Statistical Field Theory for Neural Networks PDF Download
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Author: Moritz Helias
Publisher: Springer Nature
ISBN: 303046444X
Category : Science
Languages : en
Pages : 213
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Book Description
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.
Author: Moritz Helias
Publisher: Springer Nature
ISBN: 303046444X
Category : Science
Languages : en
Pages : 213
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Book Description
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.
Author: Haiping Huang
Publisher: Springer Nature
ISBN: 9811675708
Category : Science
Languages : en
Pages : 302
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Book Description
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.
Author: Daniel A. Roberts
Publisher: Cambridge University Press
ISBN: 1316519333
Category : Computers
Languages : en
Pages : 473
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Book Description
This volume develops an effective theory approach to understanding deep neural networks of practical relevance.
Author: Giorgio Parisi
Publisher: Westview Press
ISBN: 9780738200514
Category : Science
Languages : en
Pages : 366
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Book Description
Specifically written to introduce researchers and advanced students to the modern developments in statistical mechanics and field theory, this book's leitmotiv is functional integration and its application to different areas of physics. The book acts as both an introduction to and a lucid overview of the major problems in statistical field theory.
Author: Anosh Joseph
Publisher: Springer Nature
ISBN: 3030460444
Category : Science
Languages : en
Pages : 134
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Book Description
This primer is a comprehensive collection of analytical and numerical techniques that can be used to extract the non-perturbative physics of quantum field theories. The intriguing connection between Euclidean Quantum Field Theories (QFTs) and statistical mechanics can be used to apply Markov Chain Monte Carlo (MCMC) methods to investigate strongly coupled QFTs. The overwhelming amount of reliable results coming from the field of lattice quantum chromodynamics stands out as an excellent example of MCMC methods in QFTs in action. MCMC methods have revealed the non-perturbative phase structures, symmetry breaking, and bound states of particles in QFTs. The applications also resulted in new outcomes due to cross-fertilization with research areas such as AdS/CFT correspondence in string theory and condensed matter physics. The book is aimed at advanced undergraduate students and graduate students in physics and applied mathematics, and researchers in MCMC simulations and QFTs. At the end of this book the reader will be able to apply the techniques learned to produce more independent and novel research in the field.
Author: Richard Golden
Publisher: CRC Press
ISBN: 1351051490
Category : Computers
Languages : en
Pages : 525
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Book Description
The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing, analyzing, evaluating, and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students, engineers, and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular, the material in this text directly supports the mathematical analysis and design of old, new, and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised, unsupervised, and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive, batch, minibatch, MCEM, and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics, computer science, electrical engineering, and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students, professional engineers, and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph.D., M.S.E.E., B.S.E.E.) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models.
Author: P. S. Neelakanta
Publisher: CRC Press
ISBN: 1351428969
Category : Technology & Engineering
Languages : en
Pages : 259
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Book Description
Neural Network Modeling offers a cohesive approach to the statistical mechanics and principles of cybernetics as a basis for neural network modeling. It brings together neurobiologists and the engineers who design intelligent automata to understand the physics of collective behavior pertinent to neural elements and the self-control aspects of neurocybernetics. The theoretical perspectives and explanatory projections portray the most current information in the field, some of which counters certain conventional concepts in the visualization of neuronal interactions.
Author: Henry D. I. Abarbanel
Publisher: Cambridge University Press
ISBN: 1316519635
Category : Computers
Languages : en
Pages : 207
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Book Description
The theory of data assimilation and machine learning is introduced in an accessible manner for undergraduate and graduate students.
Author: Edouard Brézin
Publisher: Cambridge University Press
ISBN: 1139490141
Category : Science
Languages : en
Pages : 177
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Book Description
Knowledge of the renormalization group and field theory is a key part of physics, and is essential in condensed matter and particle physics. Written for advanced undergraduate and beginning graduate students, this textbook provides a concise introduction to this subject. The textbook deals directly with the loop expansion of the free energy, also known as the background field method. This is a powerful method, especially when dealing with symmetries, and statistical mechanics. In focussing on free energy, the author avoids long developments on field theory techniques. The necessity of renormalization then follows.
Author: Katrin Amunts
Publisher: Springer Nature
ISBN: 3030824276
Category : Computers
Languages : en
Pages : 163
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Book Description
This open access book constitutes revised selected papers from the 4th International Workshop on Brain-Inspired Computing, BrainComp 2019, held in Cetraro, Italy, in July 2019. The 11 papers presented in this volume were carefully reviewed and selected for inclusion in this book. They deal with research on brain atlasing, multi-scale models and simulation, HPC and data infra-structures for neuroscience as well as artificial and natural neural architectures.
