Emergence of Chaotic Time Series by Adversarial Imitation Learning

Bird song is one of the phenomena that increase in complexity through evolution. A complex song is known to be advantageous for survivability and birds are known to learn how to sing a song from each other. From these facts, we have a hypothesis that adversarial imitation learning plays a major role in the evolution process of a complex song. There is a previous study that demonstrates the complexation of a bird song time series by modeling the process of adversarial imitation learning using a logistic map. However, the real bird songs have much variety and time dependencies, like grammar. Therefore, in this study, adversarial imitation learning is modeled using an artificial neural network that can approximate any function. The network learns adversarial imitation using the gradient descent method. By making such changes, the results of our study show that the generated bird songs evolve through the process of adversarial imitation learning to chaos, as seen in the previous models.