# Optimal Plasticity from Matrix Memories: Wwhat
Goes Up Must Come Down

#### David Willshaw Peter Dayan

* Neural Computation,* ** 2**, 85-93.

## Abstract

A recent article (Stanton and Sejnowski 1989) on long-term
synaptic depression in the hippocampus has re-opened the issue of the
computational efficiency of particular synaptic learning rules (Hebb
1949; Palm 1988a; Morris and Willshaw 1989) - homosynaptic {\em
versus\/} heterosynaptic and monotonic {\em versus\/} non-monotonic
changes in synaptic efficacy. We have addressed these questions by
calculating and maximising the signal/noise ratio, a measure of the
potential fidelity of recall, in a class of associative matrix
memories. Up to a multiplicative constant, there are three optimal
rules, each providing for synaptic depression such that positive and
negative changes in synaptic efficacy balance out. For one rule, which
is found to be the Stent-Singer rule (Stent 1973; Rauschecker and
Singer 1979), the depression is purely heterosynaptic; for another
(Stanton and Sejnowski 1989), the depression is purely homosynaptic;
for the third, which is a generalisation of the first two and has a
higher signal/noise ratio, it is both heterosynaptic and homosynaptic.
The third rule takes the form of a covariance rule (Sejnowski 1977a,b) and
includes, as a special case, the prescription due to Hopfield (1982)
and others (Willshaw 1971; Kohonen 1972).

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