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Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

This paper deals with the state estimation of stochastic systems and examines the possible employment of tensor decompositions in grid-based filtering routines, in particular, the tensor-train decomposition. The aim is to show that these…

In the present work, the Tensor-Train decomposition algorithm is applied to reduce the memory footprint of a stochastic discrete velocity solver for rarefied gas dynamics simulation. An energy-conserving modification to the algorithm is…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

We present an alternative approach to decompose non-negative tensors, called many-body approximation. Traditional decomposition methods assume low-rankness in the representation, resulting in difficulties in global optimization and target…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…

In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…

We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

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…

Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…

Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to…

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…