Quadratic unconstrained binary optimization formulation for rectified-linear-unit-type functions.

Sato, Go; Konoshima, Makiko; Ohwa, Takuya; Tamura, Hirotaka; Ohkubo, Jun · Phys Rev E · 2019

basic_science · Level V

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Abstract

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. [in Proceedings of the 29th International Conference on Machine Learning, Edinburgh, edited by J. Langford and J. Pineau (Omnipress, Madison, USA, 2012)], a simple discussion based on the Legendre duality is not sufficient to obtain the QUBO formulation of ReLU-type functions. In addition to the Legendre duality, we employ the Wolfe duality, and the QUBO formulation of ReLU type is derived. The QUBO formulation is available in Ising-type annealing methods, including quantum annealing machines.