Matrix Factorization

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6 papers in the last four weeks, up 100% on the four weeks before. 0.0% of all new papers.

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Over-parameterization Is Neither Robust nor Fragile in Matrix Sensing: A Geometric Theory of Solution Robustness
Oct 13, 2026Runze Shi, Ziye MaMatrix Factorization Low-Rank Matrix Decomposition
City University of Hong Kong
Shared Low-rank Basis Factorization for Data-free Mixture-of-Experts Compression
Oct 7, 2026Tianxiao Cao, Jiahe Shao, Yuning Qiu +3LLM Compression Mixture-of-Experts Language Models
Kyoto University · The University of Tokyo · RIKEN AIP
Optimizer Geometry Sets the Pace: Spectral Learning Dynamics in Matrix Factorization
Oct 3, 2026Mahalakshmi Sabanayagam, Simon LuceyGradient Descent Dynamics Spectral Bias
Australian Institute for Machine Learning, Adelaide University
Fast Differentiable SVD on GPU via Polar Decomposition
Sep 26, 2026Uliana Parkina, Askar Tsyganov, Sergei Kudriashov +2Singular Value Decomposition Matrix Factorization
HSE University
Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices
Sep 23, 2026Ali Aliev, Maxim RakhubaRiemannian Optimization Matrix Optimization
HSE University
SpaFactor: Lightweight Spatial Context-Aware Gene Program Modeling for Histology-to-Transcriptomics Inference
Sep 23, 2026Shiting Ruan, Xitong Ling, Qiming He +6Computational Pathology Spatial 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
Stiefel-AdamW: Geometry-Aware AdamW for Linear Factorization Blocks
Sep 17, 2026Emanuele Zangrando, Marco Sutti, Francesco TudiscoDeep Learning Optimization Riemannian Optimization
Gran Sasso Science Institute, L’Aquila, Italy · University of Edinburgh, Edinburgh, UK
CAST: Canonical Approximate Schur Tree for Approximate Cholesky on Graphs
Sep 8, 2026Meher Chaitanya, Cameron Musco, Aristides GionisGraph Sparsification Matrix Factorization
KTH Royal Institute of Technology Stockholm, Sweden · University of Massachusetts Amherst Amherst, Massachusetts, USA
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 Estimation Matrix Factorization
Department of Statistics and Actuarial Science, University of Iowa · Department of Molecular Physiology and Biophysics, University of Iowa
Cost Scales with Change, Not Corpus Size: Incrementally Maintaining an Evolving Semantic Substrate
Aug 17, 2026Yusuke Takahashi, Kyle Wild, Asako UrakiMatrix Factorization Retrieval-Augmented Generation
Asia AI Institute, Faculty of Data Science Musashino University Tokyo, Japan
PathFinder: Joint Decompositions of Linked Multimodal Datasets
Aug 15, 2026Ying-Qiu Zheng, Alex Fung, Stephen M Smith +2Low-Rank Matrix Decomposition Matrix Factorization
Oxford Centre for Integrative Neuroimaging University of Oxford Oxford, UK
Exact Rank-Space KL Projection for Shared-Marginal Low-Rank Factors: Application to Doubly Stochastic Clustering
Aug 9, 2026Enliang HuGraph Structure Learning Low-Rank Matrix Decomposition
Shape Mutating Expert Compression:LorExperts and BTExperts
Aug 7, 2026Inesh Chakrabarti, Sourjya Roy, Bowen Bao +3Mixture-of-Experts Language Models Low-Rank Matrix Decomposition
Advanced Micro Devices
The Loss Does Not See the Basis, but Adam Does
Aug 5, 2026Devender SinghLow-Rank Matrix Decomposition Matrix Optimization
Department of Computer Science Memorial University of Newfoundland
Sparse Weight Decomposition for Efficient Circuit Extraction
Aug 4, 2026Chuanhao Yan, Xuhan Huang, Yawen Duan +4Transformer Interpretability Mechanistic Interpretability
IQuest Research · Safe AI Forum · University of Oxford +2
Sparsity Induced Identifiability in Matrix Tri-Factorisation
Jul 29, 2026Tingting MuParameter Identifiability Matrix Factorization
Department of Computer Science University of Manchester Manchester M13 9PL, UK
Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imaging
Jul 28, 2026Christopher HahneLie Group Methods Computational Imaging
University of Bern 3008 Bern, Switzerland
Non--negative matrix factorization using the R package nnmf
Jul 22, 2026Volkan Sevinç, Nikolas Kontemeniotis, Theodoros Perdikis +1Non-Negative Matrix Factorization Dimensionality 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
Gaming Consensus: Coordinated Manipulation in Crowdsourced Fact-Checking
Jul 2, 2026Nikil Roashan Selvam, Jay Baxter, Sophie Hilgard +4Social Media Analysis Algorithmic Auditing
Stanford University, Stanford, CA, USA · X Community Notes, xAI, Palo Alto, USA
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 Decomposition Nonconvex Optimization
Department of Mathematics, ETH Zurich, Zurich, Switzerland · Department of Computer Science, ETH Zurich, Zurich, Switzerland
Muon learns balanced solutions in matrix factorization without slow saddle-to-saddle dynamics
Jun 29, 2026Mark Rhee, Jamie Simon, Dhruva KarkadaMuon Optimizer Matrix Optimization
UC Berkeley · Imbue
DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Training
Jun 27, 2026Dong Wang, Wenwu Tang, Yun Cheng +1Language Model Pretraining LLM Compression
Graz University of Technology, Austria · Swiss Data Science Center, Switzerland
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 Forecasting Cloud Computing
College of Computer and Information Science, Southwest University, Chongqing 400715, China
A Bayesian Boolean Matrix Factorization with Application to Copy Number Analysis in Cancer
Jun 16, 2026Adolphus Wagala, Mehmet Samur, Giovanni ParmigianiCancer Genomics Bayesian Inference
Department of Data Science, Dana-Farber Cancer Institute · Department of Biostatistics, Harvard T.H. Chan School of Public Health
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 Modeling Recommender Systems
Instituto de Computac¸˜ao – Universidade Federal da Bahia (UFBA) Salvador – BA – Brazil
Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis
Jun 6, 2026Qian Zhang, Meixia LinIncomplete Data Imputation Matrix 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
Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition
Jun 2, 2026Hailang Wu, Yonghe Liu, Bingxuan Yu +1Non-Negative Matrix Factorization Matrix Factorization
School of Mathematics and Statistics, Yunnan University, Kunming, China.
Riemannian Optimization for Hadamard Products of Low-Rank Matrices
May 31, 2026Pratik Jawanpuria, Ankish Chandresh, Bamdev MishraRiemannian Optimization Low-Rank Approximation
Centre for Machine Intelligence and Data Science, Indian Institute of Technology Bombay, India · Microsoft India
How Much Orthogonalization Does Muon Need?
May 29, 2026Hua HuangNewton-Schulz Iteration Neural Network Optimization
NVIDIA
Manifold-based Algorithms for the Hadamard Decomposition
May 27, 2026Nicolas Gillis, Subhayan Saha, Stefano Sicilia +1Low-Rank Matrix Decomposition Low-Rank Approximation
Department of Mathematics and Operational Research, University of Mons, Mons, Belgium. · SS is a member of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM).

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

Runze Shi, Ziye Ma

City University of Hong Kong

Matrix Factorization Low-Rank Matrix Decomposition Inverse Problems

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Over-parameterization is ubiquitous in modern machine learning, yet its effect on robustness remains poorly understood. We study this question in matrix sensing, a canonical non-convex problem that can also be viewed, under an appropriate parameterization, as training a two-layer quadratic neural network. We develop a rank-aware robustness theory for the Burer-Monteiro factorization when the search rank k may exceed the target rank r_star, thereby capturing over-parameterization. Our analysis shows that robustness depends jointly on the degree of over-parameterization and the local geometry of the attained second-order stationary point: increasing k generally worsens sensitivity, but stationary points with the same search rank can exhibit substantially different robustness. Motivated by this observation, we propose a trajectory-aware algorithm that uses spectral balancing and randomized sketching to steer optimization toward less sensitive solutions. In matrix-sensing experiments, the method reduces paired sensitivity by 18-29 percent for isotropic operators and 87-89 percent for weak-tail operators, without degrading reconstruction accuracy. These results demonstrate that parameter count alone does not determine robustness and identify solution geometry and the optimization trajectory as important levers for improving it.