**Seminar30042019**

# Tuesday, 11th of June

14h30 (room R2014, 660 building) (see location)# Ada Altieri

(LPT, ENS)# Title: Introduction to the Thouless-Anderson-Palmer formalism and recent applications

# Abstract

In physical systems displaying an enormous number of metastable states, relevant predictions can be obtained from the computation of the configurational entropy or complexity function. It corresponds to the average logarithm of the number of minima of the free energy landscape at given disorder. This free energy functional is exactly obtained within the Thouless-Anderson-Palmer (TAP) formalism.A possible way to derive the TAP equations, which turn out to be of interest especially in computer science and inference problems, is to consider a graphical representation associating a factor graph, namely a bipartite graph with a given number of variable nodes and factors, to any feasible model and to write the belief propagation equations for the incoming and outcoming messages respectively.

The aim of this talk is to present a general overview of the different ways to derive the TAP equations, both in fully connected models and finite-connectivity graphs.

I will eventually focus on some recent results in a constraint satisfaction problem, the spherical perceptron, which, originated in the domain of artificial neural networks in the eighties, allows for a simple description of universal features of disordered and glassy systems nowadays.

Contact: guillaume.charpiat at inria.fr

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