Circumventing spin glass traps by microcanonical spontaneous symmetry breaking
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The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic ground state and an intermediate spin glass phase. Conventional simulated annealing and message-passing algorithms could not reach the planted ground state but are trapped by an exponential number of spin glass states. Here we propose discontinuous microcanonical spontaneous symmetry breaking (MSSB) as a simple mechanism to circumvent all the spin glass traps. The existence of a discontinuous MSSB phase transition is confirmed by microcanonical Monte Carlo simulations. We conjecture that the planted ground state could be retrieved in polynomial time by applying machine-learning methods (such as perceptron-learning) to microcanonically sampled independent configurations. Three candidate algorithms are proposed.
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