These lecture notes provide an overview of Neural Network architectures from a mathematical point of view. Especially, Machine Learning with Neural Networks is seen as an optimization problem. Covered are an introduction to Neural Networks and the following architectures: Feedforward Neural Network, Convolutional Neural Network, ResNet, and Recurrent Neural Network.

Within one decade, Deep Learning overtook the dominating solution methods of countless problems of artificial intelligence. ``Deep'' refers to the deep architectures with operations in manifolds of which there are no immediate observations. For these deep architectures some kind of structure is pre-defined -- but what is this structure? With a formal definition for structures of neural networks, neural architecture search problems and solution methods can be formulated under ...

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the behaviour of state-of-the-art optimization algorithms in relationship to their hyperparameters setting in order to detect robustness with respect to the choice of a certain starting point in ending on different local solutions. We conduct exten...

Automated machine learning (AutoML) methods improve upon existing models by optimizing various aspects of their design. While present methods focus on hyperparameters and neural network topologies, other aspects of neural network design can be optimized as well. To further the state of the art in AutoML, this dissertation introduces techniques for discovering more powerful activation functions and establishing more robust weight initialization for neural networks. These contr...

Deep learning models have been widely used during the last decade due to their outstanding learning and abstraction capacities. However, one of the main challenges any scientist has to face using deep learning models is to establish the network's architecture. Due to this difficulty, data scientists usually build over complex models and, as a result, most of them result computationally intensive and impose a large memory footprint, generating huge costs, contributing to clima...

Neural network structures have a critical impact on the accuracy and stability of forecasting. Neural architecture search procedures help design an optimal neural network according to some loss function, which represents a set of quality criteria. This paper investigates the problem of neural network structure optimization. It proposes a way to construct a loss function, which contains a set of additive elements. Each element is called the regularizer. It corresponds to some ...

In this article, we propose the approach to structural optimization of neural networks, based on the braid theory. The paper describes the basics of braid theory as applied to the description of graph structures of neural networks. It is shown how networks of various topologies can be built using braid structures between layers of neural networks. The operation of a neural network based on the braid theory is compared with a homogeneous deep neural network and a network with ...

Deep Learning models have experienced exponential growth in complexity and resource demands in recent years. Accelerating these models for efficient execution on resource-constrained devices has become more crucial than ever. Two notable techniques employed to achieve this goal are Hardware-aware Neural Architecture Search (HW-NAS) and Automatic Code Optimization (ACO). HW-NAS automatically designs accurate yet hardware-friendly neural networks, while ACO involves searching f...

The automation of feature extraction of machine learning has been successfully realized by the explosive development of deep learning. However, the structures and hyperparameters of deep neural network architectures also make huge difference on the performance in different tasks. The process of exploring optimal structures and hyperparameters often involves a lot of tedious human intervene. As a result, a legitimate question is to ask for the automation of searching for optim...

This study investigates the use of local optima network (LON) analysis, a derivative of the fitness landscape of candidate solutions, to characterise and visualise the neural architecture space. The search space of feedforward neural network architectures with up to three layers, each with up to 10 neurons, is fully enumerated by evaluating trained model performance on a selection of data sets. Extracted LONs, while heterogeneous across data sets, all exhibit simple global st...