Piecewise Rational Functions, Uniqueness, and Reducibility

The class of piecewise rational functions is quite large, and for the rest of the paper we will confine ourselves to two types of functions in this class. Definitions of these two piecewise rational functions will be carried out in this section. Also, from this section on we will refer to the set of piecewise rational functions which are also smooth activations (see definition #defofsmooth#434>) as #tex2html_wrap_inline2823#, and to networks using them as #tex2html_wrap_inline2825# nets.