TT Decomposition

TT: Tensor Train

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Overview

Tensor-train decomposition (TT) represents a high-dimensional tensor as a sequence of smaller cores joined by rank-bounded links, reducing storage when the data has exploitable low-rank structure. Methods such as TT-SVD and TT-cross construct these representations, while ALS and DMRG optimize their cores or adapt their ranks. Researchers use TT models for high-dimensional PDEs and dynamics, probabilistic inference, signal and image processing, and compression of neural networks. A central challenge is choosing ranks and mode orderings that preserve accuracy: compression and speed depend on the data’s structure, and forcing low rank along poorly compressible modes can degrade results.

Latest papers

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19 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

  1. 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

  2. Tensor-Train Compressed Separable PINNs: A Curvature-Aware Optimization Framework for Parametric PDEs in High Dimensions

    Sep 28, 2026Denis Korolev, Martin EigelNeural PDE SolversPhysics-Informed ML

    Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Anton-Wilhelm-Amo-Straße 39, 10117 Berlin, Germany

  3. 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

  4. A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography

    Sep 8, 2026Shakir Showkat Sofi, Charlotte Vermeylen, Fatemeh Mohammadi +1Quantum State TomographyTT Decomposition

    Leuven.AI - KU Leuven institute for AI, B-3000, Leuven, Belgium · Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium; Group Science, Engineering and Technology, KU Leuven Kulak, Kortrijk, Belgium · Departments of Computer Science and Mathematics, KU Leuven, Leuven, Belgium

  5. TT-net: Quantum Inspired Tensor Network Denoising in Conditional GANs

    Aug 20, 2026Michal A. Sterzel, Marko J. RančićImage DenoisingGenerative Adversarial Networks

    University of Luxembourg, FSTM, Department of Computer Science Campus Belval, 6 Av. de la Fonte, L-4364 Esch-Belval, Esch-sur-Alzette, Luxembourg

  6. Quantum Tensor Network Learning with DMRG

    Aug 19, 2026Gustav J L Jäger, Martin B Plenio, Hans-Martin RieserTensor NetworksQuantum Machine Learning

    Deutsches Zentrum für Luft- und Raumfahrt e.V. – Institut für KI-Sicherheit Wilhelm-Runge-Straße 10, 89081 Ulm, Germany · Universität Ulm – Institut für Theoretische Physik and IQST, Albert-Einstein-Allee 11, 89081 Ulm, Germany

  7. Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling

    Jul 7, 2026Robert Gruhlke, Julius Berner, David Sommer +1Stochastic Differential EquationsDiffusion Sampling

    Freie Universität Berlin · NVIDIA · WIAS +2

  8. Tensor-Train Joint Modeling for Few-Step Discrete Diffusion

    Jul 4, 2026Byoungkwon Kim, Minhyuk SungMasked Diffusion ModelsTensor Decomposition

    KAIST

  9. Online TT-ALS for Streaming Tensor Decomposition with Incremental Orthogonalization

    Jun 30, 2026Hiroki Takeda, Yuto Miyatake, Daisuke FurihataTensor DecompositionTT Decomposition

    Department of Pure and Applied Mathematics, The University of Osaka, Japan · D3 Center, The University of Osaka, Japan

  10. Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity

    Jun 22, 2026Liangsheng He, Chao Song, Tiansheng Chen +2Implicit Neural Representations3D Reconstruction

    State Key Laboratory of Deep Earth Exploration and Imaging College of GeoExploration Science and Technology, Jilin University Changchun, Jilin, 130021, China · State Key Laboratory of DeepChaoEarthSong Exploration and Imaging College of GeoExploration Science and Technology, Jilin University Changchun, Jilin, 130021, China · Petroleum Exploration and Production Research Institute, Sinopec Beijing, 100083, China

  11. In-Context Graphical Inference

    Jun 3, 2026Zehua Cheng, Wei Dai, Jiahao SunAmortized InferenceProbabilistic Graphical Models

    Department of Computer Science, University of Oxford, Oxford, United Kingdom · FLock.io, London, United Kingdom

  12. Tensor-based computation of the Koopman generator via operator logarithm

    Apr 9, 2026Tatsuya Kishimoto, Jun OhkuboKoopman Operator LearningNonlinear System Identification

    Graduate School of Science and Engineering, Saitama University 255 Shimo-Okubo, Sakura-ku, Saitama 338–8570, Japan

  13. A Tensor-Train Framework for Bayesian Inference in High-Dimensional Systems: Applications to MIMO Detection and Channel Decoding

    Apr 7, 2026Luca Schmid, Dominik Sulz, Shrinivas Chimmalgi +1Bayesian InferenceEfficient Inference

    Communications Engineering Lab (CEL), Karlsruhe Institute of Technology (KIT), Hertzstr. 16, 76187 Karlsruhe, Germany · Technical University of Munich (TUM), Boltzmannstr. 3, 85748 Garching b. München, Germany · Qoherent, Toronto, ON, Canada

  14. Compressing Transformer Language Models via Matrix Product Operator Decomposition: A Case Study on PicoGPT

    Mar 30, 2026Younes Javanmard, Tanmoy Pandit, Masoud MardaniModel CompressionTensor Decomposition

    Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany · VTT Technical Research Centre of Finland, Tietotie 3, Espoo, Finland · National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA

  15. STN-GPR: A Singularity Tensor Network Framework for Efficient Option Pricing

    Mar 27, 2026Dominic Gribben, Carolina Allende, Alba Villarino +5Surrogate ModelingGaussian Process Regression

    Multiverse Computing, Paseo de Miramón 170, 20014 San Sebastián, Spain · Multiverse Computing, rue de la Croix Martre, 91120 Palaiseau, France · DIPC, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain +2

  16. High-Resolution Tensor-Network Fourier Methods for Exponentially Compressed Non-Gaussian Aggregate Distributions

    Mar 24, 2026Juan José Rodríguez-Aldavero, Juan José García-RipollLow-Rank CompressionTT Decomposition

    Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain

  17. A New Tensor Network: Tubal Tensor Train and Its Applications

    Mar 11, 2026Salman Ahmadi-Asl, Valentin Leplat, Anh-Huy Phan +1Tensor DecompositionTT Decomposition

    Lab of Machine Learning and Knowledge Representation, Innopolis University, Innopolis, Russia · Innopolis University, Innopolis, Russia · Skolkovo Institute of Science and Technology, Center for Artificial Intelligence Technology, Moscow, Russia +1

  18. Monte Carlo Tree Search with Tensor Factorization for Optimization Problems in Robotics

    Jul 7, 2025Teng Xue, Yan Zhang, Amirreza Razmjoo +1Monte Carlo Tree SearchTT Decomposition

    Idiap Research Institute, Martigny, Switzerland · École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

  19. MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning

    Jun 10, 2025Javier Lopez-Piqueres, Pranav Deshpande, Archan Ray +3TransformerTensor Decomposition

    Global Technology Applied Research, JPMorgan Chase, New York, NY 10001, USA