Hebbian Learning and Spike-Timing-Dependent Plasticity - Computational Neuroscience: A Comprehensive Approach - page 323

numerically for self-consistency and the results are plotted in Figure 11.7E for dif-
ferent values of b and Figure 11.7F for different values of a. Notice that increasing a
which is the slope of the gradient of correlations result in increased slope of the final
synapse values with some saturation. While increasing the mean correlation of the all
the inputs shift the curves to the left resulting in higher mean synaptic strengths. This
shift might not be a desirable feature and can be removed by introducing a variable
A − to make STDP insensitive to mean correlation but rather the difference in corre-
lations, as discussed in [43]. In Figure 11.7D, we have binned the resulting synaptic
weights from simulations for inputs with graded correlations into 20 bins and plotted
the mean synaptic weight for each bin. These values thus reflect the mean expected
value of synaptic strength for synapses in that bin. It is very similar to the solid curve
in Figure 11.7E and F which correspond to the same parameters. Although STDP
is similar to subtractive normalization with a rate-based Hebbian rule, it produces a
graded mean expected value of synaptic strengths rather than a bimodal one. This is
because although each synapse still tends to the boundaries, the stochasticity allows
the expected value for each synapse to be graded. So for synapses with similar driv-
ing force, some will be at the lower boundary and some will be at the upper boundary
and the average of them will be close to the expected value of the probability distri-
bution P . Therefore STDP combines the desired features of competitiveness of

subtractive normalization with sensitivity to correlation magnitude of multiplicative
normalization in one rule.

( w )

11.5 Temporal aspects of STDP

Since STDP incorporated timing into the plasticity rule itself, it is natural to inves-
tigate its utility in learning temporal patterns. It has been suggested as a form of
temporal difference learning to learn predictive coding by Rao and colleagues [67].
They have also used it to explain directional sensitivity in cortical cells. Similar
ideas were used earlier by Abbott and colleagues as a basis for a model of place
cells and spatial navigation in rats [11]. STDP reduces latency in the inputs. If a
cell receiving inputs with different latencies, the inputs with shorter latency will tend
to precede postsynaptic firing while the inputs with longer latency will tend to lag
behind. STDP will lead to strengthening of the synapses of the inputs with shorter
latency and weakening of the synapses of the inputs with longer latency. The final
effect of this is a reduction in the response latency of the postsynaptic cell [79]. This
was used as an explanation for the asymmetry expansion in place fields during train-
ing [54, 55]. Since STDP is very sensitive to synchrony in the inputs, when coupled
with delay lines, it can be used to learn arbitrary temporal patterns by strengthening
the appropriate delay lines so all the inputs arrive at the postsynaptic cell at the same
time. This forms the basis of a model of tuning of delay lines in the barn owl auditory
system [32]. It has also been used for sequence learning by other authors. [69]