Related papers: Solving Tensor Structured Problems with Computatio…

Solving linear systems of equations is a fundamental problem in mathematics. When the linear system is so large that it cannot be loaded into memory at once, iterative methods such as the randomized Kaczmarz method excel. Here, we extend…

Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…

We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…

Dedicated tensor accelerators demonstrate the importance of linear algebra in modern applications. Such accelerators have the potential for impressive performance gains, but require programmers to rewrite code using vendor APIs - a barrier…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

Over the last few decades, many distinct lines of research aimed at automating mathematics have been developed, including computer algebra systems (CASs) for mathematical modelling, automated theorem provers for first-order logic, SAT/SMT…

A novel tensor-based formula for solving the linear systems involving Kronecker sum is proposed. Such systems are directly related to the matrix and tensor forms of Sylvester equation. The new tensor-based formula demonstrates the…

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detection of clusters of data in the presence of structural…

Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…

We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…

Despite the omnipresence of tensors and tensor operations in modern deep learning, the use of tensor mathematics to formally design and describe neural networks is still under-explored within the deep learning community. To this end, we…

Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…

We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on toric varieties and basic linear algebra; eigenvalues, eigenvectors and coefficient matrices. We adapt Eigenvalue theorem and Eigenvector…

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…