7.2. How to change the “threshold” of nonlinear characteristics of a
neuron?
(translation by Piotr Czech, Piotr.Czech@polsl.pl)
In the previous chapter the analysed neurons were based on “all or nothing” rule. They could
work on the basis of logical categorisation of input signals (true or false – 1 or 0) or could be
based on bipolar characteristics (approval or disapproval, signals +1 or -1). In both analysed
cases the transition between two different marked states had a sudden character: either the
output signals (in sum) “exceeded the threshold” and then the signal on the output instantly
equalled +1 or the output signals were so weak (“subliminal stimulation”) that there was no
reaction (signal 0) or the reaction was totally negative (-1).
What is more, the rule of zero value of threshold was assumed, which meant that the
positive sum of input signal equalled +1 signal and the negative value was 0 (or -1) – which
limited the possibilities of the analysed networks. By the way, when we discuss the
transition of nonlinear neuron, it would be advisable to analyse also the notion of the value
of threshold because in general cases it needs not to have zero value.
In the non-linear models of neurons analysed today, the threshold will be released
which will lead to achievement of moving characteristics with the possibility to chose the
point of switch freely, with the use of parameter usually called BIAS in the programs for
modelling networks. With the use of program Example 07a you will be able to draw out a
family of threshold characteristics of neurons with changing value of BIAS – it will let you
achieve a very good overview concerning the role of that factor in the shaping of the
behaviour of single neurons and the whole networks. This program shows you what the
behaviour of the neuron with freely shaped threshold can look like (fig. 7.2).
Fig. 7.2. The family of the threshold characteristics of neuron with changeable BIAS value
(view from program Example 07a)