QUENCH, GOAL-MATCHING AND CONVERGE ― THE THREE-PHASE REASONING OF A Q'TRON NEURAL NETWORK

摘要

The Q'tron NN (neural network) finds applications in many fields including combinatorial optimization, image processing, and visual cryptography. This paper will show that this NN model to run by incorporating with the proposed noise-injection mechanism is probabilistically complete if its dedicated 'goal' is reachable. The main theme to conduct the discussion is to solve the sum-of-subset problem, which is well known NP-complete. To investigate its convergent property, it is proven that the NN performs search in three phases, namely, quench phase, goal-matching phase and convergent phase. This, as a result, reveals that the NN doesn't undertake an exhaustive search. Some experimental results will be provided to demonstrate its features. The general scheme to solve problems using the model will also be established in the paper.