arXiv:1312. 0925v4 Announce Type: replace Abstract: Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems.
By Moritz Hardt
arXiv:2609. 17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.
By Jian-Feng Cai, Xiliang Lu, Juntao You
arXiv:2607. 24518v1 Announce Type: new Abstract: Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes.
By Lavinia Ghita, Dhruv Desai, Jake Goldberg, Roman Yokunda Enzmann
The paper introduces low‑rank orthogonalization, a technique that exploits the low‑rank nature of gradients in neural network training to perform matrix orthogonalization more efficiently. Building on this, the authors present low‑rank matrix‑signed gradient descent (MSGD) and a low‑rank variant of the Muon optimizer, showing through experiments that low‑rank Muon matches or surpasses vanilla Muon on GPT‑2 and LLaMA pretraining, especially for larger models. Theoretical analysis provides iteration‑complexity bounds for both low‑rank MSGD and low‑rank Muon under heavy‑tailed noise.
By Chuan He, Zhanwang Deng, Zhaosong Lu
arXiv:2406. 10407v3 Announce Type: replace-cross Abstract: Semidefinite programs (SDPs) and their solvers are powerful tools with many applications in machine learning and data science.
By Yufan Huang, David F. Gleich
arXiv:2109. 11057v2 Announce Type: replace-cross Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights.
By Elena Tuzhilina, Trevor Hastie