Statistical Field Theory for Neural Networks [E-Book] / by Moritz Helias, David Dahmen.
Helias, Moritz. (author)
Dahmen, David, (author)
1st edition 2020.
Cham : Springer, 2020
XVII, 203 pages 127 illustrations, 5 illustrations in color (online resource)
englisch
9783030464448
10.1007/978-3-030-46444-8
Lecture Notes in Physics ; 970
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
  • 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.