Deep Neural Networks in a Mathematical Framework

Deep Neural Networks in a Mathematical Framework
Author: Anthony L. Caterini
Publisher: Springer
Total Pages: 95
Release: 2018-03-22
Genre: Computers
ISBN: 3319753045

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.

Algorithms for Verifying Deep Neural Networks

Algorithms for Verifying Deep Neural Networks
Author: Changliu Liu
Publisher:
Total Pages:
Release: 2021-02-11
Genre:
ISBN: 9781680837865

Neural networks have been widely used in many applications, such as image classification and understanding, language processing, and control of autonomous systems. These networks work by mapping inputs to outputs through a sequence of layers. At each layer, the input to that layer undergoes an affine transformation followed by a simple nonlinear transformation before being passed to the next layer. Neural networks are being used for increasingly important tasks, and in some cases, incorrect outputs can lead to costly consequences, hence validation of correctness at each layer is vital. The sheer size of the networks makes this not feasible using traditional methods. In this monograph, the authors survey a class of methods that are capable of formally verifying properties of deep neural networks. In doing so, they introduce a unified mathematical framework for verifying neural networks, classify existing methods under this framework, provide pedagogical implementations of existing methods, and compare those methods on a set of benchmark problems. Algorithms for Verifying Deep Neural Networks serves as a tutorial for students and professionals interested in this emerging field as well as a benchmark to facilitate the design of new verification algorithms.

Hands-On Mathematics for Deep Learning

Hands-On Mathematics for Deep Learning
Author: Jay Dawani
Publisher: Packt Publishing Ltd
Total Pages: 347
Release: 2020-06-12
Genre: Computers
ISBN: 183864184X

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.

Math and Architectures of Deep Learning

Math and Architectures of Deep Learning
Author: Krishnendu Chaudhury
Publisher: Simon and Schuster
Total Pages: 550
Release: 2024-03-26
Genre: Computers
ISBN: 1617296481

Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. You'll peer inside the "black box" to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Math and Architectures of Deep Learning sets out the foundations of DL usefully and accessibly to working practitioners. Each chapter explores a new fundamental DL concept or architectural pattern, explaining the underpinning mathematics and demonstrating how they work in practice with well-annotated Python code. You'll start with a primer of basic algebra, calculus, and statistics, working your way up to state-of-the-art DL paradigms taken from the latest research. Learning mathematical foundations and neural network architecture can be challenging, but the payoff is big. You'll be free from blind reliance on pre-packaged DL models and able to build, customize, and re-architect for your specific needs. And when things go wrong, you'll be glad you can quickly identify and fix problems.

The Principles of Deep Learning Theory

The Principles of Deep Learning Theory
Author: Daniel A. Roberts
Publisher: Cambridge University Press
Total Pages: 473
Release: 2022-05-26
Genre: Computers
ISBN: 1316519333

This volume develops an effective theory approach to understanding deep neural networks of practical relevance.

Neural Networks

Neural Networks
Author: Raul Rojas
Publisher: Springer Science & Business Media
Total Pages: 511
Release: 2013-06-29
Genre: Computers
ISBN: 3642610684

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.

Deep Learning Architectures

Deep Learning Architectures
Author: Ovidiu Calin
Publisher: Springer Nature
Total Pages: 760
Release: 2020-02-13
Genre: Mathematics
ISBN: 3030367215

This book describes how neural networks operate from the mathematical point of view. As a result, neural networks can be interpreted both as function universal approximators and information processors. The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.

Probability Inequalities

Probability Inequalities
Author: Zhengyan Lin
Publisher: Springer Science & Business Media
Total Pages: 192
Release: 2011-05-30
Genre: Mathematics
ISBN: 3642052614

Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.

Geometry, Mechanics, and Dynamics

Geometry, Mechanics, and Dynamics
Author: Dong Eui Chang
Publisher: Springer
Total Pages: 506
Release: 2015-04-16
Genre: Mathematics
ISBN: 1493924419

This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.