Related papers: Block Tensor Unfoldings
Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
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…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
The applications of the blockchain technology are still being discov-ered. When a new potential disruptive technology emerges, there is a tendency to try to solve every problem with that technology. However, it is still necessary to…
Tensor clustering, which seeks to extract underlying cluster structures from noisy tensor observations, has gained increasing attention. One extensively studied model for tensor clustering is the tensor block model, which postulates the…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard…
We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can…
Blocking is a critical step in entity resolution, and the emergence of neural network-based representation models has led to the development of dense blocking as a promising approach for exploring deep semantics in blocking. However,…
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing…
Most measurements in particle and nuclear physics use matrix-based unfolding algorithms to correct for detector effects. In nearly all cases, the observable is defined analogously at the particle and detector level. We point out that while…
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…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…