Related papers: Tensor Algebra on an Optoelectronic Microchip
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…
Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{Tensor power method} (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor…
From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous…
A \emph{tensor-relational} computation is a relational computation where individual tuples carry vectors, matrices, or higher-dimensional arrays. An advantage of tensor-relational computation is that the overall computation can be executed…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant challenge for efficiently computing gradients through…
The rapid growth in computing demands, particularly driven by artificial intelligence applications, has begun to exceed the capabilities of traditional electronic hardware. Optical computing offers a promising alternative due to its…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We introduce DISTAL, a compiler for dense tensor algebra that targets modern distributed and heterogeneous systems. DISTAL lets users independently describe how tensors and computation map onto target machines through separate format and…
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…
This dissertation introduces measurement-based performance modeling and prediction techniques for dense linear algebra algorithms. As a core principle, these techniques avoid executions of such algorithms entirely, and instead predict their…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
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…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…