Statistical implications of clipped Hebbian learning of cell assemblies

In this study binary associative networks of the Willshaw type are analyzed with respect to the effect of clipped Hebbian learning on the distribution of postsynaptic potentials when stimulating with random activation patterns. It is shown that the variance in the postsynaptic potentials grows with the square of the stimulation strength if the synapses have been generated by Hebbian learning of many overlapping patterns, but only linearly for independent random synapses. This result bears implications both for analysis of associative memory and the detection of Hebbian cell assemblies in neurophysiological experiments.