The Math Of Neural Networks


The Math Of Neural Networks
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The Math Of Neural Networks


The Math Of Neural Networks
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Author : Michael Taylor
language : en
Publisher: Independently Published
Release Date : 2017-10-04

The Math Of Neural Networks written by Michael Taylor and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Computers categories.


There are many reasons why neural networks fascinate us and have captivated headlines in recent years. They make web searches better, organize photos, and are even used in speech translation. Heck, they can even generate encryption. At the same time, they are also mysterious and mind-bending: how exactly do they accomplish these things ? What goes on inside a neural network?On a high level, a network learns just like we do, through trial and error. This is true regardless if the network is supervised, unsupervised, or semi-supervised. Once we dig a bit deeper though, we discover that a handful of mathematical functions play a major role in the trial and error process. It also becomes clear that a grasp of the underlying mathematics helps clarify how a network learns. In the following chapters we will unpack the mathematics that drive a neural network. To do this, we will use a feedforward network as our model and follow input as it moves through the network.



Mathematics Of Neural Networks


Mathematics Of Neural Networks
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Author : Stephen W. Ellacott
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Mathematics Of Neural Networks written by Stephen W. Ellacott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.


This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.



Deep Neural Networks In A Mathematical Framework


Deep Neural Networks In A Mathematical Framework
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Author : Anthony L. Caterini
language : en
Publisher: Springer
Release Date : 2018-03-22

Deep Neural Networks In A Mathematical Framework written by Anthony L. Caterini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-22 with Computers categories.


This SpringerBrief describes how to build a rigorous end-to-end mathematical framework for deep neural networks. The authors provide tools to represent and describe neural networks, casting previous results in the field in a more natural light. In particular, the authors derive gradient descent algorithms in a unified way for several neural network structures, including multilayer perceptrons, convolutional neural networks, deep autoencoders and recurrent neural networks. Furthermore, the authors developed framework is both more concise and mathematically intuitive than previous representations of neural networks. This SpringerBrief is one step towards unlocking the black box of Deep Learning. The authors believe that this framework will help catalyze further discoveries regarding the mathematical properties of neural networks.This SpringerBrief is accessible not only to researchers, professionals and students working and studying in the field of deep learning, but also to those outside of the neutral network community.



Discrete Mathematics Of Neural Networks


Discrete Mathematics Of Neural Networks
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Author : Martin Anthony
language : en
Publisher: SIAM
Release Date : 2001-01-01

Discrete Mathematics Of Neural Networks written by Martin Anthony and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Computers categories.


This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.



Math For Deep Learning


Math For Deep Learning
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Author : Ronald T. Kneusel
language : en
Publisher: No Starch Press
Release Date : 2021-11-23

Math For Deep Learning written by Ronald T. Kneusel and has been published by No Starch Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-23 with Computers categories.


Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits. With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network. In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.



Make Your Own Neural Network An In Depth Visual Introduction For Beginners


Make Your Own Neural Network An In Depth Visual Introduction For Beginners
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Author : Michael Taylor
language : en
Publisher: Independently Published
Release Date : 2017-10-04

Make Your Own Neural Network An In Depth Visual Introduction For Beginners written by Michael Taylor and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Computers categories.


A step-by-step visual journey through the mathematics of neural networks, and making your own using Python and Tensorflow. What you will gain from this book: * A deep understanding of how a Neural Network works. * How to build a Neural Network from scratch using Python. Who this book is for: * Beginners who want to fully understand how networks work, and learn to build two step-by-step examples in Python. * Programmers who need an easy to read, but solid refresher, on the math of neural networks. What's Inside - 'Make Your Own Neural Network: An Indepth Visual Introduction For Beginners' What Is a Neural Network? Neural networks have made a gigantic comeback in the last few decades and you likely make use of them everyday without realizing it, but what exactly is a neural network? What is it used for and how does it fit within the broader arena of machine learning? we gently explore these topics so that we can be prepared to dive deep further on. To start, we'll begin with a high-level overview of machine learning and then drill down into the specifics of a neural network. The Math of Neural Networks On a high level, a network learns just like we do, through trial and error. This is true regardless if the network is supervised, unsupervised, or semi-supervised. Once we dig a bit deeper though, we discover that a handful of mathematical functions play a major role in the trial and error process. It also becomes clear that a grasp of the underlying mathematics helps clarify how a network learns. * Forward Propagation * Calculating The Total Error * Calculating The Gradients * Updating The Weights Make Your Own Artificial Neural Network: Hands on Example You will learn to build a simple neural network using all the concepts and functions we learned in the previous few chapters. Our example will be basic but hopefully very intuitive. Many examples available online are either hopelessly abstract or make use of the same data sets, which can be repetitive. Our goal is to be crystal clear and engaging, but with a touch of fun and uniqueness. This section contains the following eight chapters. Building Neural Networks in Python There are many ways to build a neural network and lots of tools to get the job done. This is fantastic, but it can also be overwhelming when you start, because there are so many tools to choose from. We are going to take a look at what tools are needed and help you nail down the essentials. To build a neural network Tensorflow and Neural Networks There is no single way to build a feedforward neural network with Python, and that is especially true if you throw Tensorflow into the mix. However, there is a general framework that exists that can be divided into five steps and grouped into two parts. We are going to briefly explore these five steps so that we are prepared to use them to build a network later on. Ready? Let's begin. Neural Network: Distinguish Handwriting We are going to dig deep with Tensorflow and build a neural network that can distinguish between handwritten numbers. We'll use the same 5 steps we covered in the high-level overview, and we are going to take time exploring each line of code. Neural Network: Classify Images 10 minutes. That's all it takes to build an image classifier thanks to Google! We will provide a high-level overview of how to classify images using a convolutional neural network (CNN) and Google's Inception V3 model. Once finished, you will be able to tweak this code to classify any type of image sets! Cats, bats, super heroes - the sky's the limit.



An Introduction To Neural Networks


An Introduction To Neural Networks
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Author : Kevin Gurney
language : en
Publisher: CRC Press
Release Date : 2018-10-08

An Introduction To Neural Networks written by Kevin Gurney and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Computers categories.


Though mathematical ideas underpin the study of neural networks, the author presents the fundamentals without the full mathematical apparatus. All aspects of the field are tackled, including artificial neurons as models of their real counterparts; the geometry of network action in pattern space; gradient descent methods, including back-propagation; associative memory and Hopfield nets; and self-organization and feature maps. The traditionally difficult topic of adaptive resonance theory is clarified within a hierarchical description of its operation. The book also includes several real-world examples to provide a concrete focus. This should enhance its appeal to those involved in the design, construction and management of networks in commercial environments and who wish to improve their understanding of network simulator packages. As a comprehensive and highly accessible introduction to one of the most important topics in cognitive and computer science, this volume should interest a wide range of readers, both students and professionals, in cognitive science, psychology, computer science and electrical engineering.



Hands On Mathematics For Deep Learning


Hands On Mathematics For Deep Learning
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Author : Jay Dawani
language : en
Publisher: Packt Publishing Ltd
Release Date : 2020-06-12

Hands On Mathematics For Deep Learning written by Jay Dawani and has been published by Packt Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-12 with Computers categories.


A comprehensive guide to getting well-versed with the mathematical techniques for building modern deep learning architectures Key FeaturesUnderstand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networksLearn the mathematical concepts needed to understand how deep learning models functionUse deep learning for solving problems related to vision, image, text, and sequence applicationsBook Description Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL. What you will learnUnderstand the key mathematical concepts for building neural network modelsDiscover core multivariable calculus conceptsImprove the performance of deep learning models using optimization techniquesCover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizerUnderstand computational graphs and their importance in DLExplore the backpropagation algorithm to reduce output errorCover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)Who this book is for This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required.



Neural Networks


Neural Networks
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Author : Steve Ellacott
language : en
Publisher: Itp New Media
Release Date : 1996

Neural Networks written by Steve Ellacott and has been published by Itp New Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Computers categories.


Neural networks provide a powerful approach to problems of machine learning and pattern recognition. the underlying mathematics, however, has much more in common with classical applied mathematics. This book introduces teh deterministic aspects of the mathematical theory in a comprehensive way.



Neural Networks


Neural Networks
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Author : Raul Rojas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Neural Networks written by Raul Rojas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.


Neural networks are a computing paradigm that is finding increasing attention among computer scientists. In this book, theoretical laws and models previously scattered in the literature are brought together into a general theory of artificial neural nets. Always with a view to biology and starting with the simplest nets, it is shown how the properties of models change when more general computing elements and net topologies are introduced. Each chapter contains examples, numerous illustrations, and a bibliography. The book is aimed at readers who seek an overview of the field or who wish to deepen their knowledge. It is suitable as a basis for university courses in neurocomputing.