Related papers: Rank Estimation for Third-Order Tensor Completion …

Tensor network methods have been a key ingredient of advances in condensed matter physics and have recently sparked interest in the machine learning community for their ability to compactly represent very high-dimensional objects. Tensor…

Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…

In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples,…

We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor…

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN)…

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…

We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems. The error bound is obtained from…

The determination of the maximal ranks of a set of a given type of tensors is a basic problem both in theory and application. In statistical applications, the maximal rank is related to the number of necessary parameters to be built in a…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

Functional tensor decomposition can analyze multi-dimensional data with real-valued indices, paving the path for applications in machine learning and signal processing. A limitation of existing approaches is the assumption that the tensor…

We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…

While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…