Probabilistic versus Incremental Presynaptic Learning in Biologically Plausible Synapses - Foundations on Natural and Artificial Computation - page 81

Fig. 1. Synaptic weight modification of a biological synapse according to its postsy-
naptic activation. (a) For values lower than the LTD threshold (black dot) no variation
of synaptic weight takes place. For values between the LTP threshold (white dot) and
the LTD threshold, the variation of the synaptic weights is negative, i.e. the synaptic
weight decreases. For values higher than the LTP threshold, the synaptic weight in-
creases. (b) Synaptic metaplasticity: Curves corresponding to higher values of ω have
a higher LTP threshold and a lower LTD threshold.
time) of postsynaptic activations a , or a concomitant change in synaptic weight
ω (Fig. 1.b).
Let us consider the curve of figure 1.a in which the independent variable is
the postsynaptic activation and where other parameters such as a or ω are kept
constant. For example, let us evaluate the variation of weight for a specific value
of postsynaptic activation by setting the postsynaptic activation (see asterisk
in the curve of Fig. 1.a) to the value of the LTP threshold. In this case, no
variation of weight is observed. However, if the regime of synaptic activations a
is changed, so that ω reaches a higher value ω 1 , metaplasticity is manifested by
the modification of the shape of the curve as shown in figure 1.b. In this new
situation, if the same postsynaptic voltage is applied as before (see asterisk in
the curve), instead of obtaining a null variation of weight, the new curve yields
a negative variation (a decrement) of weight (see arrow).
In the first articles that study metaplasticity [2], metaplasticity was related to
the rightward shift of LTP-thresholds for higher a 's or ω 's. More recent studies
[3] showed that the LTD thresholds diminish in the same circumstances (Figure
1.b). In summary, once synapses are positively primed (i.e. there is an incre-
ment in weight), the interval between thresholds broadens, thereby favouring
subsequent synaptic depression.
Along the years, different mathematical models of synaptic computation have
been proposed (see Figure 2.a). In the classical Hebb model [4], the curve relating
the increment of synaptic weight to postsynaptic activation is a straight line
without synaptic depression. In Sejnowski's covariance model [5][6], regions of
potentiation and depression are separated by a LTP threshold (white dot).
Artola, Brocher and Singer's [8] extended model (ABS model, Figure 2.b) is
not analytical, as those just discussed, but is based on empirical experimental