  We investigate from a computational perspective the efficiency of the
Willshaw synaptic update rule in the context of familiarity discrimination, a
binary-answer, memory-related task that has been linked through psychophysical
experiments with modified neural activity patterns in the prefrontal and
perirhinal cortex regions. Our motivation for recovering this well-known
learning prescription is two-fold: first, the switch-like nature of the induced
synaptic bonds, as there is evidence that biological synaptic transitions might
occur in a discrete stepwise fashion. Second, the possibility that in the
mammalian brain, unused, silent synapses might be pruned in the long-term.
Besides the usual pattern and network capacities, we calculate the synaptic
capacity of the model, a recently proposed measure where only the functional
subset of synapses is taken into account. We find that in terms of network
capacity, Willshaw learning is strongly affected by the pattern coding rates,
which have to be kept fixed and very low at any time to achieve a non-zero
capacity in the large network limit. The information carried per functional
synapse, however, diverges and is comparable to that of the pattern association
case, even for more realistic moderately low activity levels that are a
function of network size.
