Related papers: Projected Tensor-Tensor Products for Efficient Com…

High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…

This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…

Transformer architectures achieve state-of-the-art performance across a wide range of pattern recognition and natural language processing tasks, but their scaling is accompanied by substantial parameter growth and redundancy in the…

An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

Visual analytics have played an increasingly critical role in the Internet of Things, where massive visual signals have to be compressed and fed into machines. But facing such big data and constrained bandwidth capacity, existing…

As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…

Multi-dimensional non-Cartesian MRI encoding using the precomputed interpolator can encounter the curse of dimensionality, in which the interpolator size exceeds the available memory on the parallel accelerators. Here we reformulate the…

We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose…

High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…

We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short)…

We propose an end-to-end learned image compression codec wherein the analysis transform is jointly trained with an object classification task. This study affirms that the compressed latent representation can predict human perceptual…

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization…