Whitening Reveals Cluster Commitment as the Geometric Separator of Hallucination Types
This work provides a more refined method for distinguishing hallucination types in language models, which is significant for researchers and developers working on improving the reliability and interpretability of these models.
This paper addresses the indistinguishability of two types of geometric hallucinations (Type 1 and Type 2) in full-dimensional contextual measurements by applying PCA-whitening and eigenspectrum decomposition on GPT-2-small. Whitening successfully separates Type 2 from Type 3 hallucinations based on peak cluster alignment with Holm-corrected significance, and provides a preliminary, underpowered hint of Type 1/2 separation.
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.