Related papers: The landscape of software for tensor computations

We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…

Science advances not only through the accumulation of facts but also through the evolution of tools. Crucially, tools are rarely used in isolation. They form tool portfolios, combinations shaped by a discipline's workflows and analytical…

Tensor networks are factorizations of high-dimensional tensors into networks of smaller tensors. They have applications in physics and mathematics, and recently have been proposed as promising machine learning architectures. To ease the…

Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…

In the last couple of years we have witnessed an enormous increase of machine learning (ML) applications. More and more program functions are no longer written in code, but learnt from a huge amount of data samples using an ML algorithm.…

In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…

The SageManifolds project aims at extending the mathematics software system Sage towards differential geometry and tensor calculus. Like Sage, SageManifolds is free, open-source and is based on the Python programming language. We discuss…

Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…

We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…

Tensor computations present significant performance challenges that impact a wide spectrum of applications ranging from machine learning, healthcare analytics, social network analysis, data mining to quantum chemistry and signal processing.…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

Various fields of science and engineering rely on linear algebra for large scale data analysis, modeling and simulation, machine learning, and other applied problems. Linear algebra computations often dominate the execution time of such…

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…

Numerical tensor calculus comprise basic tensor operations such as the entrywise addition and contraction of higher-order tensors. We present, TLib, flexible tensor framework with generic tensor functions and tensor classes that assists…

Deploying deep learning models on various devices has become an important topic. The wave of hardware specialization brings a diverse set of acceleration primitives for multi-dimensional tensor computations. These new acceleration…

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…