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A prominent family of low-rank LLM optimizers, pioneered by GaLore, performs gradient-subspace projection: at each step, they project the gradient into a low-dimensional subspace and map the update back to the full model. Most existing work either recomputes the gradient subspace at certain intervals, or performs post-...
The Muon optimizer derives its update rule for hidden linear layers by solving a local linearization of the loss penalized by the spectral norm, motivated by an RMS-stability argument for dense linear layers. Standard Muon implementations, however, exclude the input (embedding table) and output (language model head) la...
We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$. (MG26) provides selectors with a movement bound for the problem of chasing high-dimensional convex nested sets for every $p<q$ and generally reduces Lipschitz convex optimization...
We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p<q$) can improve convergence rates in convex optimization, and...
Inspired by Muon, this work adopts the spectral view for unlearning and proposes Spectral Saliency Unlearning (SSU), a thresholding approach that thresholds weak singular components and updates only those directions supported by a confident unlearning signal.
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