Analysis and learning of periodic orbits in dynamic binary neural networks

This paper studies the dynamic binary neural network (DBNN) that can generate a variety of binary periodic orbits. The DBNN is constructed by applying the delayed feedback to a three-layer network. It is characterized by the signum activation function and ternary/binary weighting parameters. First, we give a systematic analysis tool: the Gray-code-based return map that is useful to grasp basic characteristics of the DBNN such as the number of periodic orbits and their domain of attraction. Second, we show that the DBNN includes an equivalent system of the cellular automata: this fact encourages study of the DBNN. Third, applying a learning algorithm to a teacher signal of periodic orbit, we have confirmed storage of the teacher signal, generation of a different periodic orbit and automatic stabilization of the periodic orbits.