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Candecomp / PARAFAC (CP) decomposition, a generalization of the matrix singular value decomposition to higher-dimensional tensors, is a popular tool for analyzing multidimensional sparse data. On tensors with billions of nonzero entries,…

The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…

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…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the…

Sparse Tensor Cores offer exceptional performance gains for AI workloads by exploiting structured 2:4 sparsity. However, their potential remains untapped for core scientific workloads such as stencil computations, which exhibit irregular…

In this paper, we consider the completely positive tensor decomposition problem with ideal-sparsity. First, we propose an algorithm to generate the maximal cliques of multi-hypergraphs associated with completely positive tensors. This also…

The Canonical Polyadic (CP) tensor decomposition is a well-known method for interpretable analysis of high-dimensional data. Recently, the Generalized CP method (GCP) was introduced by Hong and Kolda to allow for flexible choice of the loss…

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…

Driven by deep learning, there has been a surge of specialized processors for matrix multiplication, referred to as TensorCore Units (TCUs). These TCUs are capable of performing matrix multiplications on small matrices (usually 4x4 or…

We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global…

In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…

Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

Recurrent neural networks (RNNs) are powerful in the tasks oriented to sequential data, such as natural language processing and video recognition. However, since the modern RNNs, including long-short term memory (LSTM) and gated recurrent…

Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…