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Deep neural networks (DNNs) have demonstrated remarkable empirical performance in large-scale supervised learning problems, particularly in scenarios where both the sample size $n$ and the dimension of covariates $p$ are large. This study…

Graph Neural Networks (GNNs) are an emerging research field. This specialized Deep Neural Network (DNN) architecture is capable of processing graph structured data and bridges the gap between graph processing and Deep Learning (DL). As…

In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of the functions, but we do not assume any separation condition.…

Fracture surfaces provide various types of information about fracture. The fracture toughness $K_{{\rm I}c}$, which represents the resistance to fracture, can be estimated using the three-dimensional (3D) information of a fracture surface,…

Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration.…

This paper is devoted to studying the optimal expressive power of ReLU deep neural networks (DNNs) and its application in approximation via the Kolmogorov Superposition Theorem. We first constructively prove that any continuous piecewise…

Edge offloading for deep neural networks (DNNs) can be adaptive to the input's complexity by using early-exit DNNs. These DNNs have side branches throughout their architecture, allowing the inference to end earlier in the edge. The branches…

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test…

Deep neural networks are a powerful tool for feature learning and extraction given their ability to model high-level abstractions in highly complex data. One area worth exploring in feature learning and extraction using deep neural networks…

Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to…

Synthetic datasets are being recognized in the deep learning realm as a valuable alternative to exhaustively labeled real data. One such synthetic data generation method is Formula Driven Supervised Learning (FDSL), which can provide an…

We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (B\"olcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a…

In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…

Deep Neural Networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) data sets. Understanding which features in the data determine the output of these nested,…

The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…

Deep Neural Networks (DNNs) are built using artificial neural networks. They are part of machine learning methods that are capable of learning from data that have been used in a wide range of applications. DNNs are mainly handcrafted and…

IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design…

As nature is ascribed as quantum, the fractals also pose some intriguing appearance which is found in many micro and macro observable entities or phenomena. Fractals show self-similarity across sizes; structures that resemble the entire are…

Successful training of convolutional neural networks is often associated with sufficiently deep architectures composed of high amounts of features. These networks typically rely on a variety of regularization and pruning techniques to…

We argue that many properties of fully-connected feedforward neural networks (FCNNs), also called multi-layer perceptrons (MLPs), are explainable from the analysis of a single pair of operations, namely a random projection into a…