Statistical Mechanics of Neural Networks

Statistical Mechanics of Neural Networks
Author: Haiping Huang
Publisher: Springer Nature
Total Pages: 302
Release: 2022-01-04
Genre: Science
ISBN: 9811675708

This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.

Statistical Field Theory for Neural Networks

Statistical Field Theory for Neural Networks
Author: Moritz Helias
Publisher: Springer Nature
Total Pages: 203
Release: 2020-08-20
Genre: Science
ISBN: 303046444X

This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.

Statistical Mechanics of Learning

Statistical Mechanics of Learning
Author: A. Engel
Publisher: Cambridge University Press
Total Pages: 346
Release: 2001-03-29
Genre: Computers
ISBN: 9780521774796

Learning is one of the things that humans do naturally, and it has always been a challenge for us to understand the process. Nowadays this challenge has another dimension as we try to build machines that are able to learn and to undertake tasks such as datamining, image processing and pattern recognition. We can formulate a simple framework, artificial neural networks, in which learning from examples may be described and understood. The contribution to this subject made over the last decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics and include many examples and exercises to make a book that can be used with courses, or for self-teaching, or as a handy reference.

Machine Learning with Neural Networks

Machine Learning with Neural Networks
Author: Bernhard Mehlig
Publisher: Cambridge University Press
Total Pages: 262
Release: 2021-10-28
Genre: Science
ISBN: 1108849563

This modern and self-contained book offers a clear and accessible introduction to the important topic of machine learning with neural networks. In addition to describing the mathematical principles of the topic, and its historical evolution, strong connections are drawn with underlying methods from statistical physics and current applications within science and engineering. Closely based around a well-established undergraduate course, this pedagogical text provides a solid understanding of the key aspects of modern machine learning with artificial neural networks, for students in physics, mathematics, and engineering. Numerous exercises expand and reinforce key concepts within the book and allow students to hone their programming skills. Frequent references to current research develop a detailed perspective on the state-of-the-art in machine learning research.

An Introduction to the Theory of Spin Glasses and Neural Networks

An Introduction to the Theory of Spin Glasses and Neural Networks
Author: Viktor Dotsenko
Publisher: World Scientific
Total Pages: 172
Release: 1994
Genre: Science
ISBN: 9789810218737

This book aims to describe in simple terms the new area of statistical mechanics known as spin-glasses, encompassing systems in which quenched disorder is the dominant factor. The book begins with a non-mathematical explanation of the problem, and the modern understanding of the physics of the spin-glass state is formulated in general terms. Next, the 'magic' of the replica symmetry breaking scheme is demonstrated and the physics behind it discussed. Recent experiments on real spin-glass materials are briefly described to demonstrate how this somewhat abstract physics can be studied in the laboratory. The final chapters of the book are devoted to statistical models of neural networks.The material here is self-contained and should be accessible to students with a basic knowledge of theoretical physics and statistical mechanics. It has been used for a one-term graduate lecture course at the Landau Institute for Theoretical Physics.

Neural Networks

Neural Networks
Author: Berndt Müller
Publisher: Springer Science & Business Media
Total Pages: 340
Release: 2012-12-06
Genre: Computers
ISBN: 3642577601

Neural Networks presents concepts of neural-network models and techniques of parallel distributed processing in a three-step approach: - A brief overview of the neural structure of the brain and the history of neural-network modeling introduces to associative memory, preceptrons, feature-sensitive networks, learning strategies, and practical applications. - The second part covers subjects like statistical physics of spin glasses, the mean-field theory of the Hopfield model, and the "space of interactions" approach to the storage capacity of neural networks. - The final part discusses nine programs with practical demonstrations of neural-network models. The software and source code in C are on a 3 1/2" MS-DOS diskette can be run with Microsoft, Borland, Turbo-C, or compatible compilers.

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.

Introduction To The Theory Of Neural Computation

Introduction To The Theory Of Neural Computation
Author: John A. Hertz
Publisher: CRC Press
Total Pages: 352
Release: 2018-03-08
Genre: Science
ISBN: 0429968213

Comprehensive introduction to the neural network models currently under intensive study for computational applications. It also provides coverage of neural network applications in a variety of problems of both theoretical and practical interest.

Deep Learning and Physics

Deep Learning and Physics
Author: Akinori Tanaka
Publisher: Springer Nature
Total Pages: 207
Release: 2021-03-24
Genre: Science
ISBN: 9813361085

What is deep learning for those who study physics? Is it completely different from physics? Or is it similar? In recent years, machine learning, including deep learning, has begun to be used in various physics studies. Why is that? Is knowing physics useful in machine learning? Conversely, is knowing machine learning useful in physics? This book is devoted to answers of these questions. Starting with basic ideas of physics, neural networks are derived naturally. And you can learn the concepts of deep learning through the words of physics. In fact, the foundation of machine learning can be attributed to physical concepts. Hamiltonians that determine physical systems characterize various machine learning structures. Statistical physics given by Hamiltonians defines machine learning by neural networks. Furthermore, solving inverse problems in physics through machine learning and generalization essentially provides progress and even revolutions in physics. For these reasons, in recent years interdisciplinary research in machine learning and physics has been expanding dramatically. This book is written for anyone who wants to learn, understand, and apply the relationship between deep learning/machine learning and physics. All that is needed to read this book are the basic concepts in physics: energy and Hamiltonians. The concepts of statistical mechanics and the bracket notation of quantum mechanics, which are explained in columns, are used to explain deep learning frameworks. We encourage you to explore this new active field of machine learning and physics, with this book as a map of the continent to be explored.