Generating gradients in the energy landscape using rectified linear type
  cost functions for efficiently solving 0/1 matrix factorization in Simulated
  Annealing
Makiko Konoshima Hirotaka Tamura Yoshiyuki Kabashima
The 0/1 matrix factorization defines matrix products using logical AND and OR
as product-sum operators, revealing the factors influencing various decision
processes. Instances and their characteristics are arranged in rows and
columns. Formulating matrix factorization as an energy minimization problem and
exploring it with Simulated Annealing (SA) theoretically enables finding a
minimum solution in sufficient time. However, searching for the optimal
solution in practical time becomes problematic when the energy landscape has
many plateaus with flat slopes. In this work, we propose a method to facilitate
the solution process by applying a gradient to the energy landscape, using a
rectified linear type cost function readily available in modern annealing
machines. We also propose a method to quickly obtain a solution by updating the
cost function's gradient during the search process. Numerical experiments were
conducted, confirming the method's effectiveness with both noise-free
artificial and real data.