Belief Propagation on Replica Symmetric Random Factor Graph Models
According to physics predictions, the free energy of random factor graph models that satisfy a certain "static replica symmetry" condition can be calculated via the Belief Propagation message passing scheme [Krzakala et al. PNAS, 2007]. Here we prove this conjecture for a wide class of random factor graph models. Specifically, we show that the messages constructed just as in the case of acyclic factor graphs asymptotically satisfy the Belief Propagation equations and that the free energy density is given by the Bethe free energy formula.
Gibbs distributions
Belief Propagation
Bethe Free Energy
Random k-SAT
27:1-27:15
Regular Paper
Amin
Coja-Oghlan
Amin Coja-Oghlan
Will
Perkins
Will Perkins
10.4230/LIPIcs.APPROX-RANDOM.2016.27
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode