Statistical Field Theory for Neural Networks
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...
| Main Authors: | , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2020, 2020
|
| Edition: | 1st ed. 2020 |
| Series: | Lecture Notes in Physics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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