Doman’s Inclined Floor Method for Early Motor Organization Simulated with a Four Neurons Robot - Foundations on Natural and Artificial Computation - page 114

Metaplasticity is depicted in Fig. 3, in which each curve shows the variation
of weight as a function of the neuron's postsynaptic activity. The parameter
that defines which curve is valid in each case is the value of the synaptic weight.
According to Fig. 3, for higher values of the synaptic weight the curves are more
elongated to the right.

Fig. 3. Synaptic plasticity curves. The value of the initial weight determines which
curve should be used for calculating weight variation. Curves with higher initial weights
are more elongated to the right.

Metaplasticity regulates weight variation, down-regulating weight increment
in synapses with high initial weights and up-regulating weight increment in
synapses with low initial weights.

Intrinsic Plasticity. Although synaptic metaplasticity makes it dicult for
synaptic weights to become either null or saturated, it does not totally preclude
either of these two extreme situations. To eliminate the possibility of either
weight annihilation or saturation, another important homeostatic property of
real neurons should be taken into account: the so-called intrinsic plasticity.[1][9]
Intrinsic plasticity regulates the position (shift) of the neuron's activation
function according to the past average level of activity in the neuron. The neu-
ron's activation function is usually modeled as a sigmoidal function:

1
1+ e − 25( α−shif t )

P ( O )= (3)

In which P(O) is the output probability of the neuron and a is the activation
given by the sum of synaptic contributions.
Intrinsic plasticity was modeled according to the following equation, that
yields the position of the sigmoid in terms of the previous position shift t− 1
and the previous sigmoid output O t− 1 .

ξO t− 1 + shift t− 1
1+ ξ

shift t = (4)