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The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low…

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…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

We propose a Deep Texture Encoding Network (Deep-TEN) with a novel Encoding Layer integrated on top of convolutional layers, which ports the entire dictionary learning and encoding pipeline into a single model. Current methods build from…

We implement stacked denoising autoencoders, a class of neural networks that are capable of learning powerful representations of high dimensional data. We describe stochastic gradient descent for unsupervised training of autoencoders, as…

Image compression is an essential approach for decreasing the size in bytes of the image without deteriorating the quality of it. Typically, classic algorithms are used but recently deep-learning has been successfully applied. In this work,…

Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network. Typically these models encode all features of the data into a single variable. Here we are interested in learning…

Deep learning based image compressed sensing (CS) has achieved great success. However, existing CS systems mainly adopt a fixed measurement matrix to images, ignoring the fact the optimal measurement numbers and bases are different for…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

Recognizing objects from subcategories with very subtle differences remains a challenging task due to the large intra-class and small inter-class variation. Recent work tackles this problem in a weakly-supervised manner: object parts are…

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…

The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field, the geometric inner-product structure suffices to introduce…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

Apart from discriminative models for classification and object detection tasks, the application of deep convolutional neural networks to basic research utilizing natural imaging data has been somewhat limited; particularly in cases where a…

Fine-grained visual classification aims to recognize images belonging to multiple sub-categories within a same category. It is a challenging task due to the inherently subtle variations among highly-confused categories. Most existing…

This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

Despite the recent success of deep learning models in numerous applications, their widespread use on mobile devices is seriously impeded by storage and computational requirements. In this paper, we propose a novel network compression method…

Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…