Related papers: Number-State Preserving Tensor Networks as Classif…

Tensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks…

Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…

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,…

We present tensor networks for feature extraction and refinement of classifier performance. These networks can be initialised deterministically and have the potential for implementation on near-term intermediate-scale quantum (NISQ)…

The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used…

In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Accurate diagnosis of neurological disorders is contingent upon advanced imaging modalities such as Magnetic Resonance Imaging (MRI), which commonly utilize sparse imaging techniques to reconstruct images from limited data, thus reducing…

Tensor Networks (TNs) are a computational paradigm used for representing quantum many-body systems. Recent works have shown how TNs can also be applied to perform Machine Learning (ML) tasks, yielding comparable results to standard…

We propose a new class of tensor network state as a model for the AdS/CFT correspondence and holography. This class is demonstrated to retain key features of the multi-scale entanglement renormalization ansatz (MERA), in that they describe…

Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a…

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…

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…

With advances in data collection technologies, tensor data is assuming increasing prominence in many applications and the problem of supervised tensor learning has emerged as a topic of critical significance in the data mining and machine…

Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…

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…

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.…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

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…

Tensor network (TN) techniques - often used in the context of quantum many-body physics - have shown promise as a tool for tackling machine learning (ML) problems. The application of TNs to ML, however, has mostly focused on supervised and…