Related papers: Tensor Algebra on an Optoelectronic Microchip

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

This paper is contributed to a fast algorithm for Hankel tensor-vector products. For this purpose, we first discuss a special class of Hankel tensors that can be diagonalized by the Fourier matrix, which is called \emph{anti-circulant}…

We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…

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…

Tuning tensor program generation involves searching for various possible program transformation combinations for a given program on target hardware to optimize the tensor program execution. It is already a complex process because of the…

We introduce Stardust, a compiler that compiles sparse tensor algebra to reconfigurable dataflow architectures (RDAs). Stardust introduces new user-provided data representation and scheduling language constructs for mapping to…

With the advent of more powerful Quantum Computers, the need for larger Quantum Simulations has boosted. As the amount of resources grows exponentially with size of the target system Tensor Networks emerge as an optimal framework with which…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Tensor contractions constitute a key computational ingredient of numerical multi-linear algebra. However, as the order and dimension of tensors grow, the time and space complexities of tensor-based computations grow quickly. Existing…

Current architectures are now equipped with matrix computation units designed to enhance AI and high-performance computing applications. Within these architectures, two fundamental instruction types are matrix multiplication and vector…

This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…

Sparse tensors are prevalent in real-world applications, often characterized by their large-scale, high-order, and high-dimensional nature. Directly handling raw tensors is impractical due to the significant memory and computational…

This work proposes a GPU tensor core approach that encodes the arithmetic reduction of $n$ numbers as a set of chained $m \times m$ matrix multiply accumulate (MMA) operations executed in parallel by GPU tensor cores. The asymptotic running…

Many research works have been performed on implementation of Vitrerbi decoding algorithm on GPU instead of FPGA because this platform provides considerable flexibility in addition to great performance. Recently, the recently-introduced…

To address the absence of a universal standard interface for tensor operations, we introduce the Tensor Algebra Processing Primitives (TAPP), a C-based interface designed to decouple the application layer from hardware-specific…

In this paper, we develop software for decomposing sparse tensors that is portable to and performant on a variety of multicore, manycore, and GPU computing architectures. The result is a single code whose performance matches optimized…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

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…

While FPGAs have been used extensively as hardware accelerators in industrial computation, no theoretical model of computation has been devised for the study of FPGA-based accelerators. In this paper, we present a theoretical model of…