Tensor Decomposition

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Overview

Tensor decomposition studies how to represent multidimensional data using simpler factors, making patterns easier to analyze and large data or models cheaper to store and process. Common approaches include CP and Tucker factorization, tensor trains and matrix product states, and t-SVD, used for tasks such as missing-data recovery, anomaly detection, scientific modeling, and neural-network compression. Current work combines these methods with Bayesian rank selection, adaptive optimization, pretrained or neural priors, and theoretical analyses of recovery and identifiability. A central tension is choosing a factorization and rank that capture useful structure without imposing unrealistic shared-subspace or ordering assumptions, while balancing accuracy, robustness, and computational cost.

Latest papers

CardsList

70 papers10 papers in the last four weeks, up 11% on the four weeks before. 0.1% of all new papers.

  1. Kronecker-Structured Video Completion with Cross-Fitted Self-Supervised Residual Learning

    Oct 26, 2026Qi Qi, Yanfei Wang, Yanjun Cui +1Tensor DecompositionResidual Learning

    Mathematical Research Center, Shandong University, Jinan 250100, China · School of Mathematics, Shandong University, Jinan 250100, China · Dartmouth College, Hanover, NH 03755, USA +1

  2. Making Tensor Decoupling More Robust and Less Parametric

    Oct 12, 2026Maxime Rochkoulets, Joppe De Jonghe, Mariya IshtevaTensor DecompositionNonparametric Regression

    Department of Computer Science, KU Leuven, Belgium · Department of Computer Science, NUMA, KU Leuven, 2440 Geel, Belgium

  3. Tensor-based Fusion of Multi-modal Data for Predicting Cancer Risk Levels

    Oct 9, 2026Ali Anaissi, Yuanzhe Jia, Qishun Peng +3Clinical Risk PredictionMultimodal Fusion

    University of Sydney, Australia · University of Technology Sydney, Australia · University of New South Wales, Australia

  4. Low-rank tensor structure of precipitation and its application to satellite-reference merging

    Oct 7, 2026Ryan Solgi, Rohan Shankar, Hugo A. LoaicigaLow-Rank ApproximationRemote Sensing

    Department of Geography, University of California-Santa Barbara, CA, USA · Department of Electrical and Computer Engineering, University of California-Santa Barbara, CA, USA · Department of Computer Science, Cornell University, NY, USA

  5. Activation-Aware Weight Tensorization: A Calibration-Time Preconditioner for Tensor-Network LLM Compression

    Oct 7, 2026Alessandro Beatini, Marco Maronese, Emanuele RodolàLLM CompressionTensor Networks

    Sapienza University of Rome · Independent Researcher

  6. Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization

    Oct 4, 2026Weiguo Zhou, Feng Zhang, Wenjin Qin +1Tensor CompletionNuclear Norm Minimization

    School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China · College of Artificial Intelligence and Advanced Interdisciplinary Sciences, Chongqing Normal University, Chongqing, 401331, China

  7. Low-Rank and Structured Sparse Tensor Decomposition for Anomaly Detection in Multivariate Functional Data

    Oct 3, 2026Mohammad N. Bisheh, Che-Yi Liao, Kamran PaynabarAnomaly DetectionIndustrial Anomaly Detection

    School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA · Stewart School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA

  8. ITC-MoE: Importance-guided Token-aware Compression for MoE Diffusion Language Models

    Oct 1, 2026Lianjun Liu, Shipeng Li, You Huang +5Tucker DecompositionMixture-of-Experts Language Models

    Hainan University, Haikou, China · Xiamen University, Xiamen, China · Zhejiang Normal University, Jinhua, China

  9. Sequential Functional Structured Tucker Compression for Large Language Model Attentions

    Sep 30, 2026Jiangfeng Chen, Xinyu Wang, Tianshuo Yan +4Tucker DecompositionLLM Compression

    University of Manitoba · McGill University · Simpleway +2

  10. Heteroskedastic Canonical Polyadic Tensor Decomposition

    Sep 30, 2026Kyle Ritscher, Carlos Llosa-ViteTensor Decomposition

    Computer Science Research Institute, Sandia National Laboratories, Albuquerque, NM · Department of Statistics & Data Science, University of California, Los Angeles, CA

  11. Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing

    Sep 29, 2026Eugene Agyei-Kodie, Longxiu Huang, Shuang Li +1Nonconvex OptimizationOptimization Convergence Analysis

    Department of Mathematics, Michigan State University, 619 Red Cedar, East Lansing, 48824, MI, USA. · Department of Computational Mathematics, Science and Engineering, Michigan State University, 428 S Shaw Ln, East Lansing, 48824, MI, USA. · Department of Electrical and Computer Engineering, Iowa State University, 2520 Osborn Dr, Ames, 50011, IA, USA.

  12. Tensor Decomposition of Transformer Key-Value Caches: Spectral Structure and Format Comparison

    Sep 23, 2026Rahul Krishnan, Volker SchulzTucker DecompositionTensor Decomposition

    Universität Trier · Fachbereich IV, Mathematik, Universität Trier

  13. Guaranteed Low-Rank Tensor Recovery from Modewise Measurements via Normalized Block-Weighted Riemannian Gradient Descent

    Sep 21, 2026Yushi Zhou, Feng ZhangRiemannian OptimizationTensor Decomposition

    School of Mathematics and Statistics, Southwest University, Chongqing, China.

  14. On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks

    Sep 20, 2026Sagad Hamid, Tanya BraunEfficient InferenceProbabilistic Graphical Models

    Computer Science Department, University of Münster, Münster, Germany

  15. Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization

    Sep 13, 2026Binghao Wang, Feng Zhang, Wendong Wang +1Tensor CompletionTensor Decomposition

    School of Mathematics and Statistics, Southwest University, Chongqing 400715, China · College of Artificial Intelligence, Southwest University, Chongqing 400715, China

  16. Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recovery

    Sep 11, 2026Bing-Zhang Fu, Zhi-Long Han, Ting-Zhu Huang +2Low-Rank Matrix DecompositionTensor Decomposition

    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Mathematics and Statistics and Ministry of Education Key Lab of Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China · Pazhou Laboratory (Huangpu), Guangzhou, Guangdong 510335, China

  17. Identifiability of Nonnegative Tensor Decompositions via Positive Scattering

    Sep 10, 2026Haoming Wang, Ming YuanNon-Negative Matrix FactorizationTensor Decomposition

    Columbia University

  18. Semi-Tensor Product-Based Multi-Term Randomized T-SVD and Its Visual Applications

    Sep 10, 2026Xingchen Xiao, Feng Zhang, Wenjin Qin +1Tensor CompletionTensor Decomposition

    School of Mathematics and Statistics, Southwest University, Chongqing, China

  19. Hyperspectral Anomaly Detection via Group Sparse Low-Rank Tensor Factorization With Automatic Anomaly Grouping

    Sep 8, 2026Quan Yu, Yu-Hong Dai, Xiongjun ZhangLow-Rank Matrix DecompositionTensor Decomposition

    School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China, and also with the Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Central China Normal University · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

  20. Coupled Tensor-Tensor Completion Method with Applications in Drug Repurposing

    Sep 2, 2026Maryam Bagherian, Albert Hung, Ivo Dinov +1Tensor CompletionLearning with Missing Data

    Department of Mathematics & Statistics, Idaho State University, Physical Science Complex — 921 S. 8th Ave., Stop 8085 — Pocatello, ID 83209 · Computer Science & Artificial Intelligence Laboratory, Massachusetts Institute of Technology · Department of Computational Medicine & Bioinformatics, University of Michigan, Ann Arbor +2

  21. A Multi-View Coupled Tensor Decomposition for Lightweight Online Adaptive Traffic Prediction

    Aug 26, 2026Quan Yu, Jie Ni, Yu-Hong Dai +1Traffic ForecastingSpatiotemporal Forecasting

    School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China, and also with the Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Central China Normal University · School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China +1

  22. Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations

    Aug 13, 2026Gaute Johannessen, Geert Roelof van der Ploeg, Evrim AcarTensor DecompositionScientific ML

    Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo · Department of Data Science and Knowledge Discovery, Simula Metropolitan Center for Digital Engineering, Oslo

  23. Hierarchical rank-evolving representation for physics-informed neural networks

    Aug 10, 2026Ruoyang Su, Xi-Le Zhao, Kun Li +1Tensor NetworksNeural PDE Solvers

    University of Electronic Science and Technology of China, No.2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu, 611731, Sichuan, P.R.China · Southwestern University of Finance and Economics, 555, Liutai Avenue, Wenjiang District, Chengdu, 611130, Sichuan, P.R.China

  24. Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling

    Aug 4, 2026HanQin Cai, Longxiu Huang, Jing Qin +1Tensor CompletionTensor Decomposition

    School of Data, Mathematical, and Statistical Sciences and Department of Computer Science, University of Central Florida, Orlando, FL 32816, USA · Department of Computational Mathematics, Science, and Engineering and Department of Mathematics, Michigan State University, East Lansing, MI 48840, USA · Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA +1

  25. Smooth Reparameterizations of Functions on Simplicial Product Spaces: Applications to Probabilistic Tensor Decomposition and Functional Data Registration

    Aug 3, 2026Shashwat Kumar, Arafat Rahman, Anuj Srivastava +1Riemannian OptimizationTensor Decomposition

    Department of Biomedical Engineering, Johns Hopkins University, USA · Department of Systems and Information Engineering, University of Virginia, USA · Department of Applied Mathematics and Statistics, Johns Hopkins University, USA +1

  26. Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning

    Jul 28, 2026Jintian Ji, Xingsu Li, Songhe FengRepresentation LearningMulti-View Learning

    Computer Science and Engineering The Hong Kong University of Science and Technology Hong Kong, China · School of Computer and Information Technology Beijing Jiaotong University, Beijing, China

  27. Leakage and Multiway Interaction Loss: What Matricization and Single-Mode Truncation Discard from Multiway Signals

    Jul 27, 2026Hiroki HasegawaTensor DecompositionLow-Rank Approximation

    Graduate School of Science and Technology, University of Tsukuba, Tsukuba, 305-8573, Japan

  28. Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis

    Jul 24, 2026Laura M. Montaldo, Ricardo A. Borsoi, Sebastian Miron +1Latent Dynamics ModelingFunctional Magnetic Resonance Imaging

    CRAN, Université de Lorraine, CNRS, Vandoeuvre-l`es-Nancy, France. · Department of CSEE, University of Maryland Baltimore County, Baltimore, MD 21250, USA.

  29. (MPO)2^2: Multivariate Polynomial Optimization based on Matrix Product Operators

    Jul 17, 2026Niccolò Ciolli, Anders Vestergaard Nørskov, Michael Kastoryano +2Tensor NetworksTensor Decomposition

  30. Factorized Spectral Representations for Reinforcement Learning

    Jul 15, 2026Junyi Wu, Dan LiTensor DecompositionRepresentation Learning for RL

    Department of Industrial and Systems Engineering University of Washington Seattle, WA, USA