Hebbian Learning and Spike-Timing-Dependent Plasticity - Computational Neuroscience: A Comprehensive Approach - page 306

that the modification of each spike pair sum linearly. Some recent experiments have
demonstrated nonlinear summations [29, 78], which needs to be addressed in fu-
ture investigations (see [43]) for some attempts). The STDP functions with both τ −

values are plotted in Figure 11.1.

0.5

0

-200 200

-0.5

∆ t(ms)

Figure 11.1
The STDP modification function. The change of the peak conductance at a synapse due to a
single pre- and postsynaptic action potential pair is F ( ∆ t ) times the maximum value g max . ∆ t
is the time of the presynaptic spike minus the time of the postsynaptic spike. In this figure,
P is expressed as a percentage. Solid line represents the form of STDP with τ − = 20 ms and
dotted line has τ − = 100 ms . Adapted with permission from [79].

11.3 Role of constraints in Hebbian learning

The simple Hebbian rule outlined in Section 11.1 is in general unstable. The total
synaptic strengths will continue to grow over time. The connection strength from
correlated inputs would continually increase and eventually drive the postsynaptic
cell to fire at catastrophic rates. An upper bound imposed on synaptic strengths
alone cannot ameliorate this situation as all connection strengths would eventually
reach the upper bound, thus rendering the postsynaptic neuron equally responsive to
all inputs. Furthermore, the simple Hebbian rule lacks competition among inputs,
strengthening of one set of inputs does not automatically lead to decreased synaptic
strengths for other inputs. Several modifications to the basic Hebbian rule have been