Hebbian Learning and Spiking Neurons

[Richard Kempter]

The following paper has appeared in Physical Review E, 59:4498-4514,1999

	Hebbian Learning and Spiking Neurons

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


Since we are out of reprints, copies of the paper are now available from

	http://diwww.epfl.ch/lami/team/gerstner/wg_pub.html

Abstract:
A correlation-based (``Hebbian'') learning rule at the spike level is
formulated, mathematically analyzed, and compared to learning in a firing-rate
description. As for spike coding, we take advantage of a ``learning window''
that describes the effect of timing of pre- and postsynaptic spikes on
synaptic weights. A differential equation for the learning dynamics is derived
under the assumption that the time scales of learning and spiking dynamics can
be separated. Formation of structured synapses is analyzed for a Poissonian
neuron model which receives time-dependent stochastic input. It is shown that
correlations between input and output spikes tend to stabilize structure
formation. With an appropriate choice of parameters, learning leads to an
intrinsic normalization of the average weight and the output firing rates.
Noise generates diffusion-like spreading of synaptic weights.