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After the discovery that fixed points of loopy belief propagation coincidewith stationary points of the Bethe free energy, several researchers proposedprovably convergent algorithms to directly minimize the Bethe free energy.These algorithms were formulated only for non-zero temperature (thus findingfixed points of the sum-product algorithm) and their possible extension to zerotemperature is not obvious. We present the zero-temperature limit of thedouble-loop algorithm by Heskes, which converges a max-product fixed point. Theinner loop of this algorithm is max-sum diffusion. Under certain conditions,the algorithm combines the complementary advantages of the max-product beliefpropagation and max-sum diffusion (LP relaxation): it yields good approximationof both ground states and max-marginals.

Zero-Temperature Limit of a Convergent Algorithm to Minimize the Bethe Free Energy