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In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…

The design and application of regression-free tensor network representations for integration is presented. Tensor network methods are demonstrated to outperform Monte Carlo for test problems, and exponential convergence is shown to be…

Tensor computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…

This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra systems. The system identification problem is rewritten in…

We present a convolutional neural network for the classification of correlation responses obtained by correlation filters. The proposed approach can improve the accuracy of classification, as well as achieve invariance to the image classes…

The Recurrent Neural Networks and their variants have shown promising performances in sequence modeling tasks such as Natural Language Processing. These models, however, turn out to be impractical and difficult to train when exposed to very…

Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Personalized recommendations are one of the most widely deployed machine learning (ML) workload serviced from cloud datacenters. As such, architectural solutions for high-performance recommendation inference have recently been the target of…

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network,…

Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…

We construct fast algorithms for evaluating transforms associated with families of functions which satisfy recurrence relations. These include algorithms both for computing the coefficients in linear combinations of the functions, given the…

Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum…

The Correlation Filter is an algorithm that trains a linear template to discriminate between images and their translations. It is well suited to object tracking because its formulation in the Fourier domain provides a fast solution,…

For image classification problems, various neural network models are commonly used due to their success in yielding high accuracies. Convolutional Neural Network (CNN) is one of the most frequently used deep learning methods for image…