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The 0/1 matrix factorization defines matrix products using logical AND and ORas product-sum operators, revealing the factors influencing various decisionprocesses. Instances and their characteristics are arranged in rows andcolumns. Formulating matrix factorization as an energy minimization problem andexploring it with Simulated Annealing (SA) theoretically enables finding aminimum solution in sufficient time. However, searching for the optimalsolution in practical time becomes problematic when the energy landscape hasmany plateaus with flat slopes. In this work, we propose a method to facilitatethe solution process by applying a gradient to the energy landscape, using arectified linear type cost function readily available in modern annealingmachines. We also propose a method to quickly obtain a solution by updating thecost function's gradient during the search process. Numerical experiments wereconducted, confirming the method's effectiveness with both noise-freeartificial and real data.

Generating gradients in the energy landscape using rectified linear type  cost functions for efficiently solving 0/1 matrix factorization in Simulated  Annealing