Analysis of Time Series Trained by Adversarial Imitation Learning in Discrete State Neural Network Model

The bird song has a grammar. It is not random nor monotonous, but complex by combining several patterns. This combination rule like a grammar can be represented as the automaton. We have a hypothesis that the adversarial imitation learning, like a dilemma, plays a major role in the evolutionary processes for developing complex songs and the emergence of grammar. In our previous studies, we modeled this learning using a neural network and showed that this learning causes the complication of the generated bird song time series. However, it is difficult to observe the emergence of the grammar-like structure in the continuous-state neural network. In this paper, to show the complication of the discrete-symbol time series, and to emerge the grammar-like structure, we extend our previous model to the discrete model. The generated sequences and song dynamics are analyzed from various points of view, and the results show that the generated sequence is chaos, and it seems that the grammar-like structure emerges.