Preprint available: Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning

[Richard Kempter]

Dear connectionists,

        to all of you who have been interested in the nice paper on
Spike-Time Dependent Plasticity by Song, Miller, and Abbott, that Ken
Miller announced on this mailing list a couple of days ago, we would
like to give a pointer to our preprint on a related topic.

Intrinsic Stabilization of Output Rates by Spike-Based Hebbian Learning
(Kempter, Gerstner, van Hemmen)

http://keck.ucsf.edu/~kempter/Publications/index.html

Abstract:

We study analytically a model of 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, while such a component
is not necessary, if the integral over 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.  While
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.

Richard Kempter and Wulfram Gerstner