Related papers: Sparse Tucker Tensor Decomposition on a Hybrid FPG…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…

Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is…

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,…

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…

General-purpose Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental kernel in scientific computing and deep learning. The emergence of new matrix computation units such as Tensor Cores (TCs) brings more opportunities for SpMM…

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decompositions or…

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…

Tensors play a vital role in machine learning (ML) and often exhibit properties best explored while maintaining high-order. Efficiently performing ML computations requires taking advantage of sparsity, but generalized hardware support is…

We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case…

Neural networks achieve state-of-the-art performance in image classification, speech recognition, scientific analysis and many more application areas. Due to the high computational complexity and memory footprint of neural networks, various…

Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

With an ongoing trend in computing hardware towards increased heterogeneity, domain-specific co-processors are emerging as alternatives to centralized paradigms. The tensor core unit (TPU) has shown to outperform graphic process units by…

High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…

Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…

This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support…

Kronecker-sparse (KS) matrices -- whose supports are Kronecker products of identity and all-ones blocks -- underpin the structure of Butterfly and Monarch matrices and offer the promise of more efficient models. However, existing GPU…

In big-data analytics, using tensor decomposition to extract patterns from large, sparse multivariate data is a popular technique. Many challenges exist for designing parallel, high performance tensor decomposition algorithms due to…