Matrix Factorization

Ask about this topic

Overview

Matrix factorization studies how to represent a matrix as products of smaller factors, revealing latent structure while reducing storage or supporting inference from missing and noisy entries. Core families include low-rank matrix completion and sensing, nonnegative and Boolean factorization, tensor and other structured decompositions, and latent-factor models; methods use alternating least squares, projected or manifold optimization, Bayesian inference, and spectral initialization. Applications range from recommendation and single-cell or connectome analysis to image recognition, categorical data completion, and compressing language-model and mixture-of-experts weights. A central challenge is balancing rank and sparsity assumptions, interpretability and robustness, and optimization speed against fidelity, while ensuring that the chosen structure and optimizer recover useful, stable factors.

Latest papers

CardsList

58 papers5 papers in the last four weeks, down 17% on the four weeks before. 0.0% of all new papers.

  1. Finite Spectral Depth Controls Gaussian Entrance Rank and Avoidance of the First Gradient-Flow Saddle

    Nov 3, 2026Yanlin LongNeural Network Training DynamicsGradient Descent Dynamics

    Independent Researcher, Guizhou, China

  2. A Self-Generated Floor on Adam's ε\varepsilon: Evidence from Power-Law Matrix Sensing

    Nov 1, 2026Lngel KyoAdaptive Gradient MethodsMatrix Factorization

    A2O Labs

  3. Structured Channel Network Pruning with Bi-Sparse Matrix Factorization

    Oct 31, 2026Jingjing Liu, Ziyang Wang, Xianchao Xiu +1Channel PruningNeural Network Pruning

    School of Microelectronics, Shanghai Key Laboratory of Chips and Systems for Intelligent Connected Vehicle, Shanghai University, Shanghai 200444, China · State Key Laboratory of Integrated Chips and Systems, Fudan University, Shanghai 201203, China · School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China +1

  4. No Cones, No Duals: A Fast and Scalable Solver for NRSfM

    Oct 25, 2026Suryansh KumarDeformable Shape ReconstructionMatrix Factorization

    Visual and Spatial AI Lab, VCCM Section, College of PVFA, Department of ECEN, Department of CSCE, Texas A&M University, College Station, Texas, USA

  5. Over-parameterization Is Neither Robust nor Fragile in Matrix Sensing: A Geometric Theory of Solution Robustness

    Oct 13, 2026Runze Shi, Ziye MaOverparameterizationMatrix Factorization

    City University of Hong Kong

  6. Shared Low-rank Basis Factorization for Data-free Mixture-of-Experts Compression

    Oct 7, 2026Tianxiao Cao, Jiahe Shao, Yuning Qiu +3LLM CompressionMixture-of-Experts Language Models

    Kyoto University · The University of Tokyo · RIKEN AIP

  7. Optimizer Geometry Sets the Pace: Spectral Learning Dynamics in Matrix Factorization

    Oct 3, 2026Mahalakshmi Sabanayagam, Simon LuceyGradient Descent DynamicsSpectral Bias

    Australian Institute for Machine Learning, Adelaide University

  8. Fast Differentiable SVD on GPU via Polar Decomposition

    Sep 26, 2026Uliana Parkina, Askar Tsyganov, Sergei Kudriashov +2Singular Value DecompositionMatrix Factorization

    HSE University

  9. Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices

    Sep 23, 2026Ali Aliev, Maxim RakhubaRiemannian OptimizationMatrix Optimization

    HSE University

  10. SpaFactor: Lightweight Spatial Context-Aware Gene Program Modeling for Histology-to-Transcriptomics Inference

    Sep 23, 2026Shiting Ruan, Xitong Ling, Qiming He +6Computational PathologySpatial Transcriptomics

    Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · Fuzhou University, Fuzhou, Fujian, China · Beijing Tsinghua Changgung Hospital, School of Clinical Medicine, Tsinghua University, Beijing, China +1

  11. Stiefel-AdamW: Geometry-Aware AdamW for Linear Factorization Blocks

    Sep 17, 2026Emanuele Zangrando, Marco Sutti, Francesco TudiscoDeep Learning OptimizationRiemannian Optimization

    Gran Sasso Science Institute, L’Aquila, Italy · University of Edinburgh, Edinburgh, UK

  12. CAST: Canonical Approximate Schur Tree for Approximate Cholesky on Graphs

    Sep 8, 2026Meher Chaitanya, Cameron Musco, Aristides GionisGraph SparsificationMatrix Factorization

    KTH Royal Institute of Technology Stockholm, Sweden · University of Massachusetts Amherst Amherst, Massachusetts, USA

  13. Sparse Separable Factor Analysis in the Complex Domain with an Application to Local Field Potential Data

    Aug 21, 2026Ian Hultman, Kirtikanth Kalapatapu, Yassine Filali +2Covariance EstimationMatrix Factorization

    Department of Statistics and Actuarial Science, University of Iowa · Department of Molecular Physiology and Biophysics, University of Iowa

  14. Cost Scales with Change, Not Corpus Size: Incrementally Maintaining an Evolving Semantic Substrate

    Aug 17, 2026Yusuke Takahashi, Kyle Wild, Asako UrakiIncremental ComputationMatrix Factorization

    Asia AI Institute, Faculty of Data Science Musashino University Tokyo, Japan

  15. PathFinder: Joint Decompositions of Linked Multimodal Datasets

    Aug 15, 2026Ying-Qiu Zheng, Alex Fung, Stephen M Smith +2Low-Rank Matrix DecompositionMatrix Factorization

    Oxford Centre for Integrative Neuroimaging University of Oxford Oxford, UK

  16. Exact Rank-Space KL Projection for Shared-Marginal Low-Rank Factors: Application to Doubly Stochastic Clustering

    Aug 9, 2026Enliang HuGraph Structure LearningLow-Rank Matrix Decomposition

  17. Shape Mutating Expert Compression:LorExperts and BTExperts

    Aug 7, 2026Inesh Chakrabarti, Sourjya Roy, Bowen Bao +3Mixture-of-Experts Language ModelsLow-Rank Matrix Decomposition

    Advanced Micro Devices

  18. The Loss Does Not See the Basis, but Adam Does

    Aug 5, 2026Devender SinghLow-Rank Matrix DecompositionMatrix Optimization

    Department of Computer Science Memorial University of Newfoundland

  19. Sparse Weight Decomposition for Efficient Circuit Extraction

    Aug 4, 2026Chuanhao Yan, Xuhan Huang, Yawen Duan +4Transformer InterpretabilityMechanistic Interpretability

    IQuest Research · Safe AI Forum · University of Oxford +2

  20. Sparsity Induced Identifiability in Matrix Tri-Factorisation

    Jul 29, 2026Tingting MuParameter IdentifiabilityMatrix Factorization

    Department of Computer Science University of Manchester Manchester M13 9PL, UK

  21. Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imaging

    Jul 28, 2026Christopher HahneLie Group MethodsComputational Imaging

    University of Bern 3008 Bern, Switzerland

  22. Non--negative matrix factorization using the R package nnmf

    Jul 22, 2026Volkan Sevinç, Nikolas Kontemeniotis, Theodoros Perdikis +1Non-Negative Matrix FactorizationDimensionality Reduction

    Muğla Sıtkı Koçman University, Faculty of Science, Department of Statistics, Kötekli Kampüsü, Muğla, Türkiye · Department of Economics, University of Crete, Gallos Campus, Rethimno, Greece · Department of Tourism Studies, University of Piraeus, Piraeus, Greece +1

  23. Gaming Consensus: Coordinated Manipulation in Crowdsourced Fact-Checking

    Jul 2, 2026Nikil Roashan Selvam, Jay Baxter, Sophie Hilgard +4Social Media AnalysisAlgorithmic Auditing

    Stanford University, Stanford, CA, USA · X Community Notes, xAI, Palo Alto, USA

  24. Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics

    Jun 30, 2026Yudong Wei, Liang Zhang, Bingcong Li +1Low-Rank Matrix DecompositionNonconvex Optimization

    Department of Mathematics, ETH Zurich, Zurich, Switzerland · Department of Computer Science, ETH Zurich, Zurich, Switzerland

  25. Muon learns balanced solutions in matrix factorization without slow saddle-to-saddle dynamics

    Jun 29, 2026Mark Rhee, Jamie Simon, Dhruva KarkadaMuon OptimizerMatrix Optimization

    UC Berkeley · Imbue

  26. DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Training

    Jun 27, 2026Dong Wang, Wenwu Tang, Yun Cheng +1Language Model PretrainingLLM Compression

    Graz University of Technology, Austria · Swiss Data Science Center, Switzerland

  27. A Novel Approach to Temporal QoS Estimation via Extended Kalman Filter-Incorporated Latent Feature Analysis

    Jun 22, 2026Ye Yuan, Song Wang, Hongxun Zhou +2Time Series ForecastingCloud Computing

    College of Computer and Information Science, Southwest University, Chongqing 400715, China

  28. A Bayesian Boolean Matrix Factorization with Application to Copy Number Analysis in Cancer

    Jun 16, 2026Adolphus Wagala, Mehmet Samur, Giovanni ParmigianiCancer GenomicsBayesian Inference

    Department of Data Science, Dana-Farber Cancer Institute · Department of Biostatistics, Harvard T.H. Chan School of Public Health

  29. How Much Do Reviews Really Contribute? A Study on Text-Enriched Matrix Factorization for Recommendations

    Jun 15, 2026Eduardo Ferreira da Silva, Mayki dos Santos Oliveira, Joel Machado Pires Denis Dantas Boaventura +1Feature Interaction ModelingRecommender Systems

    Instituto de Computac¸˜ao – Universidade Federal da Bahia (UFBA) Salvador – BA – Brazil

  30. Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis

    Jun 6, 2026Qian Zhang, Meixia LinIncomplete Data ImputationMatrix Completion

    Engineering Systems and Design, Singapore University of Technology and Design, Singapore · Institute of Statistics and Big Data, Renmin University of China, P.R. China