  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.
