Our sensations are simply effects which are produced in our organs by objective causes; precisely how these effects manifest themselves depends principally and in essence upon the type of apparatus that reacts to the objective causes. What information, then, can the qualities of such sensations give us about the characteristics of the external causes and influences which produce them? Only this: our sensations are signs, not images, of such characteristics. One expects an image to be similar in some respect to the object of which it is an image; in a statue one expects similarity of form, in a drawing similarity of perspective, in a painting similarity of colour. A sign, however, need not be similar in any way to that of which it is a sign. The sole relationship between them is that the same object, appearing under the same conditions, must evoke the same sign; thus different signs always signify different causes or influences.

Rather than represent the entire transformation from the set of input variables to the set of output variables by a single neural network function, there is often great benefit in breaking down the mapping into an initial pre-processing stage, followed by the parameterized neural network model itself. … The use of pre-processing can often greatly improve the performance of a pattern recognition system, and there are several reasons why this may be so.