相关论文: Communication Lower Bounds for Matricized Tensor T…

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

The matricized-tensor times Khatri-Rao product (MTTKRP) is the computational bottleneck for algorithms computing CP decompositions of tensors. In this paper, we develop shared-memory parallel algorithms for MTTKRP involving dense tensors.…

We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…

We give lower bounds on the communication complexity required to solve several computational problems in a distributed-memory parallel machine, namely standard matrix multiplication, stencil computations, comparison sorting, and the Fast…

Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has…

Tensor decomposition has become an essential tool in many applications in various domains, including machine learning. Sparse Matricized Tensor Times Khatri-Rao Product (MTTKRP) is one of the most computationally expensive kernels in tensor…

In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a $3$-dimensional symmetric tensor. This is a key computation in the higher-order power method for determining eigenpairs of a…

In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…

Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…

Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP) is the bottleneck kernel of sparse tensor decomposition. In this work, we propose a GPU-based algorithm design to address the key challenges in accelerating spMTTKRP computation,…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP) is the most time-consuming compute kernel in sparse tensor decomposition. In this paper, we introduce a novel algorithm to minimize the execution time of spMTTKRP across all modes…

Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA…

Sparse matricized tensor times Khatri-Rao product (MTTKRP) is one of the most computationally expensive kernels in sparse tensor computations. This work focuses on optimizing the MTTKRP operation on GPUs, addressing both performance and…

Sparse Matricized Tensor Times Khatri-Rao Product (spMTTKRP) is the bottleneck kernel of sparse tensor decomposition. In tensor decomposition, spMTTKRP is performed iteratively along all the modes of an input tensor. In this work, we…

Tensor decomposition has become an essential tool in many data science applications. Sparse Matricized Tensor Times Khatri-Rao Product (MTTKRP) is the pivotal kernel in tensor decomposition algorithms that decompose higher-order real-world…

We develop lower bounds on communication in the memory hierarchy or between processors for nested bilinear algorithms, such as Strassen's algorithm for matrix multiplication. We build on a previous framework that establishes communication…

Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case).…