a geometric taxonomy of hallucination types in language models and demonstrates that PCA-whitening reveals cluster commitment as a key separator, highlighting capacity limits and prompt-set sensitivity.

Contribution

It presents a novel whitening method to distinguish hallucination types in embedding space, clarifies the role of capacity limits, and uncovers prompt-set fragility in micro-signal detection.

Findings

Whitening separates Type 2 from Type 3 hallucinations significantly.

Type 1/2 separation is limited by model capacity, not measurement artifacts.

Prompt diversification affects micro-signal detection, revealing prompt-set sensitivity.

Abstract

A geometric hallucination taxonomy distinguishes three failure types -- center-drift (Type~1), wrong-well convergence (Type~2), and coverage gaps (Type~3) -- by their signatures in embedding cluster space. Prior work found Types~1 and~2 indistinguishable in full-dimensional contextual measurement. We address this through PCA-whitening and eigenspectrum decomposition on GPT-2-small, using multi-run stability analysis (20 seeds) with prompt-level aggregation. Whitening transforms the micro-signal regime into a space where peak cluster alignment (max\_sim) separates Type~2 from Type~3 at Holm-corrected significance, with condition means following the taxonomy's predicted ordering: Type~2 (highest commitment) $>$ Type~1 (intermediate) $>$ Type~3 (lowest). A first directionally stable but underpowered hint of Type~1/2 separation emerges via the same metric, generating a capacity prediction for larger models. Prompt diversification from 15 to 30 prompts per group eliminates a false positive in whitened entropy that appeared robust at the smaller set, demonstrating prompt-set sensitivity in the micro-signal regime. Eigenspectrum decomposition localizes this artifact to the dominant principal components and confirms that Type~1/2 separation does not emerge in any spectral band, rejecting the spectral mixing hypothesis. The contribution is threefold: whitening as preprocessing that reveals cluster commitment as the theoretically correct separating metric, evidence that the Type~1/2 boundary is a capacity limitation rather than a measurement artifact, and a methodological finding about prompt-set fragility in near-saturated representation spaces.