Biological Cybernetics 87:404-415
Mathematical Formulations of Hebbian Learning
Wulfram Gerstner and Werner Kistler
Several formulations of correlation-based Hebbian learning are reviewed.
On the presynaptic side, activity is described
either by a firing rate or by presynaptic spike arrival.
The state of the postsynaptic neuron
can be described by its membrane potential, its firing rate,
or the timing of backpropagating action potentials (BPAPs).
It is shown that all of the above
formulations can be derived from
the point of view of an expansion.
In the absence of BPAPs
potentials, it is natural
to correlate presynaptic spikes with
the postsynaptic membrane potential.
Time windows of spike time dependent
plasticity arise naturally, if
the timing of postsynaptic spikes is
available at the site of the synapse
as it is the case in the presence of BPAPs.
With an appropriate choice of parameters,
Hebbian synaptic plasticity has intrinsic
normalization properties that
stabilizes postsynaptic firing rates
and leads to subtractive weight normalization.
Hebbian learning, spike-time dependent plasticity, STDP,
correlation-based learning, PCA, co-variance rule.
spiking neurons, integrate-and-fire model, Poisson neuron.