  Accumulating evidences show that the cerebral cortex is operating near a
critical state featured by power-law size distribution of neural avalanche
activities, yet evidence of this critical state in artificial neural networks
mimicking the cerebral cortex is lacking. Here we design an artificial neural
network of coupled phase oscillators and, by the technique of reservoir
computing in machine learning, train it for predicting chaos. It is found that
when the machine is properly trained, oscillators in the reservoir are
synchronized into clusters whose sizes follow a power-law distribution. This
feature, however, is absent when the machine is poorly trained. Additionally,
it is found that despite the synchronization degree of the original network,
once properly trained, the reservoir network is always developed to the same
critical state, exemplifying the "attractor" nature of this state in machine
learning. The generality of the results is verified in different reservoir
models and by different target systems, and it is found that the scaling
exponent of the distribution is independent on the reservoir details and the
bifurcation parameter of the target system, but is modified when the dynamics
of the target system is changed to a different type. The findings shed lights
on the nature of machine learning, and are helpful to the design of
high-performance machine in physical systems.
