English
Related papers

Related papers: A New Tensor Network: Tubal Tensor Train and Its A…

200 papers

We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…

Numerical Analysis · Mathematics 2022-10-18 Saibal De , Eduardo Corona , Paramsothy Jayakumar , Shravan Veerapaneni

Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…

Machine Learning · Computer Science 2021-11-03 Cole Hawkins , Haichuan Yang , Meng Li , Liangzhen Lai , Vikas Chandra

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Information Theory · Computer Science 2016-02-18 Holger Rauhut , Reinhold Schneider , Zeljka Stojanac

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

Numerical Analysis · Mathematics 2019-05-20 Rachel Minster , Arvind K. Saibaba , Misha E. Kilmer

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Numerical Analysis · Computer Science 2016-08-24 Linxiao Yang , Jun Fang , Hongbin Li , Bing Zeng

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

Numerical Analysis · Mathematics 2025-10-16 Yani Feng , Michael K. Ng , Kejun Tang , Zhiwen Zhang

This work focuses on designing low complexity hybrid tensor networks by considering trade-offs between the model complexity and practical performance. Firstly, we exploit a low-rank tensor-train deep neural network (TT-DNN) to build an…

Machine Learning · Computer Science 2022-03-14 Jun Qi , Chao-Han Huck Yang , Pin-Yu Chen , Javier Tejedor

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

Machine Learning · Statistics 2018-12-11 Jiahao Su , Jingling Li , Bobby Bhattacharjee , Furong Huang

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

Computer Vision and Pattern Recognition · Computer Science 2020-08-13 Anh-Huy Phan , Konstantin Sobolev , Konstantin Sozykin , Dmitry Ermilov , Julia Gusak , Petr Tichavsky , Valeriy Glukhov , Ivan Oseledets , Andrzej Cichocki

In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…

Numerical Analysis · Mathematics 2020-03-03 Liqun Qi , Yannan Chen , Mayank Bakshi , Xinzhen Zhang

Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data…

Machine Learning · Statistics 2026-02-17 Tong Wu

The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…

Numerical Analysis · Computer Science 2015-06-19 A. Cichocki , D. Mandic , A-H. Phan , C. Caiafa , G. Zhou , Q. Zhao , L. De Lathauwer

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

Numerical Analysis · Mathematics 2018-12-13 Alex A. Gorodetsky , Sertac Karaman , Youssef M. Marzouk

We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor train (TT) decompositions, we propose new sequential learning methods for…

Numerical Analysis · Mathematics 2024-07-04 Yiran Zhao , Tiangang Cui

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…

Neural Network designs are quite diverse, from VGG-style to ResNet-style, and from Convolutional Neural Networks to Transformers. Towards the design of efficient accelerators, many works have adopted a dataflow-based, inter-layer pipelined…

Machine Learning · Computer Science 2023-06-23 Zhewen Yu , Christos-Savvas Bouganis

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…

Machine Learning · Computer Science 2015-09-17 Guoxu Zhou , Andrzej Cichocki , Qibin Zhao , Shengli Xie

Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random…

Machine Learning · Computer Science 2022-02-04 Beheshteh T. Rakhshan , Guillaume Rabusseau

The ability to learn compact, high-quality, and easy-to-optimize representations for visual data is paramount to many applications such as novel view synthesis and 3D reconstruction. Recent work has shown substantial success in using tensor…

Computer Vision and Pattern Recognition · Computer Science 2024-06-07 Sebastian Loeschcke , Dan Wang , Christian Leth-Espensen , Serge Belongie , Michael J. Kastoryano , Sagie Benaim

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…

Numerical Analysis · Mathematics 2024-12-20 Longhao Yuan , Chao Li , Jianting Cao , Qibin Zhao