  The role of the feedback effect on physical reservoir computing is studied
theoretically by solving the vortex-core dynamics in a nanostructured
ferromagnet. Although the spin-transfer torque due to the feedback current
makes the vortex dynamics complex, it is clarified that the feedback effect
does not always contribute to the enhancement of the memory function in a
physical reservoir. The memory function, characterized by the correlation
coefficient between the input data and the dynamical response of the vortex
core, becomes large when the delay time of the feedback current is not an
integral multiple of the pulse width. On the other hand, the memory function
remains small when the delay time is an integral multiple of the pulse width.
As a result, a periodic behavior for the short-term memory capacity is observed
with respect to the delay time, the phenomenon of which can be attributed to
correlations between the virtual neurons via the feedback current.
