SAD-LoRA: Spectral Alignment for Low-Rank Knowledge Distillation
Distilling a fine-tuned teacher into a LoRA-adapted student is a standard recipe for parameter-efficient compression, but output-level KD does not explicitly control which rank-$r$ weight subspace the adapter occupies. We propose \textbf{SAD-LoRA} (\textbf{S}pectral \textbf{A}lignment \textbf{D}istillation), which selects this subspace from the data-weighted student-space reference update $\DWT\Sigx^{1/2}$ and maintains it during training via a differentiable principal-angle loss on $\colspan(B)$. We show that the data-weighted distillation error decomposes exactly into subspace misalignment, within-subspace coefficient mismatch, and irreducible rank residual; standard KD can affect the f...
| Authors | Omer Tariq, Syed Muhammad Raza, Jeongbae Son |
|---|---|
| Primary category | cs.LG |
| Published | 5 July 2026 |
| Last updated at source | 5 July 2026 |
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