EigenLI introduces a spectral approximation framework that compresses late‑interaction representations by identifying document‑specific low‑dimensional subspaces. By selecting dominant eigendirections, it constructs reduced interaction representations that outperform clustering‑based pooling methods on ColBERTv2 and AnswerAI‑ColBERT‑small. The framework also yields EigenLI‑SV, a single‑vector ANN‑compatible representation that consistently surpasses comparable surrogates such as MUVERA across multiple datasets and text models.
By Archish S, Sabyasachi Basu, Ankit Garg, Ravishankar Krishnaswamy, Kirankumar Shiragur
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.
By Tavor Z. Baharav, Phillip B. Nicol, Rafael A. Irizarry, Rong Ma
arXiv:2606. 28328v1 Announce Type: cross Abstract: In recent years, text clustering has become a critical technique for applications including intent discovery, topic mining, and recommendation systems.
By Daoming Wan, Yizheng Huang, Jimmy X. Huang
The paper investigates Partial Least Squares (PLS) in high-dimensional settings, focusing on a model where two data matrices share a low-rank latent structure plus individual-specific components. By analyzing the singular vectors of the cross‑covariance matrix with random matrix theory, the authors derive asymptotic characterizations of how well the estimated latent directions align with the true ones. They show that the PLS variant based on Singular Value Decomposition (PLS‑SVD) outperforms separate principal component analysis in detecting the common latent subspace, while also identifying regimes where PLS‑SVD behaves counter‑intuitively or reaches fundamental limits.
By Victor L\'eger, Florent Chatelain
arXiv:2606. 24134v1 Announce Type: cross Abstract: Motivated by an application in machine learning optimization, this paper focuses on the challenges of sampling a matrix uniformly from the unit spectral norm ball.
By Michael R. Metel
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).
By Maksym Shamrai
arXiv:2104. 08928v4 Announce Type: replace-cross Abstract: Unstructured text provides decision-makers with a rich data source in many domains, ranging from product reviews in retail to nursing notes in healthcare.
By Kan Xu, Xuanyi Zhao, Hamsa Bastani, Osbert Bastani
The paper introduces MARETopic, a training‑free framework that identifies topics by selecting rank‑based prototype documents from pretrained embeddings. By projecting embeddings onto a low‑dimensional manifold and building ranked neighborhood lists, a greedy algorithm picks exactly K exemplar texts whose neighborhoods cover the corpus. Two variants—MARETopic_Corr, which uses a query‑performance predictor and rank correlation, and MARETopic_Diff, which employs a rank‑based diffusion matrix—achieve higher purity and NMI on benchmark datasets and run significantly faster, while also improving topic coherence and vocabulary diversity through a novel Maximal Marginal Relevance step.
By Thiago C\'esar Castilho Almeida, Daniel Carlos Guimar\~aes Pedronette
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:2609.09211v1 Announce Type: new
Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
By Huan Qing
arXiv:2608. 08704v1 Announce Type: cross Abstract: Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime.
By Zeqin Lin, Guangming Pan, Zhixiang Zhang, Yinbing Zhou
arXiv:2505.18918v4 Announce Type: replace-cross
Abstract: Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. Various methods have been proposed to extend...
By Javier Salazar Cavazos, Jeffrey A Fessler, Laura Balzano