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Whitening Inverts the Hierarchy: What the Norm of a Whitened Embedding Measures

arXiv · AI, language, vision and robotics · article · Sep 19, 2026 · UTC

Whitening a foundation-model embedding and using its squared norm as a training-free likelihood surrogate is motivated by the observation that whitened coordinates often appear approximately standard normal. We show that this observation follows from the projection central limit theorem and therefore does not imply a Gaussian joint distribution. Across multiple encoders and three training objectives, we find systematic over-dispersion of the whitened radius relative to the Gaussian reference, including against distributional clones with identical mean and covariance. We further show that the c

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