相关论文: On the Compression of Translation Operator Tensors…

Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…

We present a method of memory footprint reduction for FFT-based, electromagnetic (EM) volume integral equation (VIE) formulations. The arising Green's function tensors have low multilinear rank, which allows Tucker decomposition to be…

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…

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…

The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed…

This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…

In the last decades, tensors have emerged as the right tool to represent multidimensional data in a compact yet informative manner. Moreover, it is well-known that by performing low-rank factorizations of such tensors one is often able to…

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…

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…

Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…

Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

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…

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…

Tensor computation has emerged as a powerful mathematical tool for solving high-dimensional and/or extreme-scale problems in science and engineering. The last decade has witnessed tremendous advancement of tensor computation and its…

Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…

Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…