Analysis of various periodic orbits in simple dynamic binary neural networks

This paper studies various periodic orbits and their stability in dynamic binary neural networks. The networks are characterized by the signum activation function and binary connection parameters. The dynamics is simplified into a digital return map on a set of lattice points. In order to grasp the dynamics, we present a feature plane of two simple feature quantities. Calculating the feature quantities for a simple class of 2-layer networks, it is shown that the network can generate a variety of periodic orbits. In order to construct 3-layer networks, we present a blendingmethod: we preparemany 2-layer networks that have the same desired periodic orbit, blend two of the networks, and construct 3-layer networks. In the 3-layer network, stability of the desired orbit can be reinforced. Performing numerical experiments for several data sets of networks, the efficiency of the blending method is confirmed.