Faithful and unfaithful students in time series learning

A model neuron with delay line feedback connections can learn a time series generated by another neuron. In the case that both neurons have identical transfer functions, a model neuron (student) is capable of reproducing the instruction sequence generated by another neuron (teacher), but the parameters are not uniquely determined by learning a quasi-periodic time series. A student that has completed the learning can be either faithful or unfaithful, depending on whether it continues mimicking the teacher’s time series over a long interval after the learning or whether it departs from the teacher and eventually generates a time series that bears no resemblance to the teacher’s. In the case that both neurons have different transfer functions, a student is generally incapable of reproducing the instruction sequence. Each student readjusts its parameters so as to minimize the mean-squared deviation between the instruction signal and its own output, but this parameter set is not uniquely determined. In this unrealizable learning, the degeneracy among faithful students is lifted and there is no more distinction between faithful and unfaithful students.