Dynamics of the Belief Propagation for the Ising Model |
| G. Siudema,b and G. Świątekb
aFaculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland bFaculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland |
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| The Belief Propagation algorithm is a popular technique of solving inference problems for different graph-like structures. We present a discussion of the dynamics of that algorithm for the Ising model on the square lattice. Our main goal was to describe limit fixed points for that algorithm, which are strictly connected with the marginal probabilities and stationary points of the Bethe Free Energy. Analytical considerations provide an exact analysis of a class of symmetrical points while numerical simulations confirm that for small lattices there are no non-symmetrical points. Notwithstanding the prevalent use of the Belief Propagation as an inference tool we present a sociophysical interpretation of its dynamics. In that case our considerations may be viewed as an investigation of the possible fixed points of the social dynamics. |
DOI: 10.12693/APhysPolA.127.A-145 PACS numbers: 05.10.-a, 05.45.-a, 89.65.-s |