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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

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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.


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

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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 Mechanics of Neural Networks

Statistical Mechanics of Neural Networks
Author: Luis Garrido
Publisher: Springer
Total Pages: 460
Release: 1990
Genre: Neural circuitry
ISBN:

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Combined for researchers and graduate students the articles from the Sitges Summer School together form an excellent survey of the applications of neural-network theory to statistical mechanics and computer-science biophysics. Various mathematical models are presented together with their interpretation, especially those to do with collective behaviour, learning and storage capacity, and dynamical stability.


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

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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.


Models of Neural Networks III

Models of Neural Networks III
Author: Eytan Domany
Publisher: Springer Science & Business Media
Total Pages: 322
Release: 2012-12-06
Genre: Science
ISBN: 1461207231

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One of the most challenging and fascinating problems of the theory of neural nets is that of asymptotic behavior, of how a system behaves as time proceeds. This is of particular relevance to many practical applications. Here we focus on association, generalization, and representation. We turn to the last topic first. The introductory chapter, "Global Analysis of Recurrent Neural Net works," by Andreas Herz presents an in-depth analysis of how to construct a Lyapunov function for various types of dynamics and neural coding. It includes a review of the recent work with John Hopfield on integrate-and fire neurons with local interactions. The chapter, "Receptive Fields and Maps in the Visual Cortex: Models of Ocular Dominance and Orientation Columns" by Ken Miller, explains how the primary visual cortex may asymptotically gain its specific structure through a self-organization process based on Hebbian learning. His argu ment since has been shown to be rather susceptible to generalization.


Models of Neural Networks I

Models of Neural Networks I
Author: Eytan Domany
Publisher: Springer Science & Business Media
Total Pages: 371
Release: 2012-12-06
Genre: Science
ISBN: 3642798144

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One of the great intellectual challenges for the next few decades is the question of brain organization. What is the basic mechanism for storage of memory? What are the processes that serve as the interphase between the basically chemical processes of the body and the very specific and nonstatistical operations in the brain? Above all, how is concept formation achieved in the human brain? I wonder whether the spirit of the physics that will be involved in these studies will not be akin to that which moved the founders of the "rational foundation of thermodynamics". C. N. Yang! 10 The human brain is said to have roughly 10 neurons connected through about 14 10 synapses. Each neuron is itself a complex device which compares and integrates incoming electrical signals and relays a nonlinear response to other neurons. The brain certainly exceeds in complexity any system which physicists have studied in the past. Nevertheless, there do exist many analogies of the brain to simpler physical systems. We have witnessed during the last decade some surprising contributions of physics to the study of the brain. The most significant parallel between biological brains and many physical systems is that both are made of many tightly interacting components.


Neural Networks

Neural Networks
Author: Jong-Hoon Oh
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 330
Release: 1995
Genre: Science
ISBN: 9789810223243

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Models of Neural Networks

Models of Neural Networks
Author: Eytan Domany
Publisher: Springer Science & Business Media
Total Pages: 358
Release: 2012-12-06
Genre: Science
ISBN: 3642971717

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One of the great inteJlectual cha1lenges for the next few decades is the question of brain organization. What is the basic mechanism for storage of memory? What are the processes that serve as the interphase between the basically chemical processes of the body and the very specific and nonstatistical operations in the brain? Above all. how is concept formation achieved in the human brain? I wonder whether the spirit of the physics that will be involved in these studies will not be akin to that which moved the founders of the ''rational foundation of thermodynamics". CN. Yangl 10 The human brain is said 10 have roughly 10 neurons connected through about 14 10 synapses. Each neuron is itself a complex device which compares and integrates incoming electrical signals and relays a nonlinear response to other neurons. The brain certainly exceeds in complexity any system which physicists have studied in the past. Nevertheless, there do exist many analogies of the We have witnessed during the last decade brain to simpler physical systems.