Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions
We propose a quadratic unconstrained binary optimization (QUBO) formulation of rectified linear unit (ReLU) type functions. Different from the q-loss function proposed by Denchev et al. (2012), a simple discussion based on the Legendre duality is not sufficient to obtain the QUBO formulation of the ReLU-type functions. In addition to the Legendre duality, we employ the Wolfe duality, and the QUBO formulation of the ReLU-type is derived. The QUBO formulation is available in Ising-type annealing methods, including quantum annealing machines.
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