Related papers: Rademacher Random Projections with Tensor Networks

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

Tensor train (TT) decomposition, a powerful tool for analyzing multidimensional data, exhibits superior performance in many machine learning tasks. However, existing methods for TT decomposition either suffer from noise overfitting, or…

Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…

Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…

In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…

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…

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…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

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…

Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…

Joint probability mass function (PMF) estimation is a fundamental machine learning problem. The number of free parameters scales exponentially with respect to the number of random variables. Hence, most work on nonparametric PMF estimation…

In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…

The memory capacity of embedding tables in deep learning recommendation models (DLRMs) is increasing dramatically from tens of GBs to TBs across the industry. Given the fast growth in DLRMs, novel solutions are urgently needed, in order to…

We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats. We use alternating projections between the nonnegative orthant and the set of low-rank tensors, using STHOSVD and TTSVD…

A novel tensor decomposition framework, termed Tensor Star (TS) decomposition, is proposed which represents a new type of tensor network decomposition based on tensor contractions. This is achieved by connecting the core tensors in a ring…