Hugging Face Trending Papers

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp

We revisit the Sinkhorn-Knopp (SK) algorithm for the matrix scaling problem. Despite extensive literature on the global convergence of SK and its variants, its local linear convergence behavior remains less understood.

arXiv Machine Learning
Jul 21

Scaling Limits of Constant-Stepsize SGD at Flat Minima

arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.

By Jingyi Zhang, Cheng Mao, Debankur Mukherjee
arXiv Machine Learning
5d ago

Fast Length-Squared Sampling for Positive-Semidefinite Matrices

arXiv:2608. 12503v1 Announce Type: cross Abstract: We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm.

By Rajarshi Bhattacharjee, Ethan N. Epperly, Cameron Musco, Aaron Tian
arXiv Machine Learning
Jul 27

On the Convergence of Stochastic Low-Rank Adaptation

arXiv:2607. 21975v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) optimizes $J(B,A)=\mathcal L(W_\mathrm{base}+sBA)$ over two adapters $B \in \mathbb{R}^{m \times r}$ and $A \in \mathbb{R}^{r \times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\mathrm{base} \in \mathbb{R}^{m \times n}$.

By Ru Wang, Chengchang Liu, John C. S. Lui