  We consider a cerebellar ring network for the optokinetic response (OKR), and
investigate the effect of diverse recoding of granule (GR) cells on OKR by
varying the connection probability $p_c$ from Golgi to GR cells. For an optimal
value of $p_c^*~(=0.06)$, individual GR cells exhibit diverse spiking patterns
which are in-phase, anti-phase, or complex out-of-phase with respect to their
population-averaged firing activity. Then, these diversely-recoded signals via
parallel fibers (PFs) from GR cells are effectively depressed by the
error-teaching signals via climbing fibers from the inferior olive which are
also in-phase ones. Synaptic weights at in-phase PF-Purkinje cell (PC) synapses
of active GR cells are strongly depressed via strong long-term depression
(LTD), while those at anti-phase and complex out-of-phase PF-PC synapses are
weakly depressed through weak LTD. This kind of "effective" depression (i.e.,
strong/weak LTD) at the PF-PC synapses causes a big modulation in firings of
PCs, which then exert effective inhibitory coordination on the vestibular
nucleus (VN) neuron (which evokes OKR). For the firing of the VN neuron, the
learning gain degree ${\cal{L}}_g$, corresponding to the modulation gain ratio,
increases with increasing the learning cycle, and it saturates at about the
300th cycle. By varying $p_c$ from $p_c^*$, we find that a plot of saturated
learning gain degree ${\cal L}_g^*$ versus $p_c$ forms a bell-shaped curve with
a peak at $p_c^*$ (where the diversity degree in spiking patterns of GR cells
is also maximum). Consequently, the more diverse in recoding of GR cells, the
more effective in motor learning for the OKR adaptation.
