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Related papers: Adaptive Patching for Tensor Train Computations

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We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

Numerical Analysis · Mathematics 2025-12-23 Martin Eigel , Charles Miranda , Anthony Nouy , David Sommer

We are concerned with the computation of the mean-time-to-absorption (MTTA) for a large system of loosely interconnected components, modeled as continuous time Markov chains. In particular, we show that splitting the local and…

Numerical Analysis · Mathematics 2019-07-05 Leonardo Robol , Giulio Masetti

Tensor cross interpolation (TCI) is a powerful technique for learning a tensor train (TT) by adaptively sampling a target tensor based on an interpolation formula. However, when the tensor evaluations contain random noise, optimizing the TT…

Quantum Physics · Physics 2025-08-15 Kohtaroh Sakaue , Hiroshi Shinaoka , Rihito Sakurai

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…

Strongly Correlated Electrons · Physics 2017-07-24 Z. Y. Xie , H. J. Liao , R. Z. Huang , H. D. Xie , J. Chen , Z. Y. Liu , T. Xiang

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…

Numerical Analysis · Mathematics 2015-05-27 Christian Lubich , Ivan Oseledets , Bart Vandereycken

Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current…

We propose a new method for the efficient approximation of a class of highly oscillatory weighted integrals where the oscillatory function depends on the frequency parameter $\omega \geq 0$, typically varying in a large interval. Our…

Numerical Analysis · Mathematics 2015-03-25 Boris Khoromskij , Alexander Veit

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

Numerical Analysis · Computer Science 2014-08-25 Andrzej Cichocki

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

Numerical Analysis · Mathematics 2021-09-08 Hussam Al Daas , Grey Ballard , Peter Benner

Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…

Strongly Correlated Electrons · Physics 2025-12-19 Stefan Rohshap , Jheng-Wei Li , Alena Lorenz , Serap Hasil , Karsten Held , Anna Kauch , Markus Wallerberger

Quantum Neural Networks (QNNs) offer promising capabilities for complex data tasks, but are often constrained by limited qubit resources and high entanglement, which can hinder scalability and efficiency. In this paper, we introduce…

Quantum Physics · Physics 2025-03-31 Mohamed Afane , Gabrielle Ebbrecht , Ying Wang , Juntao Chen , Junaid Farooq

The application of Tensor Networks (TN) in quantum computing has shown promise, particularly for data loading. However, the assumption that data is readily available often renders the integration of TN techniques into Quantum Monte Carlo…

This study explores the quantisation-aware training (QAT) on time series Transformer models. We propose a novel adaptive quantisation scheme that dynamically selects between symmetric and asymmetric schemes during the QAT phase. Our…

Machine Learning · Computer Science 2023-10-05 Tianheng Ling , Chao Qian , Lukas Einhaus , Gregor Schiele

Elastic precision quantization enables multi-bit deployment via a single optimization pass, fitting diverse quantization scenarios.Yet, the high storage and optimization costs associated with the Transformer architecture, research on…

Computer Vision and Pattern Recognition · Computer Science 2026-02-16 Ke Xu , Yixin Wang , Zhongcheng Li , Hao Cui , Jinshui Hu , Xingyi Zhang

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Machine Learning · Statistics 2017-08-03 Masaaki Imaizumi , Takanori Maehara , Kohei Hayashi

Large language models (LLMs) demand substantial computational and memory resources, posing challenges for efficient deployment. Two complementary approaches have emerged to address these issues: token-adaptive layer execution, which reduces…

Machine Learning · Computer Science 2026-02-26 Kanghyun Noh , Jinheon Choi , Yulhwa Kim

We present MetaTT, a Tensor Train (TT) adapter framework for fine-tuning of pre-trained transformers. MetaTT enables flexible and parameter-efficient model adaptation by using a single shared TT to factorize transformer sub-modules. This…

Machine Learning · Computer Science 2025-11-18 Javier Lopez-Piqueres , Pranav Deshpande , Archan Ray , Mattia J. Villani , Marco Pistoia , Niraj Kumar

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Numerical Analysis · Mathematics 2026-02-10 Daniel Hayes , Jing-Mei Qiu , Tianyi Shi

Quantum computers face inherent scaling challenges, a fact that necessitates investigation of distributed quantum computing systems, whereby scaling is achieved through interconnection of smaller quantum processing units. However,…

Quantum Physics · Physics 2026-01-21 Felix Burt , Kuan-Cheng Chen , Kin K. Leung

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

Numerical Analysis · Mathematics 2021-09-09 Ilya Kisil , Giuseppe G. Calvi , Kriton Konstantinidis , Yao Lei Xu , Danilo P. Mandic