  A continuous one-dimensional map with period three includes all periods. This
raises the following question: Can we obtain any types of periodic orbits
solely by learning three data points? We consider learning period three with
random neural networks and report the universal property associated with it. We
first show that the trained networks have a thermodynamic limit that depends on
the choice of target data and network settings. Our analysis reveals that
almost all learned periods are unstable and each network has its characteristic
attractors (which can even be untrained ones). Here, we propose the concept of
characteristic bifurcation expressing embeddable attractors intrinsic to the
network, in which the target data points and the scale of the network weights
function as bifurcation parameters. In conclusion, learning period three
generates various attractors through characteristic bifurcation due to the
stability change in latently existing numerous unstable periods of the system.
