Statistical mechanics of neural networks

The neural networks of the brain form one of the most complex systems we know. Many qualitative features of the emerging collective phenomena, such as correlated activity, stability, response to inputs, chaotic and regular behavior, can, however, be understood in simple models that are accessible to a treatment in statistical mechanics. This course presents the fundamentals behind contemporary developments in neural network theory that are based on methods from statistical mechanics of classical systems with a large number of interacting degrees of freedom.
The focus on classical systems allows us to introduce the standard language and tools employed in statistical field theory in a simple and didactic form moments, cumulants, generating function[al]s, Wick's theorem, linked cluster theorem, perturbation theory, Feynman diagrams, mean-field approximation, loopwise expansion). We will explain and derive these concepts as far as they are needed in the context of neural networks. This
first part will be familiar to students with some knowledge in (quantum) field theory and statistical physics.