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Statistical field theory for neural ...

Helias, Moritz.

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Statistical field theory for neural networks

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Statistical field theory for neural networks/ by Moritz Helias, David Dahmen.
作者:	Helias, Moritz.
其他作者:	Dahmen, David.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xvii, 203 p. :ill., digital ;24 cm.
內容註:	Introduction -- Probabilities, moments, cumulants -- Gaussian distribution and Wick's theorem -- Perturbation expansion -- Linked cluster theorem -- Functional preliminaries -- Functional formulation of stochastic differential equations -- Ornstein-Uhlenbeck process: The free Gaussian theory -- Perturbation theory for stochastic differential equations -- Dynamic mean-field theory for random networks -- Vertex generating function -- Application: TAP approximation -- Expansion of cumulants into tree diagrams of vertex functions -- Loopwise expansion of the effective action - Tree level -- Loopwise expansion in the MSRDJ formalism -- Nomenclature.
Contained By:	Springer Nature eBook
標題:	Stochastic differential equations. -
電子資源:	https://doi.org/10.1007/978-3-030-46444-8
ISBN:	9783030464448

Statistical field theory for neural networks
Helias, Moritz.

Statistical field theory for neural networks[electronic resource] /by Moritz Helias, David Dahmen. - Cham :Springer International Publishing :2020. - xvii, 203 p. :ill., digital ;24 cm. - Lecture notes in physics,v.9700075-8450 ;. - Lecture notes in physics ;v.970..

Introduction -- Probabilities, moments, cumulants -- Gaussian distribution and Wick's theorem -- Perturbation expansion -- Linked cluster theorem -- Functional preliminaries -- Functional formulation of stochastic differential equations -- Ornstein-Uhlenbeck process: The free Gaussian theory -- Perturbation theory for stochastic differential equations -- Dynamic mean-field theory for random networks -- Vertex generating function -- Application: TAP approximation -- Expansion of cumulants into tree diagrams of vertex functions -- Loopwise expansion of the effective action - Tree level -- Loopwise expansion in the MSRDJ formalism -- Nomenclature.

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.

ISBN: 9783030464448

Standard No.: 10.1007/978-3-030-46444-8doiSubjects--Topical Terms:

621860
Stochastic differential equations.

LC Class. No.: QA274.23

Dewey Class. No.: 519.22

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520 $a 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.
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