Faithful and unfaithful students in time series learning

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