Statistical Field Theory for Neural Networks [EBook] / by Moritz Helias, David Dahmen.
Statistical Field Theory for Neural Networks [EBook] / by Moritz Helias, David Dahmen.
This book presents a selfcontained 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...
Personal Name(s):  Helias, Moritz. (author) 

Dahmen, David, (author)  
Edition: 
1st edition 2020. 
Imprint: 
Cham :
Springer,
2020

Physical Description: 
XVII, 203 pages 127 illustrations, 5 illustrations in color (online resource) 
Note: 
englisch 
ISBN: 
9783030464448 
DOI: 
10.1007/9783030464448 
Series Title: 
Lecture Notes in Physics ;
970 
Subject (LOC):  
Full Text 
Table of Contents:
 Introduction
 Probabilities, moments, cumulants
 Gaussian distribution and Wick's theorem
 Perturbation expansion
 Linked cluster theorem
 Functional preliminaries
 Functional formulation of stochastic differential equations
 OrnsteinUhlenbeck process: The free Gaussian theory
 Perturbation theory for stochastic differential equations
 Dynamic meanfield 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.