Related papers: Relocation of compact sets in $\mathbb{R}^n$ by di…

We present a comprehensive survey on removability of compact plane sets with respect to various classes of holomorphic functions. We also discuss some applications and several open questions, some of which are new.

One of the pursued objectives of deep learning is to provide tools that learn abstract representations of reality from the observation of multiple contextual situations. More precisely, one wishes to extract disentangled representations…

Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks. However, the impact of such changes on architecture's approximation capabilities is largely…

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…

Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is only applicable to fixed bandwidth kernels. In this paper, we…

This paper addresses the understanding and characterization of residual networks (ResNet), which are among the state-of-the-art deep learning architectures for a variety of supervised learning problems. We focus on the mapping component of…

We call a metric space $s$-negligible iff its $s$-dimensional Hausdorff measure vanishes. We show that every countably $m$-rectifiable subset of $\mathbb{R}^{2n}$ can be displaced from every $(2n-m)$-negligible subset by a Hamiltonian…

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…

Purpose: The aim of this work is to demonstrate that convolutional neural networks (CNN) can be applied to extremely sparse image libraries by subdivision of the original image datasets. Methods: Image datasets from a conventional digital…

We propose distributed deep neural networks (DDNNs) over distributed computing hierarchies, consisting of the cloud, the edge (fog) and end devices. While being able to accommodate inference of a deep neural network (DNN) in the cloud, a…

In applications involving matching of image sets, the information from multiple images must be effectively exploited to represent each set. State-of-the-art methods use probabilistic distribution or subspace to model a set and use specific…

This paper proposes a new deep convolutional neural network (DCNN) architecture that learns pixel embeddings, such that pairwise distances between the embeddings can be used to infer whether or not the pixels lie on the same region. That…

Semantic segmentation necessitates approaches that learn high-level characteristics while dealing with enormous amounts of data. Convolutional neural networks (CNNs) can learn unique and adaptive features to achieve this aim. However, due…

When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…

The recently discovered Neural collapse (NC) phenomenon states that the last-layer weights of Deep Neural Networks (DNN), converge to the so-called Equiangular Tight Frame (ETF) simplex, at the terminal phase of their training. This ETF…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…

Image generating neural networks are mostly viewed as black boxes, where any change in the input can have a number of globally effective changes on the output. In this work, we propose a method for learning disentangled representations to…

We consider deep feedforward neural networks with rectified linear units from a signal processing perspective. In this view, such representations mark the transition from using a single (data-driven) linear representation to utilizing a…

The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is…

Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications. While some…