Function Emulation using Radial Basis Function Networks

SRINIVASA V. CHAKRAVARTHY and  JOYDEEP GHOSH


While learning an unknown input-output task, humans first  strive
to understand the qualitative structure of the function.  Accura-
cy of performance is then improved with  practice.  In  contrast,
existing neural network function approximators do not have an ex-
plicit means for abstracting the qualitative structure of a  tar-
get  function.  To fill this gap, we introduce the concept of {\m
function emulation}, according  to  which  the  central  goal  of
training  is to `emulate' the qualitative structure of the target
function. The framework of Catastrophe or Singularity  Theory  is
used  to characterize the qualitative structure of a smooth func-
tion, which is organized by the critical points of the  function.
The  proposed  scheme of function emulation uses the Radial Basis
Function Network to realize a modular architecture  wherein  each
module  emulates  the   target  function in the neighborhood of a
critical point. The network size required to emulate  the  target
in the neighborhood of a critical point is shown to be related to
a certain  complexity measure of the critical point. For a  large
class  of  smooth functions, the present scheme produces a graph-
like abstraction of the target, thereby providing  a  qualitative
representation of a quantitative input-output relation.

Functions, Qualitative learning, Critical points,  Func-
tion approximation.