Related papers: Deep tensor networks with matrix product operators

Recent advances in deep learning have enabled us to address the curse of dimensionality (COD) by solving problems in higher dimensions. A subset of such approaches of addressing the COD has led us to solving high-dimensional PDEs. This has…

We consider a classifier whose test set is exposed to various perturbations that are not present in the training set. These test samples still contain enough features to map them to the same class as their unperturbed counterpart. Current…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

Deep neural networks have become the default choice for many applications like image and video recognition, segmentation and other image and video related tasks.However, a critical challenge with these models is the lack of…

Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…

Principal component analysis, dictionary learning, and auto-encoders are all unsupervised methods for learning representations from a large amount of training data. In all these methods, the higher the dimensions of the input data, the…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Current Deep Learning approaches have been very successful using convolutional neural networks (CNN) trained on large graphical processing units (GPU)-based computers. Three limitations of this approach are: 1) they are based on a simple…

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…

Deep convolutional neural networks have proven to be well suited for image classification applications. However, if there is distortion in the image, the classification accuracy can be significantly degraded, even with state-of-the-art…

Quantization of weights of deep neural networks (DNN) has proven to be an effective solution for the purpose of implementing DNNs on edge devices such as mobiles, ASICs and FPGAs, because they have no sufficient resources to support…

We introduce a machine learning model, the q-CNN model, sharing key features with convolutional neural networks and admitting a tensor network description. As examples, we apply q-CNN to the MNIST and Fashion MNIST classification tasks. We…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…

Deep neural networks (DNNs) have been used to create models for many complex analysis problems like image recognition and medical diagnosis. DNNs are a popular tool within machine learning due to their ability to model complex patterns and…

In this work, we introduce pixel wise tensor normalization, which is inserted after rectifier linear units and, together with batch normalization, provides a significant improvement in the accuracy of modern deep neural networks. In…

SAR image classification naturally has to deal with huge noise and a high dynamic range particularly requiring robust classification models. Additionally, the deployment of these models on edge devices, such as drones and military aircraft,…

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…

Nowadays the deep learning technology is growing faster and shows dramatic performance in computer vision areas. However, it turns out a deep learning based model is highly vulnerable to some small perturbation called an adversarial attack.…