Spectral Analysis of Input Spike Trains by Spike-Timing-Dependent Plasticity
Figure 2
Single neuron with STDP-plastic excitatory synapses.
(A) Schematic representation of the neuron (top gray-filled circle) and the synapses (pairs of black-filled semicircles) that are stimulated by the input spike trains
(bottom arrows). (B) Detail of synapse
, whose weight is
, postsynaptic response kernel
, axonal and dendritic delays
and
, respectively. The arrows indicate that
describes the propagation along the axon to the synapse, while
relates to both conduction of postsynaptic potential (PSP) toward soma and back-propagation of action potential toward the synaptic site. (C) Example of temporally Hebbian weight-dependent learning window
that determines the STDP contribution of pairs of pre- and postsynaptic spikes. The curve corresponds to (22). Darker blue indicates a stronger value for
, which leads to less potentiation and more depression. (D) Schematic evolution of the weight
for given pre- and postsynaptic spike trains
and
. The size of each jump is indicated by the nearby expression. Comparison between plain STDP for which only pairs contribute and STDP+SCC where single spikes also modify the weight via the terms
. Here only the pair of latest spikes falls into the temporal range of STDP and thus significantly contributes to STDP. (E) Scaling functions of
that determine the weight dependence for LTP and LTD. In the left panel, the blue solid curve corresponds to log-STDP [16] with
,
and
in (23). The parameter
controls the saturation of the LTD curve: the dashed curve corresponds to
and the dashed-dotted curve to
. In the right panel, the red solid curves represent
for nlta-STDP [13] with
and
in (24); the black dashed-dotted horizontal lines indicate the add-STDP that is weight independent; the green dashed line corresponds to a linearly dependent LTD for mlt-STDP [38].