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.
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
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.
arXiv:2606. 31390v1 Announce Type: cross Abstract: Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization.
arXiv:2606. 15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.
arXiv:2608. 08642v1 Announce Type: new Abstract: We study exact Kullback--Leibler (KL) projection for low-rank factorizations whose two nonnegative factors have prescribed row marginals and a shared, learned column marginal.
arXiv:2606. 19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design.
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
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.
arXiv:2606. 02887v1 Announce Type: new Abstract: Symmetric nonnegative matrix factorization (Symmetric NMF) approximates a matrix as $WW^T$ with nonnegative rectangular factor $W$.
arXiv:2606. 30523v1 Announce Type: new Abstract: Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings.
arXiv:2606. 08291v1 Announce Type: new Abstract: We study the symmetric multi-type orthogonal non-negative matrix tri-factorization problem, where several symmetric non-negative matrices are simultaneously approximated by factors of the form $GS_{i}G^{\top}$, with a shared non-negative and orthogonal factor $G$.
arXiv:2606. 13767v1 Announce Type: cross Abstract: Low-rank adaptation (LoRA) and its variants provide a memory- and compute-efficient alternative to full fine-tuning of pre-trained models.