A third aspect of the network model is that for all the care taken
in the previous steps, they will not suffice in settling quickly to
a set of weights that will generate the required logical function
unless there is a great multiplicity of ways in which this can be done.
This is to say that a learning network needs to have an excess margin
of weights and elements beyond the minimum required to generate the
functions which are to be learned.
This is analogous to the situation that prevails for a single element
as regards the allowed range of values on its weights. It can be shown
for example, that any function for n=6 that can be generated by a
single element can be obtained with each weight restricted to the range
of integer values -9,-8, ..., +9. Yet no modification of the stated
weight change rule is known which restricts weight values to these and
yet has any chance of ever being learned for most functions.