The paper introduces D‑SLR, a closed‑form decomposition that combines a low‑rank approximation with a disjoint row‑sparse component, offering a drop‑in replacement for truncated SVD. Unlike previous joint methods, D‑SLR restricts each row to either be stored verbatim or approximated by the low‑rank fit, achieving the joint optimum without extra parameters and without iterative solvers or regularization tuning. The authors provide an assumption‑free, a‑posteriori error bound for every shape, and demonstrate performance gains on synthetic data, LLM embedding tables, network traffic, and hyperspectral images.
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.
The paper compares two popular data‑integration techniques—Stack‑SVD, which concatenates datasets before performing singular value decomposition, and SVD‑Stack, which first decomposes each dataset separately and then aggregates the leading singular vectors. By deriving exact asymptotic performance expressions and phase transitions in a proportional regime, the authors show that neither method uniformly dominates the other when unweighted, but optimally weighted Stack‑SVD outperforms optimally weighted SVD‑Stack when the low‑rank signal is fully shared. They also demonstrate that SVD‑Stack can excel with partially shared components and provide practical algorithms for estimating optimal weights, supported by simulations and genomic experiments.
arXiv:2602. 04795v3 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) is a popular data embedding technique.
arXiv:2606. 03723v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) enables parameter-efficient specialization of foundation models, but the proliferation of task-specific adapters fragments capabilities across many adapters, complicating reuse and deployment.
arXiv:2603.29715v2 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) approximates a nonnegative matrix, X, by the product of two nonnegative factors, WH, where W has r columns a...
arXiv:2608.21607v1 Announce Type: cross Abstract: We investigate when a sparse nonnegative matrix can be recovered from a real-valued matrix of much lower rank by zeroing out its negative elements. T...
arXiv:2606. 16045v1 Announce Type: new Abstract: In the data selection problem, the objective is to choose a small, representative subset of data that can be used to efficiently train a machine learning model.
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:2507.19290v2 Announce Type: replace-cross Abstract: We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-...
arXiv:2601. 11626v2 Announce Type: replace-cross Abstract: Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD).
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...
arXiv:2511.02821v2 Announce Type: replace-cross Abstract: We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex s...