A Neural Network Program of Tsume-Go

Abstract

Go is a difficult game to make a computer program because of the space complexity. Therefore, it is important to explore another approach that does not rely on search algorithms only. In this paper, we focus on tsume-go problems (local Go problems) that have a unique solution. A three-layer neural network program has been developed to find a solution at a given position of tsume-go problems, where the attacker is to kill the defender’s territory on a 9 × 9 board. The network consists of 162 neurons for the input layer, 300 neurons for the middle layer, and 81 neurons for the output layer. We let the network learn the current stone patterns and, hence, process a direct answer. The network learns 2000 patterns of tsume-go by the back-propagation method. Within 500 repeats, the network learns 2000 patterns correctly. We tested the network ability: the top three selected moves contain about 60% correct answers, and the top five, about 70% for unknown problems at 500 repeats of learning. We compare the rate of correct answers by the network with that of human players who replied in a few seconds only. The ability of the network is roughly equivalent to 1-dan strength of human player. Application of neural networks for a computer program of tsume-go (and also Go) combined with a pattern classifier might provide a prospective approach to create a strong Go-playing program.