Related papers: The Tensor as an Informational Resource

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…

Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…

Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…

Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…

Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…

DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…

We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…

Graphs emerge in almost every real-world application domain, ranging from online social networks all the way to health data and movie viewership patterns. Typically, such real-world graphs are big and dynamic, in the sense that they evolve…

Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…

Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…

SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application…

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…

This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to…

Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks…

Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to…

In this paper, we exhibit the tradeoffs between the (training) sample, computation and storage complexity for the problem of supervised classification using signal subspace estimation. Our main tool is the use of tensor subspaces, i.e.…

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…

Strassen (Strassen, J. Reine Angew. Math., 375/376, 1987) introduced the subrank of a tensor as a natural extension of matrix rank to tensors. Subrank measures the largest diagonal tensor that can be obtained by applying linear operations…

The content of this paper can be roughly organized into a three-level hierarchy of generality. At the first, most general level, we introduce a new language which allows us to express various categorical structures in a systematic and…

In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples,…