Recurrent and multi-layer neural networks playing Even-Odd": reflection against regression

Reflection understood as an internal representation of the external world by the subject is the key property of consciousness. In a refined form this property is manifested in reflective games. To win a reflective game a player has to use reflection of strictly one rank higher than the opponent. So it can be assumed that there are only two game modes - when only one player uses reflection and wins and when both players use reflection but one of them chooses incorrect reflection rank. The option of random move selection is not considered since firstly, starting the game for a draw is strange, and secondly, it is technically impossible to make random moves without a special device. Experiments with recurrent neural networks playing with each other showed that the entire set of game patterns (time series of the game score) is split into two sharply different groups that can be associated with two modes mentioned above. Experiments, in which a multilayer neural network, which is basically incapable of reflection, played against a recurrent neural network, showed that a recurrent neural network has a clear advantage winning confidently in more than 90% of the games. At the same time game patterns demonstrate splitting into two sharply different groups as was observed in experiments with the game of two recurrent neural networks and in the reflexive game of living people.