Spectral Rank Certification for Foundation Model Adapters
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 rank-one reference experiment, with an unknown signal direction integrated under a rotation-invariant reference prior. The resulting series yields a computable finite-sample Le Cam bound at concrete layer sizes, an explicit remainder bound for numerical truncation, and the rectangular Baik-Ben Arous-Peche (BBP) limit. A compact-manifold Laplace expansion shows that finite-sa...
| Authors | Mohammed Ahnouch, Lotfi Elaachak |
|---|---|
| Primary category | cs.LG |
| Published | 15 August 2026 |
| Last updated at source | 15 August 2026 |
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