Related papers: High-Performance Tensor Contraction without Transp…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…

Tensor Compressive Sensing (TCS) is a multidimensional framework of Compressive Sensing (CS), and it is advantageous in terms of reducing the amount of storage, easing hardware implementations and preserving multidimensional structures of…

Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional…

Transformer-based models are becoming deeper and larger recently. For better scalability, an underlying training solution in industry is to split billions of parameters (tensors) into many tasks and then run them across homogeneous…

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…

Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, long-horizon…

We approach the problem of implementing mixed-datatype support within the general matrix multiplication (GEMM) operation of the BLIS framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or…

Tensor networks (TNs) are a central computational tool in quantum science and artificial intelligence. However, the lack of unified software interface across tensor-computing frameworks severely limits the portability of TN applications,…

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…

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor…

Tensor processing units (TPUs) are one of the most well-known machine learning (ML) accelerators utilized at large scale in data centers as well as in tiny ML applications. TPUs offer several improvements and advantages over conventional ML…

Tsetlin machine (TM) is a logic-based machine learning approach with the crucial advantages of being transparent and hardware-friendly. While TMs match or surpass deep learning accuracy for an increasing number of applications, large clause…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

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…

Tabular data is the primary data format in industrial relational databases, underpinning modern data analytics and decision-making. However, the increasing scale of tabular data poses significant computational and storage challenges to…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…