Related papers: M\'ethodes de calcul avec r\'eseaux de tenseurs en…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed…
Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
Infinite projected entangled-pair states (iPEPS) provide a powerful tool for studying strongly correlated systems directly in the thermodynamic limit. A core component of the algorithm is the approximate contraction of the iPEPS, where the…
This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…
We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions…
Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a…
Tensors (also commonly seen as multi-linear operators or as multi-dimensional arrays) are ubiquitous in scientific computing and in data science, and so are the software efforts for tensor operations. Particularly in recent years, we have…
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…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
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…
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…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…