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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…

Machine Learning · Computer Science 2023-04-19 Evelyn Herberg

The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…

Machine Learning · Computer Science 2018-11-30 Laurent Boué

Convolution Neural Networks (CNN), known as ConvNets are widely used in many visual imagery application, object classification, speech recognition. After the implementation and demonstration of the deep convolution neural network in…

Computer Vision and Pattern Recognition · Computer Science 2017-11-10 Pushparaja Murugan

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…

Neural and Evolutionary Computing · Computer Science 2019-11-18 Dylan Richard Muir

In recent years, China, the United States and other countries, Google and other high-tech companies have increased investment in artificial intelligence. Deep learning is one of the current artificial intelligence research's key areas. This…

Machine Learning · Computer Science 2018-08-29 Rong Zhang , Weiping Li , Tong Mo

In this paper, the branches of recursive and recurrent neural networks are classified in detail according to the network structure, training objective function and learning algorithm implementation. They are roughly divided into three…

Neural and Evolutionary Computing · Computer Science 2025-10-22 Jian-wei Liu , Bing-rong Xu , Zhi-yan Song

In this paper, we explore different ways to extend a recurrent neural network (RNN) to a \textit{deep} RNN. We start by arguing that the concept of depth in an RNN is not as clear as it is in feedforward neural networks. By carefully…

Neural and Evolutionary Computing · Computer Science 2014-04-25 Razvan Pascanu , Caglar Gulcehre , Kyunghyun Cho , Yoshua Bengio

These lecture notes provide an introduction to the verification of neural networks from a theoretical perspective. We discuss feed-forward neural networks, recurrent neural networks, attention mechanisms, and transformers, together with…

Logic in Computer Science · Computer Science 2026-04-29 Benedikt Bollig

Artificial neural networks are algorithms which have been developed to tackle a range of computational problems. These range from modelling brain function to making predictions of time-dependent phenomena to solving hard (NP-complete)…

Astrophysics · Physics 2007-05-23 C. A. L. Bailer-Jones , R. Gupta , H. P. Singh

Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled.…

Machine Learning · Computer Science 2018-11-09 Davide Bacciu , Antonio Carta , Alessandro Sperduti

This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…

Neural and Evolutionary Computing · Computer Science 2018-03-28 Bart Jacobs , David Sprunger

We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…

Neural and Evolutionary Computing · Computer Science 2016-06-09 Adam Trischler , Gabriele MT D'Eleuterio

In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarises relevant work, much of it from the previous…

Neural and Evolutionary Computing · Computer Science 2014-11-20 Juergen Schmidhuber

The back-propagation algorithm is the cornerstone of deep learning. Despite its importance, few variations of the algorithm have been attempted. This work presents an approach to discover new variations of the back-propagation equation. We…

Neural and Evolutionary Computing · Computer Science 2018-08-09 Maximilian Alber , Irwan Bello , Barret Zoph , Pieter-Jan Kindermans , Prajit Ramachandran , Quoc Le

Advanced deep learning architectures consist of tens of fully connected and convolutional hidden layers, currently extended to hundreds, are far from their biological realization. Their implausible biological dynamics relies on changing a…

Computer Vision and Pattern Recognition · Computer Science 2023-01-31 Yuval Meir , Itamar Ben-Noam , Yarden Tzach , Shiri Hodassman , Ido Kanter

Recurrent Networks are one of the most powerful and promising artificial neural network algorithms to processing the sequential data such as natural languages, sound, time series data. Unlike traditional feed-forward network, Recurrent…

Machine Learning · Computer Science 2018-07-11 Pushparaja Murugan

State-of-the-art solutions in the areas of "Language Modelling & Generating Text", "Speech Recognition", "Generating Image Descriptions" or "Video Tagging" have been using Recurrent Neural Networks as the foundation for their approaches.…

Machine Learning · Computer Science 2019-12-13 Robin M. Schmidt

The brain cortex, which processes visual, auditory and sensory data in the brain, is known to have many recurrent connections within its layers and from higher to lower layers. But, in the case of machine learning with neural networks, it…

Machine Learning · Computer Science 2020-10-22 Sebastian Sanokowski

An object-oriented approach to implementing artificial neural networks is introduced in this article. The networks obtained in this way are highly connected in that they admit edges between nodes in any layers of the network, and dynamic,…

Machine Learning · Computer Science 2023-02-20 Clint van Alten

After the tremendous development of neural networks trained by backpropagation, it is a good time to develop other algorithms for training neural networks to gain more insights into networks. In this paper, we propose a new algorithm for…

Machine Learning · Computer Science 2020-07-01 Benyamin Ghojogh , Fakhri Karray , Mark Crowley
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