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Deep neural networks represent a powerful class of function approximators that can learn to compress and reconstruct images. Existing image compression algorithms based on neural networks learn quantized representations with a constant…
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…
Deep learning methods have shown state of the art performance in a range of tasks from computer vision to natural language processing. However, it is well known that such systems are vulnerable to attackers who craft inputs in order to…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
Convolutional neural networks (CNNs) achieved the state-of-the-art performance in medical image segmentation due to their ability to extract highly complex feature representations. However, it is argued in recent studies that traditional…
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…
Over the last few years, convolutional neural networks (CNNs) have proved to reach super-human performance in visual recognition tasks. However, CNNs can easily be fooled by adversarial examples, i.e., maliciously-crafted images that force…
There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…
Privacy-preserving inference of convolutional neural networks (CNNs) using homomorphic encryption has emerged as a promising approach for enabling secure machine learning in untrusted environments. In our previous work, we introduced a…
Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…
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…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…
Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements.…
The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by…
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…
This article presents a generic approach to convolution that significantly differs from conventional methodologies in the current Machine Learning literature. The approach, in its mathematical aspects, proved to be clear and concise,…
Deep convolutional neural networks accurately classify a diverse range of natural images, but may be easily deceived when designed, imperceptible perturbations are embedded in the images. In this paper, we design a multi-pronged training,…
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…
It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of…