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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 G...
Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity. This article develops a finite-sample framework for inferring effective rank structure in public foundation-model adapters. The theoretical core is an exact chi-square divergence for the fixed-dimensional Gaussian...
Four complementary quantities are distinguished---edge count $m$ effective contrast rank $s$, effective contrast rank $s$, population support rank $r$, and graph spectral gap $\eta$---and characterize their roles in audit coverage and deployment reliability.
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