Tensor Networks

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Overview

Tensor networks study how to represent large arrays, probability distributions, quantum states, and neural-network parameters as networks of smaller tensors linked by bond indices. Common forms such as matrix product states, tree tensor networks, and matrix product operators support compression, inference, scientific computing, and quantum-circuit simulation by exploiting low-rank structure. Researchers develop rank-selection and contraction algorithms alongside learning methods, including Riemannian optimization, tensorized neural networks, and hardware-aware implementations. A central tension is that compact representations can reduce memory and computation, but their accuracy and practical speed depend on the data’s structure, the chosen network geometry, and the costs of training and contraction.

Latest papers

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50 papers5 papers in the last four weeks, down 29% on the four weeks before. 0.0% of all new papers.

  1. Tensor Network Datamodels for Training Data Attribution

    Oct 17, 2026Farzaneh Heidari, Md Rifat Arefin, Louis Jaburi +1Training Data AttributionTensor Networks

    Mila – Quebec AI Institute · DIRO, Université de Montréal · EleutherAI +1

  2. 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

  3. Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning

    Oct 5, 2026Shi-Tuan Wang, Zidu Liu, Li-Wei YuTensor NetworksGaussian Processes

    Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China · Max Planck Institute of Quantum Optics, 85748 Garching, Germany

  4. Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity

    Sep 30, 2026Eftychios Protopapadakis, Konstantinos Makantasis, Konstantinos M. GiannoutakisTensor NetworksPrototype Learning

    Department of Applied Informatics, University of Macedonia, 156 Egnatia Street, 54636 Thessaloniki, Greece · Department of Artificial Intelligence, Faculty of Information & Communication Technology, University of Malta, Msida, Malta

  5. Pre-registered tests of solid-state-physics-inspired LLM compression: a cluster-level negative result at small-language-model scale

    Sep 28, 2026Jun-qiang LuTensor NetworksLLM Compression

    Department of Physics, University of Puerto Rico, Mayagüez, PR 00680, USA

  6. 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

  7. Quantum-Inspired Trainable and Parameter-Efficient Tensor Networks for Image Inpainting

    Sep 15, 2026Shiwen An, Konstantinos SlavakisTensor NetworksQuantum-Inspired ML

    Institute of Science Tokyo, Department of Information and Communications Engineering, Yokohama, Japan

  8. Benign Loss Landscapes Can Coexist with Worst-Case Hardness

    Sep 11, 2026Zach Furman, Stephan Wäldchen, Yangda Bei +1Tensor NetworksStatistical Learning Theory

    University of Melbourne · Iliad

  9. Tensor Network Moral Graph Recovery of Discrete Probability Distributions

    Sep 8, 2026Á. Troyano Olivas, Chi-Hang Fred Fung, Hans H. Brunner +2Tensor NetworksGraph Structure Learning

    Heisenberg Research Center (Munich), Huawei Technologies Duesseldorf GmbH, Germany · Center for Computational Simulation, Universidad Politécnica de Madrid, Madrid, Spain

  10. Tensor network representations of discrete maximum entropy distributions via mean polytopes

    Sep 7, 2026Alex Goessmann, Martin EigelTensor NetworksExponential Family

    Weierstrass Institute of Applied Analysis and Stochastics Anton-Wilhelm-Amo-Straße 39 Berlin, 10117, Germany

  11. Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography

    Sep 3, 2026Matthias C. Caro, Natalie McHugh, Sergii StrelchukTensor NetworksQuantum State Tomography

    Department of Computer Science, University of Warwick, Coventry, UK · Department of Computer Science, University of Oxford, Oxford, UK

  12. Stochastic Optimization of Tree Tensor Networks

    Sep 1, 2026Marius Willner, Maximilian Scharf, André Uschmajew +2Tensor NetworksRiemannian Optimization

    Institute of Mathematics, University of Augsburg, 86159 Augsburg, Germany · Centre for Advanced Analytics and Predictive Sciences, University of Augsburg, 86159 Augsburg, Germany · Tensor AI Solutions GmbH, 89284 Pfaffenhofen an der Roth, Germany +1

  13. 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

  14. Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions

    Aug 17, 2026Xiao Wang, Tomohiro Hashizume, Pia Siegl +1Tensor Networks

    Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom · The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg 22761, Germany. · Institute for Quantum Physics, University of Hamburg, Luruper Chaussee 149, Hamburg 22761, Germany +1

  15. Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians

    Aug 12, 2026Timothy Heightman, Elena Orlova, Philip Mantrov +1Tensor NetworksNeural Quantum States

    1ICFO – Institut de Ci`encies Fot`oniques, The Barcelona Institute of Science and Technology · Castelldefels, Barcelona, Spain · 2Simulacra Research Inc., London, UK & Chicago, USA

  16. sLTN: Structural Logic Tensor Networks

    Aug 11, 2026Davide Rinaldi, Luciano SerafiniTensor NetworksLogic Tensor Networks

    Nokia Bell Labs · Fondazione Bruno Kessler

  17. 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

  18. Tensor Network Kernel Machines: A JAX Framework for Machine Learning and Nonlinear System Identification

    Aug 7, 2026Albert Saiapin, Kim BatselierTensor NetworksNonlinear System Identification

    Delft Center for Systems and Control, TU Delft, Netherlands

  19. Learning to Rank Tensor Network Contraction Plans for GPU-Accelerated Quantum Circuit Simulation

    Aug 6, 2026Alfred M. Pastor, Maribel Castillo, Jose M. BadiaTensor NetworksLearning to Rank

    Department of Computer Science, Universitat de València, 46100 Burjassot, Spain · Department of Computer Science and Engineering, Universitat Jaume I, 12071 Castelló de la Plana, Spain

  20. Tensor Network Machine Learning for Wildfire Susceptibility Mapping: from Grokking Dynamics to Quantum Mixedness of Class Representations

    Jul 21, 2026Domenico Pomarico, Alessandra Costantino, Gabriel Ramirez Sanchez +12Tensor NetworksNeural Network Interpretability

    1Dipartimento Interuniversitario di Fisica, Universit`a degli Studi di Bari Aldo Moro, Bari, I-70126, Italy · 2Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Bari, I-70126, Italy · 3Dipartimento di Biomedicina Traslazionale e Neuroscienze (DiBraiN), Universit`a degli Studi di Bari Aldo Moro, Bari, I-70124, Italy +2

  21. Entanglement geometry separates circuit cutting, classical hardness, and trainability

    Jul 20, 2026Maria Gragera Garces, Sabina Drăgoi, Lirandë PiraTensor NetworksQuantum Circuit Simulation

    Quantum Software Lab University of Edinburgh, UK · ETH ZÜrich, ZÜrich, Switzerland IBM Research, RÜschlikon, Switzerland · Centre for Quantum Technologies, National University of Singapore, Singapore

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

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

  23. Multi-agent Autoformalization of Tensor Network Theory

    Jul 8, 2026Sirui Lu, Erickson Tjoa, J. Ignacio CiracTensor NetworksMulti-Agent LLM Systems

    Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany · Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 Munich, Germany

  24. Entropy-Guided Tensor Compression for Multimodal Federated Learning on Edge Devices

    Jul 7, 2026Quoc Bao Phan, Tuy Tan NguyenTensor NetworksMultimodal Federated Learning

    Department of Electrical and Computer Engineering, Center for Advanced Power Systems, FAMU-FSU College of Engineering, Florida State University, Tallahassee, FL 32310, USA

  25. First-Order Temporal Logic Tensor Networks

    Jun 29, 2026Luca Boscarato, Ivan Donadello, Alessandro Artale +2Tensor NetworksLogic Tensor Networks

    Free University of Bozen-Bolzano

  26. fTNN: a tensor neural network for fractional PDEs

    Jun 25, 2026Qingkui Ma, Hehu Xie, Xiaobo YinTensor NetworksNeural PDE Solvers

    School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China · SKLMS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No.55, Zhongguancun Donglu, Beijing 100190, China · School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China +1

  27. Stochastic trace estimation with tensor train random vectors

    Jun 14, 2026Zvonimir Bujanović, Daniel Kressner, Hrvoje OlićTensor NetworksRandomized Sketching

    University of Zagreb, Faculty of Science, Department of Mathematics, Croatia. · Institute of Mathematics, EPFL, Switzerland.

  28. Family-Aware Residual Architecture for Predicting Quantum Circuit Simulation Performance

    Jun 10, 2026Honjar Xing, Yehong Jiang, Xianbang Wang +2Tensor NetworksQuantum Circuit Simulation

    Massachusetts Institute of Technology Cambridge, MA 02139, USA

  29. EinSort: Sorting is All We Need for Tensorizing LLM

    Jun 7, 2026Toshiaki Koike-Akino, Jing Liu, Ye WangTensor NetworksLLM Compression

    Mitsubishi Electric Research Laboratories (MERL), 20 Broadway, Cambridge, MA 02139, USA.

  30. Algorithmic algorithm development with LLMs: A Case Study on LLM-Usage for Contraction Order Optimization in Tensor Networks

    Jun 1, 2026Fabian Hoppe, Melven Röhrig-Zöllner, Philipp KnechtgesTensor NetworksAutomated Algorithm Discovery

    German Aerospace Center (DLR), Institute of Software Technology, department High-Performance Computing, Cologne (Germany)