*Submitted to Neural Compututation Dec. 1999, revised Sept. 2000;
to appear in September 2001;
manuscript number 2167.*

##
Intrinsic stabilization of output rates
by spike-based Hebbian learning

R. Kempter, W. Gerstner, and J. L. van Hemmen

We study analytically a model of long-term synaptic plasticity where
synaptic changes are triggered by presynaptic spikes, postsynaptic
spikes, and the time differences between pre- and postsynaptic spikes.
We show that plasticity can lead to an intrinsic stabilization of the
mean firing rate of the postsynaptic neuron. Subtractive
normalization of the synaptic weights (summed over all presynaptic
inputs converging on a postsynaptic neuron) follows if, in addition,
the mean input rates and the mean input correlations are identical at
all synapses. If the integral over the learning window is positive,
firing-rate stabilization requires a non-Hebbian component, whereas
such a component is not needed, if the integral of the learning window
is negative. A negative integral corresponds to `anti-Hebbian'
learning in a model with slowly varying firing rates. For spike-based
learning, a strict distinction between Hebbian and `anti-Hebbian'
rules is questionable since learning is driven by correlations on the time
scale of the learning window. The correlations between presynaptic
and postsynaptic firing are evaluated for a piecewise-linear Poisson
model and for a noisy spiking neuron model with refractoriness.
Whereas a negative integral over the learning window leads to
intrinsic rate stabilization, the positive part of the learning window
picks up spatial and temporal correlations in the input.

Manuscript:
Preprint (ps.Z) |