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 first term only indirectly through output gradients. On controlled synthetic problems with a flat teacher spectrum, SAD-LoRA reduces the subspace-misalignment term from $51\%$ to nearly zero and lifts final subspace alignment from $0.49$ to $1.00$. On RoBERTa-large to RoBERTa-base distillation across six GLUE tasks, SAD-LoRA improves rank efficiency: at $r{=}4$, it matches or beats the strongest included spectral baseline on five of six tasks, and at $r{=}8$ it gives the best result on SST-2 and CoLA. Ablations identify subspace alignment as the load-bearing component, while coefficient matching is auxiliary.
Omer Tariq, Syed Muhammad Raza, J. Son· 0 citations
Knowledge distillation (KD) trains a compact student by attracting it towards a converged teacher. It is silent about which directions the teacher itself learned to suppress: repulsive and bias-aware objectives exist, but none exploits the teacher's own trajectory to identify what the student should avoid. We observe that the missing signal is already encoded in the teacher's optimization trajectory: features that an early-stage teacher emphasizes but that a converged teacher attenuates are precisely the shortcut directions worth pushing the student away from. We instantiate this observation as \textbf{A}nti-\textbf{S}hortcut \textbf{D}istillation (ASD), a push--pull KD framework that treats the converged teacher $\Tfinal$ as a positive semantic anchor and an early-checkpoint teacher $\Tearly$ as a temporal negative reference. ASD couples two losses: a temporal contrastive loss ($\Ltc$) that places the early-teacher feature as a same-sample negative against in-batch and memory-bank final-teacher features in an InfoNCE objective; and a shortcut suppression loss ($\Lss$) that penalizes student projection onto the top eigenvectors of $\E[\Dh\Dh^{\top}]$, the uncentered second-moment matrix of early-to-final feature displacements. Across 13 teacher--student pairs on CIFAR-100, ImageNet-100, and TinyImageNet, ASD attains the highest clean top-1 accuracy on more than 10 pairs and outperforms standard KD on 12. On CIFAR-100-C corruption robustness, ASD obtains the lowest mean Corruption Error ($86.1$\,mCE) on the most challenging cross-architecture pair (WRN-40-2$\to$ShuffleNet-V2). Mechanistic diagnostics confirm the intended geometry: the ASD student is systematically anti-aligned with the shortcut direction, while its projection onto the robust subspace is substantially larger ($0.45$ vs.\ $0.12$).
Syed Muhammad Raza, Omer Tariq, J. Son· 0 citations