Related papers: Learning Relevant Features of Data with Multi-scal…

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…

We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…

Learning features from massive unlabelled data is a vast prevalent topic for high-level tasks in many machine learning applications. The recent great improvements on benchmark data sets achieved by increasingly complex unsupervised learning…

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…

The success of state-of-the-art machine learning is essentially all based on different variations of gradient descent algorithms that minimize some version of a cost or loss function. A fundamental limitation, however, is the need to train…

In this paper, we focus on the unsupervised multi-view feature selection which tries to handle high dimensional data in the field of multi-view learning. Although some graph-based methods have achieved satisfactory performance, they ignore…

We introduce deep tensor networks, which are exponentially wide neural networks based on the tensor network representation of the weight matrices. We evaluate the proposed method on the image classification (MNIST, FashionMNIST) and…

Convolutional Neural Networks (ConvNets) have shown excellent results on many visual classification tasks. With the exception of ImageNet, these datasets are carefully crafted such that objects are well-aligned at similar scales. Naturally,…

The paper discusses the capabilities of multilayer perceptron neural networks implementing metric recognition methods, for which the values of the weights are calculated analytically by formulas. Comparative experiments in training a neural…

It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the…

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…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a…

Graph-regularized semi-supervised learning has been used effectively for classification when (i) instances are connected through a graph, and (ii) labeled data is scarce. If available, using multiple relations (or graphs) between the…

In the context of neural network models, overparametrization refers to the phenomena whereby these models appear to generalize well on the unseen data, even though the number of parameters significantly exceeds the sample sizes, and the…

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Data and knowledge representation are fundamental concepts in machine learning. The quality of the representation impacts the performance of the learning model directly. Feature learning transforms or enhances raw data to structures that…

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…

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,…

Manipulating data, such as weighting data examples or augmenting with new instances, has been increasingly used to improve model training. Previous work has studied various rule- or learning-based approaches designed for specific types of…