Related papers: Tensor Networks for Latent Variable Analysis. Part…

In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional geometrical domain in the tensor train format; secondly, to develop a new algorithm…

Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

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…

Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…

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…

Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

We introduce the tubal tensor train (TTT) decomposition, a tensor-network model that combines the t-product algebra of the tensor singular value decomposition (T-SVD) with the low-order core structure of the tensor train (TT) format. For an…

In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…

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…

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA),…

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…

Despite the recent success of deep learning models in numerous applications, their widespread use on mobile devices is seriously impeded by storage and computational requirements. In this paper, we propose a novel network compression method…