Related papers: A Multi-Scale Tensor Network Architecture for Clas…

Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…

Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…

We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data…

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…

High-dimensional tensor models are notoriously computationally expensive to train. We present a meta-learning algorithm, MMT, that can significantly speed up the process for spatial tensor models. MMT leverages the property that spatial…

Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an…

Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…

Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay 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,…

Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…

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.…

We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…

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 show how tensor networks help in developing explainability of machine learning algorithms. Specifically, we develop an unsupervised clustering algorithm based on Matrix Product States (MPS) and apply it in the context of a…

We propose a deep learning methodology for multivariate regression that is based on pattern recognition that triggers fast learning over sensor data. We used a conversion of sensors-to-image which enables us to take advantage of Computer…

Neural networks with at least two hidden layers are called deep networks. Recent developments in AI and computer programming in general has led to development of tools such as Tensorflow, Keras, NumPy etc. making it easier to model and draw…