Related papers: TLib: A Flexible C++ Tensor Framework for Numerica…

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…

A fundamental process in the implementation of any numerical tensor network algorithm is that of contracting a tensor network. In this process, a network made up of multiple tensors connected by summed indices is reduced to a single tensor…

Tensor contraction operations in computational chemistry consume significant fractions of computing time on large-scale computing platforms. The widespread use of tensor contractions between large multi-dimensional tensors in describing…

How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…

Tensor processing units (TPUs) are one of the most well-known machine learning (ML) accelerators utilized at large scale in data centers as well as in tiny ML applications. TPUs offer several improvements and advantages over conventional ML…

TensorNetwork is an open source library for implementing tensor network algorithms in TensorFlow. We describe a tree tensor network (TTN) algorithm for approximating the ground state of either a periodic quantum spin chain (1D) or a lattice…

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…

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for…

The general linear model is a universally accepted method to conduct and test multiple linear regression models. Using this model one has the ability to simultaneously regress covariates among different groups of data. Moreover, there are…

Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…

Tensor algebra is widely used in many applications, such as scientific computing, machine learning, and data analytics. The tensors represented real-world data are usually large and sparse. There are tens of storage formats designed for…

Activation functions (AFs) are an important part of the design of neural networks (NNs), and their choice plays a predominant role in the performance of a NN. In this work, we are particularly interested in the estimation of flexible…

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…

Simulation is essential for developing quantum hardware and algorithms. However, simulating quantum circuits on classical hardware is challenging due to the exponential scaling of quantum state space. While factorized tensors can greatly…

This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…

Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…

TensorFlow is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous…

We propose a software framework based on the ideas of the Learning-Compression (LC) algorithm, that allows a user to compress a neural network or other machine learning model using different compression schemes with minimal effort.…

Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…