Abstract
AbstractIn graphical models whose factor graph has a locally tree-like structure, belief propagation may fail because variables become correlated at large distances. This phenomenon has been observed in many problems, from satisfiability to colouring or error correcting codes. This chapter describes a physics-based approach for dealing with such a problem, the ‘one step replica symmetry breaking’ (1RSB) cavity method. It is based on the idea of counting solutions to belief propagation equations, and has strong connections with the theory of pure states decomposition. Its algorithmic side, the survey propagation algorithm, is motivated and described in details. The general theory is illustrated through its application to the XORSAT problem studied in Chapter 18.
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