Distinguishing humans from computers in the game of go: a complex network approach

We compare complex networks built from the game of go and obtained from databases of human-played games with those obtained from computer-played games. Our investigations show that statistical features of the human-based networks and the computer-based networks differ, and that these differences can be statistically significant on a relatively small number of games using specific estimators. We show that the deterministic or stochastic nature of the computer algorithm playing the game can also be distinguished from these quantities. This can be seen as tool to implement a Turing-like test for go simulators. Introduction. – Computers are more and more present in everyday life, and they often perform tasks that were previously reserved to human beings. In particular, the raise of Artificial Intelligence in recent years showed that many situations of decision-making can be handled by computers in a way comparable to or more efficient than that of humans. However, the processes used by computers are often very different from the ones used by human beings. These different processes can affect the decisionmaking in ways that are difficult to assess but should be explored to better understand the limitations and advantages of the computer approach. A particularly spectacular way of testing these differences was put forward by Alan Turing: in order to distinguish a human from a computer one could ask a person to dialog with both anonymously and try to assess which one is the biological agent. As the question of human-computer interaction gets more pregnant, there is an ever growing need to understand these differences [1]. Many complex problems can illustrate the deep differences between human reasoning and the computer approach. Board games such as chess or go, which are perfect-information zero-sum games, provide an interesting testbed for such investigations. The complexity of these games is such that computers cannot use brute force, as in complex decision making, and have to rely on refined algorithms from Artificial Intelligence. Indeed, the number of legal positions is about 10 in chess and 10 in go [2], and the number of possible games of go was recently estimated to be at least 10 108 [3]. This makes any exhaustive analysis impossible, even for machines, and pure computer power is not enough to beat humans. Indeed, the most recent program of go simulation AlphaGo [4] used state of the art tools such as deep learning neural networks in order to beat world champions. Various approaches were considered to overcome the vastness of configuration space. A cornerstone of the computer approach to board games is a statistical physics treatment of game features. A first possibility is to explore the tree of all games stochastically, an approach which allowed for instance to investigate the topological structure of the state space of chess [5]. A second option is to consider only opening sequences in the game tree. This allowed e.g. to identify Zipf’s law in the tree of openings in chess [6] and in go [7]. A third possibility is to restrict oneself to local features of the game, by considering only local patterns. This approach was taken for instance in [8], where the frequency distribution of patterns in professional go game records was investigated. Local patterns play an essential part in the most recent approaches to computer go simulators [9]. Pioneering software was based on deterministic algorithms [10, 11]. Today, computer algorithms implement Monte-Carlo go [12, 13] or Monte-Carlo tree search techniques [14–17], which are based on a statistical approach : typically, the p-1 ar X iv :1 70 7. 04 04 4v 2 [ cs .S I] 1 5 N ov 2 01 7